Bulletin of the Seismological Society of America

Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake sequencesusing coda-based methods

--Manuscript Draft--

Manuscript Number: BSSA-D-20-00132R1

Article Type: Article

Section/Category: Observations, Mechanisms and Hazards of Induced Seismicity

Full Title: Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake sequencesusing coda-based methods

Corresponding Author: Junkee Rhie, Ph.D.Seoul National UniversitySeoul, KOREA, REPUBLIC OF

Corresponding Author's Institution: Seoul National University

Corresponding Author E-Mail: rhie@snu.ac.kr

Order of Authors: Gyeongdon Chai, M.S.

Seung-Hoon Yoo, Ph.D.

Junkee Rhie, Ph.D.

Tae-Seob Kang, Ph.D.

Abstract: Two M5 earthquakes struck the southeastern Korean Peninsula in September 2016and November 2017, causing damage near the epicentral areas. We analyze   thestress drop scaling of these two earthquake sequences using coda-based methodsand Bayesian inversion. The 2016 Gyeongju earthquake sequence is a typicalearthquake sequence generated by tectonic processes. In contrast, the 2017 Pohangearthquake sequence is believed to be related to fluid injections conducted fordevelopment of enhanced geothermal systems. As the two sequences occurred in thesame tectonic regime, our study provides a good opportunity to compare stress dropscaling between a tectonic earthquake sequence and an earthquake sequenceinfluenced by fluid injections. We found that the stress drops of events in the Pohangsequences are lower than those of the Gyeongju sequence with similar magnitude.Although it is likely that this difference results from focal depth variations, a reduction ofstress drop due to fluid injections cannot be ruled out.

Author Comments:

Suggested Reviewers: Rengin GökLawrence Livermore National Laboratorygok1@llnl.gov

William Scott PhillipsLos Alamos National Laboratorywsp@lanl.gov

William WalterLawrence Livermore National Laboratorywalter5@llnl.gov

Adrian OthEuropean Center for Geodynamics and Seismologyadrien.oth@ecgs.lu

Opposed Reviewers:

Response to Reviewers:

Additional Information:

Question Response

Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation

<b>Key Point #1: </b><br><i>Three keypoints will be printed at the front of yourmanuscript so readers can get a quickoverview. Please provide threeCOMPLETE sentences addressing thefollowing: 1) state the problem you areaddressing in a FULL sentence; 2) stateyour main conclusion(s) in a FULLsentence; and 3) state the broaderimplications of your findings in a FULLsentence. Each point must be 110characters or less (including spaces).

Tectonic (Gyeongju) and possible anthropogenic (Pohang) earthquakes occurred inthe same tectonic regime.

Key Point #2: The stress drop of the Pohang sequence is lower than that of the Gyeongju sequence.

Key Point #3: Low stress drop may be attributed to the fluid injection.

Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation

Dear Editor:

I am submitting the revised research article for publication in the Bulletin of the Seismological

Society of America, titled “Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake

sequences using coda-based methods” by Gyeongdon Chai, Seung-Hoon Yoo, Junkee Rhie, and

Tae-Seob Kang (Manuscript # BSSA-D-20-00132_R1).

Following all of comments by the editor and anonymous reviewers, we revised figures and text for

improving our original manuscript. And we used a professional English editing service to check

the English of the revised manuscript. We hope our revised manuscript concur in the standard of

the Bulletin of the Seismological Society of America.

Thank you for your consideration.

Sincerely,

Junkee Rhie

Seoul National University

1 Gwanak-ro, Gwanak-gu, Seoul, Republic of Korea (08826)

+82 2 880 8172

+82 2 871 3269

rhie@snu.ac.kr

Letter to Editor Click here to access/download;Letter toEditor;cover_letter_GC02.docx

Thank you for your manuscript submission to the Bulletin. Please note that I have now received

the two external reviews which I requested. Based on these reviews and my own reading of

your manuscript, I find that it presents very well a detailed and careful analysis, on a topic of

interest for our readership. This being said, the reviewers raised a number of questions and

made several comments which I think that you need to study and address. Consequently, I

recommend that you undertake a careful revision, for the benefit of your work.

Since I appreciate that their reviews are clear and to the point, I don’t believe that it is necessary

to summarize them here. Instead, allow me to add a few remarks of my own:

(a) Based on the referenced information, I am not convinced that Pohang earthquake was

induced, and so its classification as such is rather speculative. The differences in stress behavior

between the two earthquake sequences don’t have to be justified by fluid induced changes. A

depth dependent tectonic stress, supported by the significant depth difference between the two

sequences, can explain your results very well.

We have revised the discussion and conclusion sections after considering your comments.

(b) The presentation flows nicely and it is easy to follow, but I appreciate that the conclusions

and discussion read a little too much like speculation rather than objective material, based on

the results obtained in the analysis. I suggest that you look to remedy this on the one hand by

changing the narrative to remove some of the speculative part, and on the other hand by adding

perhaps some information (results) based on discussions suggested by the reviewers.

We have revised the discussion and conclusion sections after considering your comments.

(c) Table 2 lists location parameters and magnitudes with two decimals, while corner

frequencies and stress drops with four decimals. There is no error information presented for

the location parameters and magnitudes to allow the reader to estimate whether listing the

respective values with decimals is relevant (although I doubt it for the magnitudes). However,

errors are given for the remaining parameters, and listing the values with four decimals is

unnecessary. Note that magnitude is given with two decimals throughout the manuscript, while

stress drops are presented elsewhere with only two decimals. You may want to look into this,

ensuring both relevance and consistency.

We have revised Table 2 to show the precision of the parameters used in this study to two

decimals places. However, we have not changed the presentation of the location parameters

because they were adopted in their original form from other studies.

(d) For text and figures: you are often using “main” and “fore” as they would be nouns, which

they are not. I suggest that you use “main shock” and “foreshock”.

We appreciate your comment and have revised the manuscript accordingly.

(e) Figures are generally well done, but I suggest that you check the following:

Fig 2: indicate what colours represent;

Fig 4: use only symbols for source parameters, without add their full names;

Fig 6a,b: I don’t see why colours are needed here, but if you insist to have them, let the reader

know in the caption;

Fig 7b: indicate the legends that you indicated in 7a.

We have modified these figures to include your suggestions.

Reviewer #1: Review of BSSA-D-20-00132

Response to Reviews

"Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake sequences using coda-

based methods" by Chai et al.

This is a well written paper comparing and contrasting the spectral and inferred stress drop

characteristics of two moderate earthquake sequences in South Korea. Given the sequences

have different average depths and mechanisms, and one of these sequences is related to

geothermal fluid injection, this study will be of high interest to the seismological community

and BSSA readers. I recommend this paper be published after addressing the relatively minor

comments below.

The paper uses coda envelopes to estimate source spectra (e.g. Mayeda et al 2003). This has

advantages in getting good azimuthally averaged source spectra, which is helpful given the

network is mostly west of the events. The authors might wish to mention this when discussing

how the coda measures are more stable.

We appreciate your kind suggestion and have added the following sentence in the revised

manuscript (Lines 195-198) to incorporate this information.

Because the excitations of the coda waves are nearly insensitive to the radiation pattern

(Mayeda et al., 2003), we were able to obtain azimuthally averaged source spectra, even

though the stations were mainly located westward of the events.

A challenge with using coda is its amplitude dependence on depth, particularly for shallow

events with depths less than say 3-5 km (e.g. Mayeda and Walter, JGR 1996; Walter et al GRL

2017). The authors need to provide some more details on if they are using the same envelope

shapes for the both earthquake sequences (which may be fine if they don't show much

variation).

Of greater importance is the authors should be using or testing different site and excitation

corrections for the different earthquake sequences. See the comments at lines 74-101 below.

We used the same coda envelopes for both sequences because there were no significant

differences in the coda envelope shapes between the two sequences (Please refer to Figure R1).

However, we separately derived the site and source excitation terms for the Gyeongju and

Pohang sequences.

Figure R1. Coda envelopes recorded at BUS2 station for GJ main shock (Mw 5.58), GJ

foreshock (Mw 5.13), and PH main shock (Mw 5.44).

There are other ways to get at stress differences between events than the two methods used

here. For example, methods by Peter Shearers and colleagues and methods looking at spectral

ratio levels the second author here Seung-Hoon Yoo has been involved in previously. Given

the highest frequency studied here is 14 Hz perhaps it is not high enough to look at spectral

ratio levels? This area could use a little more discussion in the paper.

We agree that 14 Hz may be too low to constrain fc for very small events; however, in our

study, we did not analyze very small events that have fc higher than 14 Hz. From Table 2, it is

seen that the highest fc estimated in our study is ~6 Hz. Therefore, we believe that 14 Hz is

sufficiently high for our study.

Finally, the differences in stress behavior between the two sequences is quite interesting. Given

the different mechanisms for sequences close in space it implies either depth dependent

tectonic stress or fluid induced changes in tectonic stress. Perhaps this is a topic better covered

in other papers, but it could use some more discussion here.

Strike slip and thrust earthquakes coexist in the study area, leading us to believe that the

different faulting types are due to depth-dependent tectonic stress and fault geometry (strike

and dip).

Detailed comments:

Line 32 - which event is this ML 5.8, "the largest instrumentally recorded earthquake in this

region"? Should give at least a date here.

We have rephrased the sentence as follows in the revised manuscript (Lines 32-33):

However, the largest earthquake recorded in this region with instruments is the ML 5.8

Gyeongju earthquake of 12 September, 2016 (Korean Meteorological Administration;

KMA).

Lines 41 - Would be helpful to put labels on inset boxes in Figure 2 if possible, like a "GJ" and

"PH". In Figure 2 caption note that ISOLA is software and give references (Sokos and

Zahradnik, 2008; Vackář et al., 2017) there.

We have modified Figure 2 and its caption as suggested.

Line 51-53 - accuracy in the determination of the depths of these earthquakes is important.

How good is the depth determination? Are there seismic stations within a focal depth of the

events to really constrain the depth well?

We agree that the accuracy of the determined focal depth is important in our study. For the GJ

main shock, there was no observation at close distance. However, the focal depths of the

aftershocks are very well constrained using the data from the dense aftershock monitoring

networks deployed in the epicentral area. Because the focal depths of the main shock and

aftershocks are similar, we are confident that the depth estimate of the main shock has an

acceptable degree of accuracy. For the PH main shock, many stations in the epicentral area

were in operation at the time of the event. In addition, the estimates of the focal depths reported

by different researchers, including the one cited by us, are more or less consistent.

Lines 61 - It is asserted that both earthquake sequences occurred in the same tectonic regime,

but the mechanisms are different - GJ being strike-slip and PH being more thrust. Authors may

need to discuss more. Is this because the largest tectonic stresses are similar and horizontal and

vertical so both strike-slip and thrust mechanisms are common? Or if the fluid injection

changed the local stress regime and caused the change from tectonic strike-slip mechanism to

thrust mechanisms for the PH sequence.

We do not believe that the fluid injection changed the local stress regime in the Pohang area.

In general, the direction of SHmax (sigma 1) in the Korean Peninsula is spatially homogeneous

and nearly parallel to the E-W direction. Therefore, events with strike slip and thrust

mechanisms are commonly observed in both regions (GJ and PH). We have clarified in the text

that both these mechanisms are popular in the study area.

Strike slip and thrust mechanisms are both popular mechanisms in our study area (Lines

54-55)

Lines 74-101 - Are the authors using the same envelopes for both sequences or did they develop

one set for the PH and a different set of the GJ? If so need to state this explicitly. If not, why

not? Given the different average depths of the sequences and the strong dependence of coda

excitation on depth, this seems important to do to get the right answer.

Earthquakes causing the two seismic sequences depicted in Figure R1 have enough similarities

in the shapes and decay rates of their coda envelopes to enable measurement of the coda

amplitudes using the same envelope function. Therefore, we have used the same coda

envelopes for both sequences. However, we derived site correction terms separately for the two

sequences to account for the different coda excitations due to the different source depths. We

have revised the manuscript to clearly indicate our use of the coda envelope shape.

Because the coda envelope shapes for both sequences are similar, we used the same set of

reference coda envelopes for both sequences (Lines 84-85).

Line 116 - I would argue only applicable to events with similar Hypocenters (not epicenters)

and significant differences in magnitude. The depths cannot be very different due to the depth

dependence of coda for shallow events.

We appreciate your comment and have changed “epicenters” to “hypocenters” accordingly

(Line 120).

Lines 198-204 - So what is going on here? Why the discrepancy between the ratio and spectral

results? Are the new corner frequencies within the error bounds in the ratios and they just could

not be determined very well? The Figure 6 caption needs to better explain what figure 6c is,

it's the spectra determined use the ratio corner frequencies.

To clarify our analysis, we have added some details and modified the caption of Figure 6.

First, we determined the Brune spectra, which fit the corrected NDCA for each event,

and then recalculated the site correction terms by averaging the differences between the

Brune spectra and the NDCAs for the three events (Lines 211-214).

(c) Yellow dashed lines indicate the Brune spectra calculated using the fc values from

the spectral ratios. Symbols (open triangles, squares, and circles) show the NDCAs for

stations after revision using the recalculated site correction terms. [Caption of Figure

6]

Lines 211-212 - What is highest resolved frequency here? Based on Table 1 its 14 Hz. Is this

20 Hz Nyquist frequency but then limited to 14 Hz analysis? Need to provide these details. If

you cannot sample high enough in frequency, then may not be able to get accurate corner

frequency for small events. Or is the Signal-to-noise ratio poor at high frequencies? Paper

would benefit form some more details.

We agree that higher frequency envelopes are required to constrain the fc values of very small

events. However, this does not affect our study because we are not interested in very small

events. The minimum magnitude of interest in this work is around 3, and its corner frequency

is much lower than 14 Hz (~ 6 Hz), as shown in Table 2.

Line 217-221 - So the PH sequence might follow a different stress drop versus magnitude trend

than the GJ sequence in addition to the PH sequence having systematically lower stress drops

because of its shallower depth. Not all earthquake sequences follow a pattern of increase

between 4.5 and 5.5 - see for example the Parkfield sequence which shows little change in

stress drop.

Thank you for your comment. We have added a new sentence to note that there was a study

reporting a non-increasing trend in a given magnitude range.

No significant increase in the stress drop for the specific magnitude range was reported for

the Parkfield sequence (Lines 232-233)

Lines 264-267 - I don't understand this comment. If depth rather than fluid injection is the main

cause of the lower stress drop of the PH sequence, then all the events should be low stress

regardless of if they are directly or indirectly related to fluid injection.

Our comment was intended to convey that the difference in focal depth may not fully explain

the variation in stress drop for the PH sequence. We found that the stress drop of the PH

sequence was lower than that of the GJ sequence. Furthermore, two events in the PH sequence

had much lower stress drops, and they were more likely to be affected by the fluid injection:

the main shock and an event that occurred during the injection period. With the exception of

these two events, all the other events were aftershocks. However, we are not sure whether the

change due to fluid injection necessarily explains the lower stress drops for these two events.

Line 507 - very happy to see this full table of events and their parameters included.

Thank you for the encouraging comment!

Reviewer #2: Nice study, definitely recommend for publication. I have few comments about

the flow and clarification of the paper.

1) Coda envelope ratio method provides ground truth events (mainly the stress drop) to feed

into the NDCA Mw and (sigma,fc) calculation for the site term improvement. What is

presented here is to sort of feeding values in between two methods and correcting. You may

want to state this or rephrase it at the beginning.

We have added a sentence in the revised manuscript to address this concern.

We used the information obtained from the ratio of the NDCAs to define the site correction

terms, and then applied these terms to study the source spectra of the events. (Lines 123-

124)

2) Ratio method may also be suffering from trade off (smaller event Mw inaccuracy may affect

fc)

We agree that the fc values determined from the ratio method can be inaccurate for smaller

events. For this reason, we only used the fc values of large events for further analyses.

3)The paragraph around L151-153 needs further clarification. What is "final values for only

large events"?

The final fc values estimated for large events are better constrained than those for small events

because of their large SNRs. Therefore, we only used the fc values of large events to define the

correction terms. To clarify this, we have rephrased the first sentence as follows.

Because the final fc values for large events (Mw >= 4.0) are more accurate owing to their

large signal-to-noise ratios, we only used the fc values of large events for further analyses

(Lines 157-159)

4) L200-203 Figure 6 b,c: How was the recalculation estimated? Spectral ratio fitting or

NDCA? There is no information about it.

The detailed process of recalculation is as follows: 1) Correct the NDCAs for the three events

using the site terms determined by the spectral ratios. 2) Find the best fitting Brune spectra for

the three events. 3) Recalculate the site terms by measuring the differences between the

observed NDCAs and the best fitting Brune spectra. We have added the following sentence to

clarify this in our revised manuscript and have also changed the caption of Figure 6.

First, we determined the Brune spectra, which fit the corrected NDCA for each event,

and then recalculated the site correction terms by averaging the differences between the

Brune spectra and the NDCAs for the three events (Lines 211-214).

(c) Yellow dashed lines indicate the Brune spectra calculated using the fc values from

the spectral ratios. The symbols (open triangles, squares, and circles) show the NDCAs

for stations after revision using the recalculated site correction terms. [Caption of

Figure 6]

We appreciate your comments!

1

Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake 1

sequences using coda-based methods 2

3

Gyeongdon Chai1, Seung-Hoon Yoo2, Junkee Rhie1*, and Tae-Seob Kang3 4

5 1School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, South 6

Korea 7

2Applied Research Associates, Inc., Arlington, VA 22203, USA 8

3Division of Earth Environmental System Science, Pukyong National University, Busan 9

48513, South Korea 10

11

Abstract 12

Two M5 earthquakes struck the southeastern Korean Peninsula in September 2016 and 13

November 2017, causing damage near the epicentral areas. We analyze the stress drop 14

scaling of these two earthquake sequences using coda-based methods and Bayesian inversion. 15

The 2016 Gyeongju earthquake sequence is a typical earthquake sequence generated by 16

tectonic processes. In contrast, the 2017 Pohang earthquake sequence is believed to be related 17

to fluid injections conducted for development of enhanced geothermal systems. As the two 18

sequences occurred in the same tectonic regime, our study provides a good opportunity to 19

compare the stress drop scaling between a tectonic earthquake sequence and an earthquake 20

sequence influenced by fluid injections. We found that the stress drops of events in the 21

Pohang sequences are lower than those of the Gyeongju sequence with similar magnitude. 22

Although it is likely that this difference results from focal depth variations, a reduction of 23

stress drop due to fluid injections cannot be ruled out. 24

25

Annotated Manuscript Click here to access/download;AnnotatedManuscript;ChaiGD.BSSA.R01_GC08_JR01_annotated.docx

2

Introduction 26

A study of the scaling relationship between magnitude and stress drop for earthquakes 27

occurring in a given region is important not only for understanding the fundamentals of the 28

earthquake rupture process but also for mitigating earthquake damage by precisely predicting 29

the ground motions of possible future earthquakes. There are many historical documents on 30

the occurrence of large earthquakes (M >6) in the southeastern part of the Korean Peninsula. 31

However, the largest earthquake recorded in this region with instruments is the ML 5.8 32

Gyeongju earthquake of 12 September, 2016 (Korean Meteorological Administration; KMA). 33

This region is susceptible to large earthquakes. Efforts toward mitigating the seismic risk in 34

this region are very important because this region has valuable infrastructure, including 35

nuclear power plants and cities with dense populations. In this study, we analyze the stress 36

drop scaling of two moderate earthquake sequences that occurred in the southeastern Korean 37

Peninsula using the analysis of coda waves, which is known to be more stable than the 38

analysis of direct waves (Mayeda et al., 2007; Yoo et al., 2010). 39

The two earthquake sequences considered in this study are the 2016 Mw 5.6 Gyeongju (GJ) 40

earthquake and the 2017 Mw 5.5 Pohang (PH) earthquake sequences (Figures 1 and 2). The 41

distance between the epicenters of the GJ and PH main shocks is approximately 43 km, and 42

both earthquakes occurred in the Gyeongsang Basin. The Gyeongsang Basin is a tectonic unit 43

classified based on the tectonic evolution in the Korean Peninsula. Although the Pohang 44

Basin, where the PH sequence occurred, had been tectonically active until recently compared 45

to the epicentral region of the GJ sequence, the current tectonic environment for generating 46

earthquakes in both regions should be similar because they belong to the same tectonic unit 47

(Park et al., 2007; Soh et al., 2018). We can also expect that tectonic stresses in both regions 48

are similar because they are spatially close to each other. However, the reported source 49

characteristic of the two sequences, especially the main shocks, are quite different. The focal 50

3

depths of the GJ and PH main shocks are 14.5 km (Woo et al., 2019a) and 4.27 km (Lee et al., 51

2019; Woo et al., 2019b), respectively. The focal mechanism for the GJ main shock 52

determined by moment tensor inversion is strike slip. The faulting style of the PH main shock 53

is strike slip with a significant thrust component. Strike slip and thrust mechanisms are both 54

popular mechanisms in our study area (Rhie and Kim, 2010). The most important difference 55

between the two earthquakes is whether fluid injection affected the occurrence of earthquake. 56

The GJ main shock is a natural earthquake generated because of tectonic stress, whereas the 57

PH main shock is a “runaway” earthquake triggered by stress perturbation caused by 58

injecting fluids for the development of enhanced geothermal systems (EGS) (Ellsworth et al., 59

2019). The objective of this study is to show that different mechanisms between tectonic and 60

“runaway” earthquakes can be revealed by comparing source parameters of the GJ and PH 61

earthquake sequences, which occurred in the same tectonic region. 62

63

Data and Methods 64

Data used in this study are seismic waveforms recorded at broadband stations operated by the 65

Korea Meteorological Administration (KMA) and the Korea Institute of Geoscience and 66

Mineral Resources (KIGAM) (Figure 1), and they were divided into two sets for different 67

research purposes. The first data set was used to define a reference coda envelope, which is 68

necessary for calculating the source spectrum. For the lower frequency range (0.05–8.0 Hz), 69

we used waveforms from earthquakes with magnitudes greater than 4.0 that occurred in and 70

around the Korean Peninsula between 2006 and 2012. The sampling rate of this data set is 20 71

Hz. For the higher frequency range (8.0–14.0 Hz), we used waveforms from earthquakes in 72

the 2016 Gyeongju sequence with magnitudes greater than 3.0; their sampling rate is 100 Hz. 73

The second data set was used for analysis of source spectra for the GJ and PH sequences. 74

4

To determine a reference coda envelope, we defined its theoretical functional form following 75

a previous study (Mayeda et al., 2003) to be 76

𝐸(𝑡, 𝑓, 𝑟) = 𝐻 (𝑡 −𝑟

𝑣(𝑓,𝑟)) (𝑡 −

𝑟

𝑣(𝑓,𝑟))

−𝛾(𝑓,𝑟)

× exp [𝑏(𝑓, 𝑟) (𝑡 −𝑟

𝑣(𝑓,𝑟))], (1) 77

where r, f, and t indicate distance in km, frequency in Hz, and the time elapsed from the event 78

origin time in s, respectively; H is the Heaviside step function; and 𝑣(𝑓, 𝑟) is the velocity of 79

the peak arrival in km/s. Two functions, 𝑏(𝑓, 𝑟) and 𝛾(𝑓, 𝑟), control the shape of the coda 80

envelope. To define the reference coda envelope, we determined 𝑣(𝑓, 𝑟), 𝑏(𝑓, 𝑟), and 81

𝛾(𝑓, 𝑟) from the observed data by following the procedures presented in Yoo et al. (2011). 82

We defined reference coda envelopes for 14 consecutive narrow frequency bands (Table 1, 83

Figure 3). Because the coda envelope shapes for both sequences are similar, we used the 84

same set of reference coda envelopes for both sequences. 85

The relation between the observed and reference coda envelopes can be represented as 86

follows: 87

𝐴𝐶(𝑡, 𝑓, 𝑟) = 𝑊0(𝑓)𝑆(𝑓)𝑃(𝑓, 𝑟)𝐸(𝑡, 𝑓, 𝑟), (2) 88

where 𝐴𝐶(𝑡, 𝑓, 𝑟) , 𝑆(𝑓) , 𝑃(𝑓, 𝑟) , and 𝑊0(𝑓) are the observed coda envelope, site 89

correction, path correction, and S-wave source amplitude, respectively. 90

To measure 𝐴𝐶(𝑡, 𝑓, 𝑟), we removed the instrument response of two horizontal component 91

waveforms to velocity seismograms. A four-pole two-pass Butterworth filter, for which 92

corner frequencies correspond to 14 consecutive narrow frequency bands was applied, and 93

then an envelope for each frequency was calculated using 94

𝐸obs = √𝑣(𝑡)2 + ℎ(𝑡)2, (3) 95

where 𝑣(𝑡) and ℎ(𝑡) are the band-pass-filtered horizontal velocity seismogram and its 96

Hilbert transform, respectively. To distinguish the observed and reference envelopes, we use 97

𝐸obs for the observed envelope. The final observed envelope was calculated by taking the 98

5

logarithm base 10 of two horizontal envelopes and then averaging them. By doing this, we 99

measured 𝐴𝐶(𝑡, 𝑓, 𝑟) for each frequency and epicentral distance. We can see in Eq. (2) that 100

changes in 𝐴𝐶(𝑡, 𝑓, 𝑟) with time for a given frequency and distance should be the same as 101

the changes in 𝐸(𝑡, 𝑓, 𝑟). The difference between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟) is called non-102

dimensional coda amplitude (NDCA), and it can be measured by finding the optimum DC 103

shift, which minimizes the L1 norm between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟). We then compared 104

the reference and observed coda envelopes at each frequency band. 105

Two methods are widely used to study seismic sources using measured NDCA. The first 106

method involves directly estimating 𝑊0(𝑓) by correcting 𝑃(𝑓, 𝑟) and 𝑆(𝑓) from NDCA. 107

The advantage of this method is that it can be used to estimate source spectra of all events in 108

a given region once models for 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are defined. Because source spectra are 109

available, we can estimate M0 and fc, the seismic moment in Newton meters and the corner 110

frequency in Hertz, which are two representative source parameters, but we can also estimate 111

radiated energy. However, unless 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are precise enough, the reliability of 112

estimated source spectra can be low. The second method is to estimate fc only, or fc and M0 113

together, from the ratio of NDCA between two events without calculating the individual 114

source spectrum of each event (Mayeda et al., 2007). This method is based on the assumption 115

that if NDCAs are measured at the identical station and two earthquakes occurred at close 116

locations, 𝑃(𝑓, 𝑟) and 𝑆(𝑓) for both events should be identical and the ratio of NDCA is 117

the same as the ratio of the source spectra. In this case, we do not need to determine 𝑃(𝑓, 𝑟) 118

and 𝑆(𝑓) to apply the method. However, this method is only applicable to event pairs with 119

similar hypocenters but large differences in magnitude. In this study, we are interested in 120

examining the source characteristics of two earthquake sequences, where the earthquakes in 121

each sequence are spatially clustered. Therefore, a combined procedure of the two methods 122

can be applied. We used the information obtained from the ratio of the NDCAs to define the 123

6

site correction terms, and then applied these terms to study the source spectra of the events. 124

The detailed procedure is as follows. First, we selected event pairs with a magnitude 125

difference larger than 1 in each sequence. Total numbers of selected events and 126

corresponding event pairs for the GJ sequence are 9 and 15, respectively, and 6 and 7 for the 127

PH sequence. The maximum distance between epicenters among event pairs is 7 km. Mw for 128

each event was independently calculated using ISOLA (Sokos and Zahradnik, 2008; Vackář 129

et al., 2017) software based on the waveform inversion method (Figure 2). We considered 66 130

stations for our analysis, but the actual number of data points used for each process was not 131

consistent (Figure 1). To estimate fc of both events from the spectral ratio for a given event 132

pair, we used the Bayesian inversion method. A hierarchical scheme was applied to account 133

for data error in the inversion (Bodin et al., 2012; Kim et al., 2016). We assumed that prior 134

probability of Δσ is uniform in the range 10−3 − 103 MPa. Once we selected Δσ, we 135

calculated fc by using the following equation, because M0 of the event is pre-defined: 136

𝑓𝑐 =2.34𝛽

2𝜋 ( 7

16∙𝑀0∆𝜎

)

13

. (4) 137

Equation (4) was derived from the following two equations based on the circular fault model 138

(Eshelby, 1957). Shear wave velocity (𝛽) was set to be 3.5 km/s. 139

Δσ =7

16

𝑀0

𝑟3 (5) 140

𝑟 =2.34β

2π𝑓𝑐. (6) 141

Using fc and M0 of both events, we can define a spectral ratio between two events based on 142

Brune’s source model as follows (Aki, 1967; Brune, 1970; 1971): 143

𝑅(𝑓) =𝑀01[1+(𝑓/𝑓𝑐2)2]

𝑀02[1+(𝑓/𝑓𝑐1)2]. (7) 144

The misfit between the synthetic and observed spectral ratio was measured using the L1 norm, 145

and the likelihood function was defined as 146

7

𝐿 =1

2𝜎× exp [∑

|𝑅syn(𝑓𝑖)−𝑅obs(𝑓𝑖)|

𝜎

𝑛𝑖=1 ], (8) 147

where 𝑅syn and 𝑅obs indicate the synthetic and observed spectral ratio, respectively, and 𝑓𝑖 148

represents the center frequency of a given frequency band. To consider the data error in the 149

inversion, we assumed that 𝜎 has a positive uniform prior probability. We updated model 150

parameters (two stress drops and 𝜎) 200,000 times using the Metropolis-Hastings sampling 151

(MHS) method (Metropolis et al., 1953; Hastings, 1970). After the first half of the 152

calculations, which is considered a burn-in period, we selected 1 sample per every 100 153

calculations to estimate the posterior probability density (PPD) of two values of stress drop 154

(or fc) and 𝜎. For each event pair, we selected the fc with highest PPD. The final fc value for 155

each event was calculated by averaging selected fc values for all event pairs. 156

Because the final fc values for large events (Mw >= 4.0) are more accurate owing to their 157

large signal-to-noise ratios, we only used the fc values of only large events for further 158

analyses. The number of final fc values was three for each of the PH and GJ sequences. Once 159

we determined fc and M0, the theoretical Brune’s source spectrum can be calculated using the 160

following equation: 161

𝑀(𝑓) =𝑀0

(1+(𝑓

𝑓𝑐)

2). (9) 162

For each station, a site correction term can be determined by measuring the difference 163

between the theoretical Brune’s source spectrum and the corresponding NDCA. We note that 164

a site correction term contains 𝑃(𝑓, 𝑟) and 𝑆(𝑓) in Eq. (1). Because we define the site 165

correction terms of individual stations separately for PH and GJ sequences, we can ignore 166

variation in the site correction term with distance. We calculated the difference between the 167

theoretical Brune’s spectrum and the NDCA for each event and then averaged them for each 168

sequence to determine the final site correction term as a function of frequency. Once a site 169

correction term was defined, we calculated the source spectrum for each event by correcting 170

8

NDCA. By averaging the estimated source spectra of each event for all available stations, we 171

calculated the final source spectrum for each event. To estimate the PPD of stress drop (or fc) 172

and Mw from the final source spectrum, we used Bayesian inversion, which is similar to the 173

method previously applied for spectral ratio. We assumed that the stress drop and M0 have 174

uniform prior probability in the ranges between 10–3 and 103 MPa and between –2 and 2 in 175

logarithmic scale about the maximum value of the corrected NDCA, respectively. The 176

parameter fc was determined from a given stress drop and M0. To consider data error, we 177

adopted two parameters, 𝜎𝑓rms and 𝜎𝑓

SD. Here, 𝜎𝑓rms indicates an envelope fitting error 178

when measuring coda amplitudes of observed envelopes at a given frequency and 𝜎𝑓SD is 179

defined as one standard deviation of the site-correction term at the given frequency. The 180

likelihood function is defined as 181

𝐿 =1

2× exp [∑

|𝑀syn(𝑓𝑖)−𝑀obs(𝑓𝑖)|

𝜎𝑓rms+𝜎𝑓

SD𝑛𝑖=1 ]. (10) 182

The same sampling procedure of Bayesian inversion using the MHS method that was used for 183

the spectral ratio method was applied to estimate the PPD of Mw and fc. The PPD of stress 184

drop was also determined from Eqs. (5) and (6). We can technically estimate source 185

parameters of all events with measured NDCA. However, low signal-to-noise ratio of small 186

events can distort the results. Therefore, we used 9 and 6 events with Mw larger than 3.0 for 187

the GJ and PH sequences, respectively. We calculated Brune’s source spectrum using M0 and 188

fc estimated by Bayesian inversion and used this spectrum to calculate a site correction term. 189

190

Results and Discussion 191

We applied coda-based methods and Bayesian inversion to the GJ and PH earthquake 192

sequences. We calculated the reference coda envelopes and compared them with the observed 193

coda envelopes. Figure 3 depicts an example of the comparison between the reference and 194

observed coda envelopes at selected frequency bands. Because the excitations of the coda 195

9

waves are nearly insensitive to the radiation pattern (Mayeda et al., 2003), we were able to 196

obtain azimuthally averaged source spectra, even though the stations were mainly located 197

westward of the events. The final fc value was calculated for each event using the MHS 198

method and the PPD was estimated; for each event pair, we selected the fc with the highest 199

PPD. Figure 4 shows examples of spectral ratios determined for selected events. The 200

calculated difference between the theoretical Brune’s spectrum and the NDCA for each event 201

was averaged for each sequence to determine the final site correction term as a function of 202

frequency, as shown in Figure 5 for three events in the GJ sequence. 203

If the site correction term is well-defined, we can expect the estimated source spectra of the 204

events involved in determining the site correction terms to be consistent with the site-205

corrected NDCA for the same event. In the case of the GJ sequence, we can see that the two 206

values are well-matched, as expected (Figure 6(a)). However, there are significant 207

discrepancies in the PH sequence (Figure 6(c)). The reason for these discrepancies appears to 208

be that the original estimates of fc obtained from the spectral ratio method for the PH 209

sequence are not accurate because the number of applicable earthquakes is insufficient. To 210

overcome this problem, we recalculated the site correction term for the PH sequence. First, 211

we determined the Brune spectra, which fit the corrected NDCA for each event, and then 212

recalculated the site correction terms by averaging the differences between the Brune spectra 213

and the NDCAs for the three events. The corrected NDCA using the recalculated site 214

correction term demonstrates a significantly improved fit to the theoretical Brune’s spectrum 215

(Figure 6(b)). 216

Using coda-based methods and Bayesian inversion, we estimated the PPD of Mw, fc, and 217

stress drop for 12 and 7 earthquakes in the GJ and PH sequences, respectively (Table 2). The 218

stress drop scaling for both the GJ and PH sequences show that stress drop increases with 219

increasing magnitude on the overall scale (Figure 7). The observed trends in stress drop 220

10

scaling cannot be explained by the self-similar model with a constant stress drop (Aki, 1967). 221

The estimates of the stress drop appear to be considerably scattered for smaller earthquakes 222

(Mw < ~3.5) in both sequences. This may indicate that estimates of stress drop for smaller 223

events are not stable because of the low signal-to-noise ratio. The stress drop of the smallest 224

PH event (PH01 in Table 2) is much smaller than that of other events with similar magnitudes. 225

For relatively larger events (Mw >= 4.0) in the GJ sequence, it is likely that the stress drop 226

increases with increasing Mw in a range between Mw 4.5 and 5.5. This observation is 227

consistent with other previous studies using similar coda-based methods (Mayeda and 228

Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; Yoo and Mayeda, 2013). For the 229

PH sequence, we do not observe an increasing trend in the given magnitude range because 230

the stress drop of the PH main shock (PH02) is smaller than those of the shocks of similar 231

magnitude in the GJ sequence. No significant increase in the stress drop for the specific 232

magnitude range was reported for the Parkfield sequence (Allman and Shearer, 2007). 233

Additionally, the stress drops of two other PH events (PH04 and PH07) with Mw larger than 234

4.0 are also smaller than the stress drops of similar-sized GJ events. 235

To summarize the characteristics of stress drop scaling for the two sequences, the stress drops 236

of the PH sequence appear to be smaller than those of the GJ sequence, and two PH events 237

(PH01 and PH02) have much smaller stress drops in comparison with those of events with 238

similar magnitudes in the GJ sequence. The stress drop of PH01 (Mw 3.3) is smaller than that 239

of GJ13 (Mw 3.3) by a factor of approximately 4. The stress drop of PH02 (Mw 5.5) is smaller 240

than that of GJ03 (Mw 5.6) and GJ01 (Mw 5.1) by a factor of 4.3 and 2.5, respectively. 241

Estimates of the stress drops for the GJ and PH main shocks reported by other studies show 242

similar results. Son et al. (2018) reported that the stress drop of GJ03 is 11.2 MPa based on 243

the analysis of the S-wave source spectrum. The mean stress drop of the same event derived 244

from finite fault inversion using the empirical Green’s function method is 23 MPa (Uchide 245

11

and Song, 2018). These values are somewhat larger than our estimate (8.29 MPa). For PH02, 246

Song and Lee (2019) estimated the mean stress drop of PH02 to be approximately 2 MPa 247

from finite fault inversion using InSAR data, and this value is consistent with our result (1.92 248

MPa). We note that PH02 and PH01 are considered anthropogenic earthquakes (Kim et al., 249

2018; Grigoli et al., 2018; Lee et al., 2019; Ellsworth et al., 2019; Woo et al., 2019b). PH01 250

was an induced earthquake, which occurred during a period when fluid injections for EGS 251

development were conducted. PH02 (the PH main shock) is considered a “runaway” 252

earthquake, which implies that its occurrence is affected by fluid injections even though it 253

releases strain energy accumulated through natural tectonic processes (Ellsworth et al., 2019). 254

Therefore, a question arises as to whether the low stress drops of PH02 and PH01 result from 255

the influence of fluid injections. There have been several studies reporting that stress drops of 256

induced earthquakes are smaller than those of tectonic earthquakes (Sumy et al., 2017; Boyd 257

et al., 2017; Hough, 2014). Hough (2014) argued that the stress drops of induced earthquakes 258

are smaller than those of tectonic earthquakes by a factor of 2–10 based on differences in 259

intensity between tectonic and induced earthquakes measured by a “Did You Feel It?” system. 260

Although the difference in the stress drop between the PH and GJ main shocks derived in this 261

study lies within the range proposed by Hough (2014), it is not sufficient to conclude that the 262

low stress drops observed in the PH sequence, especially for PH02 and PH01, are caused by 263

fluid injections. It is well known that the stress drop is controlled by many other factors, such 264

as focal depth, faulting type, and heat flow. Therefore, it is possible that the discrepancy in 265

the stress drop can be attributed to other factors. The PH and GJ main shocks differ in several 266

ways besides fluid injection. First, the focal depth of the PH main shock (4.27 km; Lee et al., 267

2019) is much shallower than that of the GJ main shock (14.5 km; Woo et al., 2019a). 268

Second, while the faulting type of the GJ main shock is nearly pure strike-slip, that of the PH 269

main shock is strike slip with considerable thrust-faulting components. 270

12

Although several studies have found that there is no clear depth dependence of stress drop 271

(Wu et al., 2018; Allmann and Shearer, 2009), most previous studies support the theory that 272

shallow earthquakes have lower stress drops than deep earthquakes (Huang et al., 2017; Oth, 273

2013). Huang et al. (2017) reported that induced earthquakes with deep focal depths (<5 km) 274

show similar stress drops as those of tectonic earthquakes in the central United States and 275

concluded that induced and tectonic earthquakes are not distinguishable based only on 276

differences in stress drop. Therefore, it is possible that the lower stress drop of the PH main 277

shock compared to the GJ main shock is caused only by the difference in focal depth. The 278

difference in focal depth can explain why the stress drops of the PH events are relatively 279

lower than those of the GJ events. Regarding the faulting style of earthquakes, the relations 280

between faulting style and stress drop reported by previous studies are not consistent. In 281

general, it is well-accepted that reverse-faulting earthquakes have higher stress drops (e.g., 282

McGarr, 1984; McGarr and Fletcher, 2002). However, Allmann and Shearer (2009) 283

suggested that the stress drop of strike-slip is higher than that of other faulting types. Our 284

observation shows that the stress drop of the GJ main shock, which has pure strike-slip 285

mechanism, is higher than that of the PH main shock, which has considerable reverse-faulting 286

components; this is consistent with the result presented by Allmann and Shearer (2009). Oth 287

(2013) suggested that stress drop variations are strongly correlated with heat flow variations 288

in crustal earthquakes in Japan. Therefore, heat flows can be another factor that affects stress 289

drop; however, we do not have sufficient information on whether there is a considerable 290

difference in heat flow between the epicentral regions of the GJ and PH sequences. 291

292

Conclusions 293

We analyzed the stress drop scaling of two moderate earthquake sequences that occurred in 294

the same tectonic regime. The stress drop seems to increase with an increasing magnitude in 295

13

both sequences. The observed magnitude dependence in stress drop scaling cannot be 296

explained by a self-similar model with a constant stress drop (Aki, 1967). The scaling of the 297

GJ sequence is similar to the results of other earthquake sequences studied using similar 298

coda-based methods (Mayeda and Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; 299

Yoo and Mayeda, 2013). The characteristic feature is that stress drop rapidly increases with 300

Mw in the range between Mw 4.5 and 5.5. This rapid increase in stress drop is not found in the 301

PH sequence. On average, stress drops of the PH sequence are lower than those of the GJ 302

sequence. Stress drops of PH02 and PH01 are much smaller than the events with similar 303

magnitudes in the GJ sequence. Considering previous studies on factors controlling the stress 304

drop, it is likely that differences in focal depth between the two sequences cause differences 305

in the stress drop. Although the focal depths of all PH events are similar, the stress drops for 306

the two PH events (PH01 and PH02) are particularly lower than those of the other PH events. 307

In addition, these two events are likely to be influenced by fluid injections. It may be inferred 308

that the much lower stress drops for the two events are caused by fluid injection. However, it 309

is not conclusive that the effect of fluid injection is adequate to explain the lower stress drops 310

based on only the observations in our study. 311

312

Data and Resources 313

Waveform data were acquired from seismograph networks and data centers in the region, 314

including those of the Korea Institute of Geology and Mineral Resources (KIGAM) and the 315

Korea Meteorological Administration (KMA) (the event catalog and data are available from 316

authors upon request). Geotectonic lines were obtained from KIGAM 317

(https://mgeo.kigam.re.kr, last accessed March 2017). The figures in this article were 318

generated using generic mapping tools (GMT; https://www.soest.hawaii.edu/gmt/, last 319

accessed March 2017). 320

14

321

Acknowledgments 322

We thank Vanessa Napoli (Applied Research Associates, Inc.) whose comments/suggestions 323

helped improve and clarify the original manuscript. This work was supported by the Nuclear 324

Safety Research Program through the Korea Foundation of Nuclear Safety (KoFONS) using 325

the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the 326

Republic of Korea (No. 1705010). Seung-Hoon Yoo received support under the Air Force 327

Research Laboratory contract FA9453-16-C-0022. And we appreciate to Cezar I. Trifu, 328

associate editor of Bulletin of the Seismological Society of America, and anonymous 329

reviewers for the revision comments/suggestions. 330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

15

References 346

Aki, K. (1967). Scaling law of seismic spectrum, J. Geophys. Res. 72(4) 1217-1231, doi: 347

10.1029/JZ072i004p01217. 348

349

Allmann, B. P., and P. M. Shearer (2009). Global variations of stress drop for moderate to 350

large earthquakes, J. Geophys. Res. Solid Earth 114(B1) B01310, doi: 351

10.1029/2008JB005821. 352

353

Allmann, B. P., and Shearer, P. M. (2007). Spatial and temporal stress drop variations in 354

small earthquakes near Parkfield, California, J. Geophys. Res.: Solid Earth 112(B4), doi: 355

https://doi.org/10.1029/2006JB004395. 356

357

Bodin, T., Sambridge, M., Rawlinson, N., and Arroucau, P. (2012). Transdimensional 358

tomography with unknown data noise, Geophys. J. Int. 189(3) 1536-1556, 359

doi.org/10.1111/j.1365-246x.2012.05414.x . 360

361

Boyd, O. S., D. E. McNamara, S. Hartzell, and G. Choy (2017). Influence of lithostatic stress 362

on earthquake stress drops in North America, Bull. Seismol. Soc. Am. 107(2) 856-868, doi: 363

10.1785/0120160219. 364

365

Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes, 366

J. Geophys. Res. 75(26) 4997-5009, doi: 10.1029/JB075i026p04997. 367

368

Brune, J. N. (1971). Correction to “Tectonic stress and the spectra of seismic shear waves 369

from earthquakes,” J. Geophys. Res. 76(20) 5002, doi: 10.1029/JB076i020p05002. 370

371

16

Ellsworth, W. L., D. Giardini, J. Townend, S. Ge, and T. Shimamoto (2019). Triggering of 372

the Pohang, Korea, Earthquake (Mw 5.5) by enhanced geothermal system stimulation, Seismol. 373

Res. Lett. 90(5) 1844-1858, doi: 10.1785/0220190102. 374

375

Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and 376

related problems, Proc. Roy. Soc. Lond. Math. Phys. Sci. 241(1226) 376-396, doi: 377

10.1098/rspa.1957.0133. 378

379

Grigoli, F., S. Cesca, A. P. Rinaldi, A. Manconi, J. A. López-Comino, J. F. Clinton, R. 380

Westaway, C. Cauzzi, T. Dahm, and S. Wiemer (2018). The November 2017 Mw 5.5 Pohang 381

earthquake: A possible case of induced seismicity in South Korea, Science 360(6392) 1003-382

1006, doi: 10.1126/science.aat2010. 383

384

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their 385

applications, Biometrika 57(1) 97–109, doi: 0.2307/2334940. 386

387

Hough, S. E. (2014). Shaking from injection‐induced earthquakes in the central and eastern 388

United States, Bull. Seismol. Soc. Am. 104(5) 2619-2626, doi: 10.1785/0120140099. 389

390

Huang, Y., W. L. Ellsworth, and G. C. Beroza (2017). Stress drops of induced and tectonic 391

earthquakes in the central United States are indistinguishable, Sci. Adv. 3(8) e1700772, doi: 392

10.1126/sciadv.1700772. 393

394

Kim, K. H., J. H. Ree, Y. Kim, S. Kim, S. Y. Kang, and W. Seo (2018). Assessing whether 395

the 2017 Mw 5.4 Pohang earthquake in South Korea was an induced event, Science 360(6392) 396

1007-1009, doi: 10.1126/science.aat6081. 397

398

17

Kim, S., J. Dettmer, J. Rhie, and H. Tkalčić (2016). Highly efficient Bayesian joint inversion 399

for receiver-based data and its application to lithospheric structure beneath the southern 400

Korean Peninsula, Geophys. J. Int. 206(1) 328-344, doi: 10.1093/gji/ggw149. 401

402

Lee, K.-K., W. L. Ellsworth, D. Giardini, J. Townend, S. Ge, T. Shimamoto, I.-W. Yeo, T.-S. 403

Kang, J. Rhie, D.-H. Sheen, C. Chang, J.-U. Woo, and C. Langenbruch (2019). Managing 404

injection-induced seismic risks, Science 364(6442) 730-732, doi: 10.1126/science.aax1878. 405

406

Malagnini, L., S. Nielsen, K. Mayeda, and E. Boschi (2010). Energy radiation from 407

intermediate‐ to large‐ magnitude earthquakes: Implications for dynamic fault weakening, J. 408

Geophys. Res. Solid Earth 115(B6) B06319, doi: 10.1029/2009JB006786. 409

410

Mayeda, K., A. Hofstetter, J. L. O’Boyle, and W. R. Walter (2003). Stable and transportable 411

regional magnitudes based on coda-derived moment-rate spectra, Bull. Seismol. Soc. Am. 412

93(1) 224-239, doi: 10.1785/0120020020. 413

414

Mayeda, K., L. Malagnini, and W. R. Walter (2007). A new spectral ratio method using 415

narrow band coda envelopes: Evidence for non‐ self‐ similarity in the Hector Mine sequence, 416

Geophys. Res. Lett. 34(11) L11303, doi: 10.1029/2007GL030041. 417

418

Mayeda, K., and L. Malagnini (2009). Apparent stress and corner frequency variations in the 419

1999 Taiwan (Chi‐ Chi) sequence: Evidence for a step‐ wise increase at Mw∼5.5, Geophys. 420

Res. Lett. 36(10) L10308, doi: 10.1029/2009GL037421. 421

422

McGarr, A. (1984). Scaling of ground motion parameters, state of stress, and focal depth, J. 423

Geophys. Res. Solid Earth 89(B8) 6969-6979, doi: 10.1029/JB089iB08p06969. 424

425

18

McGarr, A., and J. B. Fletcher (2002). Mapping apparent stress and energy radiation over 426

fault zones of major earthquakes, Bull. Seismol. Soc. Am. 92(5) 1633-1646, doi: 427

10.1785/0120010129. 428

429

Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, and A. H. Teller (1953). Equation of 430

state calculations by fast computing machines, J. Chem. Phys. 21(6) 1087-1092, doi: 431

10.1063/1.1699114. 432

433

Oth, A. (2013). On the characteristics of earthquake stress release variations in Japan. Earth 434

Planet. Sci. Lett. 377-378 132-141, doi: 10.1016/j.epsl.2013.06.037. 435

436

Park, J. C., Kim, W., Chung, T. W., Baag, C. E., and Ree, J. H. (2007). Focal mechanisms of 437

recent earthquakes in the Southern Korean Peninsula, Geophys. J. Int. 169(3) 1103-1114. 438

439

Rhie, J., & Kim, S. (2010). Regional moment tensor determination in the southern Korean 440

Peninsula. Geosci. J. 14(4) 329-333. 441

442

Soh, I., Chang, C., Lee, J., Hong, T. K., and Park, E. S. (2018). Tectonic stress orientations 443

and magnitudes, and friction of faults, deduced from earthquake focal mechanism inversions 444

over the Korean Peninsula. Geophys. J. Int. 213(2) 1360-1373. 445

446

Sokos, E. N., and J. Zahradnik (2008). ISOLA a Fortran code and a Matlab GUI to perform 447

multiple-point source inversion of seismic data, Comput. Geosci. 34(8) 967-977, doi: 448

0.1016/j.cageo.2007.07.005. 449

450

Son, M., C. S. Cho, J. S. Shin, H.-M. Rhee, and D.-H. Sheen (2018). Spatiotemporal 451

distribution of events during the first three months of the 2016 Gyeongju, Korea, earthquake 452

sequence, Bull. Seismol. Soc. Am. 108(1) 210-217, doi: 10.1785/0120170107. 453

19

454

Song, S. G., and H. Lee (2019). Static slip model of the 2017 Mw 5.4 Pohang, South Korea, 455

earthquake constrained by the InSAR data, Seismol. Res. Lett. 90(1) 140-148, doi: 456

10.1785/0220180156. 457

458

Sumy, D. F., C. J. Neighbors, E. S. Cochran, and K. M. Keranen (2017). Low stress drops 459

observed for aftershocks of the 2011 Mw 5.7 Prague, Oklahoma, earthquake, J. Geophys. Res. 460

Solid Earth 122(5) 3813-3834, doi: 10.1002/2016JB013153. 461

462

Uchide, T., and S. G. Song (2018). Fault rupture model of the 2016 Gyeongju, South Korea, 463

earthquake and its implication for the underground fault system, Geophys. Res. Lett. 45(5) 464

2257-2264, doi: 10.1002/2017GL076960. 465

466

Vackář, J., J. Burjánek, F. Gallovič, J. Zahradník, and J. Clinton (2017). Bayesian ISOLA: 467

New tool for automated centroid moment tensor inversion, Geophys. J. Int. 210(2) 693-705, 468

doi: 10.1093/gji/ggx158. 469

470

Woo, J.-U., M. Kim, D.-H. Sheen, T.-S. Kang, J. Rhie, F. Grigoli, W. L. Ellsworth, and D. 471

Giardini (2019a). An in‐ depth seismological analysis revealing a causal link between the 472

2017 Mw 5.5 Pohang earthquake and EGS project, J. Geophys. Res. Solid Earth in press, doi: 473

10.1029/2019JB018368. 474

475

Woo, J.-U., J. Rhie, S. Kim, T.-S. Kang, K.-H. Kim, and Y. Kim (2019b). The 2016 476

Gyeongju earthquake sequence revisited: aftershock interactions within a complex fault 477

system, Geophys. J. Int. 217(1) 58-74, doi: 10.1093/gji/ggz009. 478

479

20

Wu, Q., M. Chapman, and X. Chen (2018). Stress‐ drop variations of induced earthquakes in 480

Oklahoma, Bull. Seismol. Soc. Am. 108(3A) 1107-1123, doi: 10.1785/0120170335. 481

482

Yoo, S.-H. and K. Mayeda (2013). Validation of non‐self‐similar source scaling using ground 483

motions from the 2008 Wells, Nevada, earthquake sequence, Bull. Seismol. Soc. Am. 103(4) 484

2508-2519, doi: 10.1785/0120120327. 485

486

Yoo, S.-H., J. Rhie, H. Choi, and K. Mayeda (2010). Evidence for non‐ self‐ similarity and 487

transitional increment of scaled energy in the 2005 west off Fukuoka seismic sequence, J. 488

Geophys. Res. Solid Earth 115(B8) B08308, doi: 10.1029/2009JB007169. 489

490

Yoo, S.-H., J. Rhie, H. Choi, and K. Mayeda (2011). Coda-derived source parameters of 491

earthquakes and their scaling relationships in the Korean Peninsula, Bull. Seismol. Soc. Am. 492

101(5) 2388-2398, doi: 10.1785/0120100318. 493

494

495

Full mailing address of each author 496 497

498

Gyeongdon Chai1; cgd1605@gmail.com 499

Seung-Hoon Yoo2; syoo@ara.com 500

Junkee Rhie1* ; rhie@snu.ac.kr 501

Tae-Seob Kang3; tskang@pknu.ac.kr 502

503

504

505

506

507

508

509

510

511

21

Table 1. Consecutive 14 frequency bands used for making coda envelopes. 512

513

No. Frequency (Hz)

FREQ01 0.05 ~ 0.1

FREQ02 0.1 ~ 0.2

FREQ03 0.2 ~ 0.3

FREQ04 0.3 ~ 0.5

FREQ05 0.5 ~ 0.7

FREQ06 0.7 ~ 1.0

FREQ07 1.0 ~ 1.5

FREQ08 1.5 ~ 2.0

FREQ09 2.0 ~ 3.0

FREQ10 3.0 ~ 4.0

FREQ11 4.0 ~ 6.0

FREQ12 6.0 ~ 8.0

FREQ13 8.0 ~ 11.0

FREQ14 11.0 ~ 14.0

514

515

516

517

518

519

520

521

522

523

524

525

526

527

22

Table 2. Source parameters of the 2016 Gyeongju and 2017 Pohang earthquake sequences. 528

Seq. Event (No.) Lat Lon Dep Mw(1) Mw(2) fc(1) (Hz) fc(2) (Hz) Δσ(1) (MPa) Δσ(2) (MPa)

2016.256.104432 (GJ01) 35.77 129.20 14.96 5.14 5.13 0.71 ± (0.03) 0.73 ± (0.00) 4.73 ± (0.08) 4.75 ± (0.01)

2016.256.111050 (GJ02) 35.76 129.19 15.83

3.19

3.23 ± (0.01)

0.51 ± (0.03)

2016.256.113254 (GJ03) 35.75 129.19 14.46 5.57 5.58 0.57 ± (0.02) 0.52 ± (0.00) 10.55 ± (0.06) 8.27 ± (0.01)

2016.256.141827 (GJ04) 35.78 129.20 13.83 3.07 3.14 2.79 ± (0.03) 2.91 ± (0.01) 0.26 ± (0.08) 0.32 ± (0.02)

2016.256.145230 (GJ05) 35.76 129.19 13.52 3.21 3.26 3.73 ± (0.04) 2.55 ± (0.04) 0.98 ± (0.12) 0.32 ± (0.08)

2016.256.153710 (GJ06) 35.78 129.21 13.53

3.07

4.71 ± (0.01)

1.05 ± (0.03)

Gyeongju 2016.256.232447 (GJ07) 35.76 129.18 13.00 3.23 3.25 4.34 ± (0.03) 3.93 ± (0.01) 1.65 ± (0.09) 1.15 ± (0.03)

2016.257.053142 (GJ08) 35.76 129.19 13.96

3.03

3.81 ± (0.01)

0.47 ± (0.03)

2016.263.113358 (GJ09) 35.75 129.18 15.80 4.46 4.49 1.15 ± (0.03) 1.22 ± (0.01) 1.94 ± (0.09) 2.47 ± (0.02)

2016.265.025354 (GJ10) 35.76 129.19 13.79 3.43 3.42 4.84 ± (0.03) 4.45 ± (0.01) 4.38 ± (0.09) 2.95 ± (0.03)

2016.272.073430 (GJ11) 35.76 129.19 12.96

3.14

3.63 ± (0.02)

0.60 ± (0.03)

2016.276.115307 (GJ12) 35.75 129.20 15.42 2.98 2.94 6.41 ± (0.03) 5.41 ± (0.01) 2.14 ± (0.10) 1.01 ± (0.03)

2016.284.135910 (GJ13) 35.75 129.19 14.40 3.3 3.31 3.10 ± (0.03) 2.89 ± (0.01) 0.97 ± (0.10) 0.55 ± (0.03)

2017.105.023113 (PH01) 36.11 129.36 5.0 3.33 3.34 2.75 ± (0.05) 1.80 ± (0.03) 0.73 ± (0.16) 0.14 ± (0.05)

2017.319.052931 (PH02) 36.11 129.37 5.0 5.48 5.44 0.34 ± (0.03) 0.38 ± (0.01) 1.73 ± (0.08) 1.92 ± (0.01)

2017.319.060949 (PH03) 36.09 129.34 8.0(KMA) 3.45 3.10 ± (0.05) 0.89 ± (0.09)

Pohang 2017.319.074930 (PH04) 36.12 129.36 6.6 4.31 4.3 1.04 ± (0.02) 1.31 ± (0.01) 0.81 ± (0.07) 1.66 ± (0.01)

2017.323.144547 (PH05) 36.12 129.36 4.2 3.53 3.54 3.66 ± (0.04) 2.61 ± (0.02) 2.78 ± (0.13) 0.90 ± (0.04)

2017.323.210515 (PH06) 36.14 129.36 4.0 3.59 3.62 2.95 ± (0.03) 2.17 ± (0.02) 1.86 ± (0.08) 0.63 ± (0.03)

2018.041.200303 (PH07) 36.08 129.33 8.0 4.61 4.6 1.22 ± (0.04) 0.77 ± (0.01) 3.86 ± (0.11) 1.08 ± (0.01)

529

*hypoDD relocation data from Woo et al. (2019b) were used for Gyeongju, and Pohang 530

sequence location data were obtained from the KMA catalog; focal depths were computed by 531

ISOLA. (1) and (2) denote the results of coda spectral ratio and source calibration methods, 532

respectively. 533

534

535

536

23

List of Figure Captions 537

1) Map showing the seismic stations used in this study to create synthetic coda envelope 538

models and perform the coda-based spectral ratio and source calibration study. The white and 539

black triangles indicate the station networks operated by Korea Meteorological 540

Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 541

respectively. The area in the dashed square is shown in Figure 2. 542

2) Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 543

earthquake sequences occurred. The focal mechanisms determined by ISOLA software 544

(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 545

Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 546

aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 547

Pohang sequence has reverse and strike-slip faulting events. 548

3) Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, showing 549

the frequency-dependent decaying trends. The synthetic coda envelope models fit well with 550

the observed data envelopes (grey lines). 551

4) Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) main shock 552

and largest aftershock with the same EGF events in sequence. The focal mechanisms and 553

Pohang event depth information were determined using ISOLA, and the Gyeongju event 554

depth information was obtained from Woo et al. (2019b). Dashed lines (yellow) indicate the 555

use of posterior distribution to determine the corner frequency by full-Bayesian MCMC. The 556

black and white colors of triangles indicate the corner frequencies of the target and EGF 557

events. 558

5) To correct the site effect, we prepared the site-term with the GJ main shock (Mw 5.58), 559

foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). In 560

addition, we created the synthetic Brune model (the lines overlaying the squares) for the 561

events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 562

we determined the correction-term (grey dotted lines) for each event. The site-term (black 563

line) of this station was obtained by averaging all the correction-terms. The site-term of the 564

station was applied to obtain the site-corrected amplitudes for every recorded event. 565

6) Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) Pohang. 566

The symbols represent the mean values of the site-corrected amplitude data with one standard 567

deviation. Synthetic Brune curves (black lines) are the results of the source calibration. The 568

stars denote the corner frequencies on the Brune curve with posterior distributions (yellow 569

lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, MHS; Metropolis-570

Hastings Sampling method). The same colors as in Figure 2 are used here for the 571

corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using the 572

fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show the 573

NDCAs for stations after revision using the recalculated site correction terms. Blue lines are 574

the same as the black lines in (b). 575

7) Scaling relations of corner frequency and stress drop versus seismic moment for two 576

earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented by 577

grey dotted lines. Black vertical and horizontal lines with the symbols represent one standard 578

24

deviation. The source scaling trend of the Gyeongju sequence is consistent with the 579

previously reported trend (thick dotted lines) of coda-based source studies. Both source 580

scaling trends cannot be explained by a constant stress drop model. 581

25

582

Figure 1. Map showing the seismic stations used in this study to create synthetic coda 583

envelope models and perform the coda-based spectral ratio and source calibration study. The 584

white and black triangles indicate the station networks operated by Korea Meteorological 585

Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 586

respectively. The area in the dashed square is shown in Figure 2. 587

26

588 589

Figure 2. Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 590

earthquake sequences occurred. The focal mechanisms determined by ISOLA software 591

(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 592

Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 593

aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 594

Pohang sequence has reverse and strike-slip faulting events. 595

596

597

27

598

Figure 3. Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, 599

showing the frequency-dependent decaying trends. The synthetic coda envelope models fit 600

well with the observed data envelopes (grey lines). 601

602

603

604

605

28

606

Figure 4. Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) 607

main shock and largest aftershock with the same EGF events in sequence. The focal 608

mechanisms and Pohang event depth information were determined using ISOLA, and the 609

Gyeongju event depth information was obtained from Woo et al. (2019b). Dashed lines 610

(yellow) indicate the use of posterior distribution to determine corner frequency by full-611

Bayesian MCMC. The black and white colors of triangles indicate the corner frequencies of 612

the target and EGF events. 613

29

614

Figure 5. To correct the site effect, we prepared the site-term with the GJ main shock (Mw 615

5.58), foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). 616

In addition, we created the synthetic Brune model (the lines overlaying the squares) for the 617

events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 618

we determined the correction-term (grey dotted lines) for each event. The site-term (black 619

line) of this station was obtained by averaging all the correction-terms. The site-term of the 620

station was applied to obtain the site-corrected amplitudes for every recorded event. 621

30

622

623 624

625

626

31

Figure 6. Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) 627

Pohang. The symbols represent the mean values of the site-corrected amplitude data with one 628

standard deviation. Synthetic Brune curves (black lines) are the results of the source 629

calibration. The stars denote the corner frequencies on the Brune curve with posterior 630

distributions (yellow lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, 631

MHS; Metropolis-Hastings Sampling method). The same colors as in Figure 2 are used for 632

the corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using 633

the fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show 634

the NDCAs for stations after revision using the recalculated site correction terms. Blue lines 635

are the same as the black lines in (b). 636

32

637

Figure 7. Scaling relations of corner frequency and stress drop versus seismic moment for 638

two earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented 639

by grey dotted lines. Black vertical and horizontal lines with the symbols represent one 640

standard deviation. The source scaling trend of the Gyeongju sequence is consistent with the 641

previously reported trend (thick dotted lines) of coda-based source studies. Both source 642

scaling trends cannot be explained by a constant stress drop model. 643

1

Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake 1

sequences using coda-based methods 2

3

Gyeongdon Chai1, Seung-Hoon Yoo2, Junkee Rhie1*, and Tae-Seob Kang3 4

5 1School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, South 6

Korea 7

2Applied Research Associates, Inc., Arlington, VA 22203, USA 8

3Division of Earth Environmental System Science, Pukyong National University, Busan 9

48513, South Korea 10

11

Abstract 12

Two M5 earthquakes struck the southeastern Korean Peninsula in September 2016 and 13

November 2017, causing damage near the epicentral areas. We analyze the stress drop 14

scaling of these two earthquake sequences using coda-based methods and Bayesian inversion. 15

The 2016 Gyeongju earthquake sequence is a typical earthquake sequence generated by 16

tectonic processes. In contrast, the 2017 Pohang earthquake sequence is believed to be related 17

to fluid injections conducted for development of enhanced geothermal systems. As the two 18

sequences occurred in the same tectonic regime, our study provides a good opportunity to 19

compare the stress drop scaling between a tectonic earthquake sequence and an earthquake 20

sequence influenced by fluid injections. We found that the stress drops of events in the 21

Pohang sequences are lower than those of the Gyeongju sequence with similar magnitude. 22

Although it is likely that this difference results from focal depth variations, a reduction of 23

stress drop due to fluid injections cannot be ruled out. 24

25

Manuscript Click here toaccess/download;Manuscript;ChaiGD.BSSA.R01_GC08_JR01

2

Introduction 26

A study of the scaling relationship between magnitude and stress drop for earthquakes 27

occurring in a given region is important not only for understanding the fundamentals of the 28

earthquake rupture process but also for mitigating earthquake damage by precisely predicting 29

the ground motions of possible future earthquakes. There are many historical documents on 30

the occurrence of large earthquakes (M >6) in the southeastern part of the Korean Peninsula. 31

However, the largest earthquake recorded in this region with instruments is the ML 5.8 32

Gyeongju earthquake of 12 September, 2016 (Korean Meteorological Administration; KMA). 33

This region is susceptible to large earthquakes. Efforts toward mitigating the seismic risk in 34

this region are very important because this region has valuable infrastructure, including 35

nuclear power plants and cities with dense populations. In this study, we analyze the stress 36

drop scaling of two moderate earthquake sequences that occurred in the southeastern Korean 37

Peninsula using the analysis of coda waves, which is known to be more stable than the 38

analysis of direct waves (Mayeda et al., 2007; Yoo et al., 2010). 39

The two earthquake sequences considered in this study are the 2016 Mw 5.6 Gyeongju (GJ) 40

earthquake and the 2017 Mw 5.5 Pohang (PH) earthquake sequences (Figures 1 and 2). The 41

distance between the epicenters of the GJ and PH main shocks is approximately 43 km, and 42

both earthquakes occurred in the Gyeongsang Basin. The Gyeongsang Basin is a tectonic unit 43

classified based on the tectonic evolution in the Korean Peninsula. Although the Pohang 44

Basin, where the PH sequence occurred, had been tectonically active until recently compared 45

to the epicentral region of the GJ sequence, the current tectonic environment for generating 46

earthquakes in both regions should be similar because they belong to the same tectonic unit 47

(Park et al., 2007; Soh et al., 2018). We can also expect that tectonic stresses in both regions 48

are similar because they are spatially close to each other. However, the reported source 49

characteristic of the two sequences, especially the main shocks, are quite different. The focal 50

3

depths of the GJ and PH main shocks are 14.5 km (Woo et al., 2019a) and 4.27 km (Lee et al., 51

2019; Woo et al., 2019b), respectively. The focal mechanism for the GJ main shock 52

determined by moment tensor inversion is strike slip. The faulting style of the PH main shock 53

is strike slip with a significant thrust component. Strike slip and thrust mechanisms are both 54

popular mechanisms in our study area (Rhie and Kim, 2010). The most important difference 55

between the two earthquakes is whether fluid injection affected the occurrence of earthquake. 56

The GJ main shock is a natural earthquake generated because of tectonic stress, whereas the 57

PH main shock is a “runaway” earthquake triggered by stress perturbation caused by 58

injecting fluids for the development of enhanced geothermal systems (EGS) (Ellsworth et al., 59

2019). The objective of this study is to show that different mechanisms between tectonic and 60

“runaway” earthquakes can be revealed by comparing source parameters of the GJ and PH 61

earthquake sequences, which occurred in the same tectonic region. 62

63

Data and Methods 64

Data used in this study are seismic waveforms recorded at broadband stations operated by the 65

Korea Meteorological Administration (KMA) and the Korea Institute of Geoscience and 66

Mineral Resources (KIGAM) (Figure 1), and they were divided into two sets for different 67

research purposes. The first data set was used to define a reference coda envelope, which is 68

necessary for calculating the source spectrum. For the lower frequency range (0.05–8.0 Hz), 69

we used waveforms from earthquakes with magnitudes greater than 4.0 that occurred in and 70

around the Korean Peninsula between 2006 and 2012. The sampling rate of this data set is 20 71

Hz. For the higher frequency range (8.0–14.0 Hz), we used waveforms from earthquakes in 72

the 2016 Gyeongju sequence with magnitudes greater than 3.0; their sampling rate is 100 Hz. 73

The second data set was used for analysis of source spectra for the GJ and PH sequences. 74

4

To determine a reference coda envelope, we defined its theoretical functional form following 75

a previous study (Mayeda et al., 2003) to be 76

𝐸(𝑡, 𝑓, 𝑟) = 𝐻 (𝑡 −𝑟

𝑣(𝑓,𝑟)) (𝑡 −

𝑟

𝑣(𝑓,𝑟))

−𝛾(𝑓,𝑟)

× exp [𝑏(𝑓, 𝑟) (𝑡 −𝑟

𝑣(𝑓,𝑟))], (1) 77

where r, f, and t indicate distance in km, frequency in Hz, and the time elapsed from the event 78

origin time in s, respectively; H is the Heaviside step function; and 𝑣(𝑓, 𝑟) is the velocity of 79

the peak arrival in km/s. Two functions, 𝑏(𝑓, 𝑟) and 𝛾(𝑓, 𝑟), control the shape of the coda 80

envelope. To define the reference coda envelope, we determined 𝑣(𝑓, 𝑟), 𝑏(𝑓, 𝑟), and 81

𝛾(𝑓, 𝑟) from the observed data by following the procedures presented in Yoo et al. (2011). 82

We defined reference coda envelopes for 14 consecutive narrow frequency bands (Table 1, 83

Figure 3). Because the coda envelope shapes for both sequences are similar, we used the 84

same set of reference coda envelopes for both sequences. 85

The relation between the observed and reference coda envelopes can be represented as 86

follows: 87

𝐴𝐶(𝑡, 𝑓, 𝑟) = 𝑊0(𝑓)𝑆(𝑓)𝑃(𝑓, 𝑟)𝐸(𝑡, 𝑓, 𝑟), (2) 88

where 𝐴𝐶(𝑡, 𝑓, 𝑟) , 𝑆(𝑓) , 𝑃(𝑓, 𝑟) , and 𝑊0(𝑓) are the observed coda envelope, site 89

correction, path correction, and S-wave source amplitude, respectively. 90

To measure 𝐴𝐶(𝑡, 𝑓, 𝑟), we removed the instrument response of two horizontal component 91

waveforms to velocity seismograms. A four-pole two-pass Butterworth filter, for which 92

corner frequencies correspond to 14 consecutive narrow frequency bands was applied, and 93

then an envelope for each frequency was calculated using 94

𝐸obs = √𝑣(𝑡)2 + ℎ(𝑡)2, (3) 95

where 𝑣(𝑡) and ℎ(𝑡) are the band-pass-filtered horizontal velocity seismogram and its 96

Hilbert transform, respectively. To distinguish the observed and reference envelopes, we use 97

𝐸obs for the observed envelope. The final observed envelope was calculated by taking the 98

5

logarithm base 10 of two horizontal envelopes and then averaging them. By doing this, we 99

measured 𝐴𝐶(𝑡, 𝑓, 𝑟) for each frequency and epicentral distance. We can see in Eq. (2) that 100

changes in 𝐴𝐶(𝑡, 𝑓, 𝑟) with time for a given frequency and distance should be the same as 101

the changes in 𝐸(𝑡, 𝑓, 𝑟). The difference between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟) is called non-102

dimensional coda amplitude (NDCA), and it can be measured by finding the optimum DC 103

shift, which minimizes the L1 norm between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟). We then compared 104

the reference and observed coda envelopes at each frequency band. 105

Two methods are widely used to study seismic sources using measured NDCA. The first 106

method involves directly estimating 𝑊0(𝑓) by correcting 𝑃(𝑓, 𝑟) and 𝑆(𝑓) from NDCA. 107

The advantage of this method is that it can be used to estimate source spectra of all events in 108

a given region once models for 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are defined. Because source spectra are 109

available, we can estimate M0 and fc, the seismic moment in Newton meters and the corner 110

frequency in Hertz, which are two representative source parameters, but we can also estimate 111

radiated energy. However, unless 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are precise enough, the reliability of 112

estimated source spectra can be low. The second method is to estimate fc only, or fc and M0 113

together, from the ratio of NDCA between two events without calculating the individual 114

source spectrum of each event (Mayeda et al., 2007). This method is based on the assumption 115

that if NDCAs are measured at the identical station and two earthquakes occurred at close 116

locations, 𝑃(𝑓, 𝑟) and 𝑆(𝑓) for both events should be identical and the ratio of NDCA is 117

the same as the ratio of the source spectra. In this case, we do not need to determine 𝑃(𝑓, 𝑟) 118

and 𝑆(𝑓) to apply the method. However, this method is only applicable to event pairs with 119

similar hypocenters but large differences in magnitude. In this study, we are interested in 120

examining the source characteristics of two earthquake sequences, where the earthquakes in 121

each sequence are spatially clustered. Therefore, a combined procedure of the two methods 122

can be applied. We used the information obtained from the ratio of the NDCAs to define the 123

6

site correction terms, and then applied these terms to study the source spectra of the events. 124

The detailed procedure is as follows. First, we selected event pairs with a magnitude 125

difference larger than 1 in each sequence. Total numbers of selected events and 126

corresponding event pairs for the GJ sequence are 9 and 15, respectively, and 6 and 7 for the 127

PH sequence. The maximum distance between epicenters among event pairs is 7 km. Mw for 128

each event was independently calculated using ISOLA (Sokos and Zahradnik, 2008; Vackář 129

et al., 2017) software based on the waveform inversion method (Figure 2). We considered 66 130

stations for our analysis, but the actual number of data points used for each process was not 131

consistent (Figure 1). To estimate fc of both events from the spectral ratio for a given event 132

pair, we used the Bayesian inversion method. A hierarchical scheme was applied to account 133

for data error in the inversion (Bodin et al., 2012; Kim et al., 2016). We assumed that prior 134

probability of Δσ is uniform in the range 10−3 − 103 MPa. Once we selected Δσ, we 135

calculated fc by using the following equation, because M0 of the event is pre-defined: 136

𝑓𝑐 =2.34𝛽

2𝜋 ( 7

16∙𝑀0∆𝜎

)

13

. (4) 137

Equation (4) was derived from the following two equations based on the circular fault model 138

(Eshelby, 1957). Shear wave velocity (𝛽) was set to be 3.5 km/s. 139

Δσ =7

16

𝑀0

𝑟3 (5) 140

𝑟 =2.34β

2π𝑓𝑐. (6) 141

Using fc and M0 of both events, we can define a spectral ratio between two events based on 142

Brune’s source model as follows (Aki, 1967; Brune, 1970; 1971): 143

𝑅(𝑓) =𝑀01[1+(𝑓/𝑓𝑐2)2]

𝑀02[1+(𝑓/𝑓𝑐1)2]. (7) 144

The misfit between the synthetic and observed spectral ratio was measured using the L1 norm, 145

and the likelihood function was defined as 146

7

𝐿 =1

2𝜎× exp [∑

|𝑅syn(𝑓𝑖)−𝑅obs(𝑓𝑖)|

𝜎

𝑛𝑖=1 ], (8) 147

where 𝑅syn and 𝑅obs indicate the synthetic and observed spectral ratio, respectively, and 𝑓𝑖 148

represents the center frequency of a given frequency band. To consider the data error in the 149

inversion, we assumed that 𝜎 has a positive uniform prior probability. We updated model 150

parameters (two stress drops and 𝜎) 200,000 times using the Metropolis-Hastings sampling 151

(MHS) method (Metropolis et al., 1953; Hastings, 1970). After the first half of the 152

calculations, which is considered a burn-in period, we selected 1 sample per every 100 153

calculations to estimate the posterior probability density (PPD) of two values of stress drop 154

(or fc) and 𝜎. For each event pair, we selected the fc with highest PPD. The final fc value for 155

each event was calculated by averaging selected fc values for all event pairs. 156

Because the final fc values for large events (Mw >= 4.0) are more accurate owing to their 157

large signal-to-noise ratios, we only used the fc values of only large events for further 158

analyses. The number of final fc values was three for each of the PH and GJ sequences. Once 159

we determined fc and M0, the theoretical Brune’s source spectrum can be calculated using the 160

following equation: 161

𝑀(𝑓) =𝑀0

(1+(𝑓

𝑓𝑐)

2). (9) 162

For each station, a site correction term can be determined by measuring the difference 163

between the theoretical Brune’s source spectrum and the corresponding NDCA. We note that 164

a site correction term contains 𝑃(𝑓, 𝑟) and 𝑆(𝑓) in Eq. (1). Because we define the site 165

correction terms of individual stations separately for PH and GJ sequences, we can ignore 166

variation in the site correction term with distance. We calculated the difference between the 167

theoretical Brune’s spectrum and the NDCA for each event and then averaged them for each 168

sequence to determine the final site correction term as a function of frequency. Once a site 169

correction term was defined, we calculated the source spectrum for each event by correcting 170

8

NDCA. By averaging the estimated source spectra of each event for all available stations, we 171

calculated the final source spectrum for each event. To estimate the PPD of stress drop (or fc) 172

and Mw from the final source spectrum, we used Bayesian inversion, which is similar to the 173

method previously applied for spectral ratio. We assumed that the stress drop and M0 have 174

uniform prior probability in the ranges between 10–3 and 103 MPa and between –2 and 2 in 175

logarithmic scale about the maximum value of the corrected NDCA, respectively. The 176

parameter fc was determined from a given stress drop and M0. To consider data error, we 177

adopted two parameters, 𝜎𝑓rms and 𝜎𝑓

SD. Here, 𝜎𝑓rms indicates an envelope fitting error 178

when measuring coda amplitudes of observed envelopes at a given frequency and 𝜎𝑓SD is 179

defined as one standard deviation of the site-correction term at the given frequency. The 180

likelihood function is defined as 181

𝐿 =1

2× exp [∑

|𝑀syn(𝑓𝑖)−𝑀obs(𝑓𝑖)|

𝜎𝑓rms+𝜎𝑓

SD𝑛𝑖=1 ]. (10) 182

The same sampling procedure of Bayesian inversion using the MHS method that was used for 183

the spectral ratio method was applied to estimate the PPD of Mw and fc. The PPD of stress 184

drop was also determined from Eqs. (5) and (6). We can technically estimate source 185

parameters of all events with measured NDCA. However, low signal-to-noise ratio of small 186

events can distort the results. Therefore, we used 9 and 6 events with Mw larger than 3.0 for 187

the GJ and PH sequences, respectively. We calculated Brune’s source spectrum using M0 and 188

fc estimated by Bayesian inversion and used this spectrum to calculate a site correction term. 189

190

Results and Discussion 191

We applied coda-based methods and Bayesian inversion to the GJ and PH earthquake 192

sequences. We calculated the reference coda envelopes and compared them with the observed 193

coda envelopes. Figure 3 depicts an example of the comparison between the reference and 194

observed coda envelopes at selected frequency bands. Because the excitations of the coda 195

9

waves are nearly insensitive to the radiation pattern (Mayeda et al., 2003), we were able to 196

obtain azimuthally averaged source spectra, even though the stations were mainly located 197

westward of the events. The final fc value was calculated for each event using the MHS 198

method and the PPD was estimated; for each event pair, we selected the fc with the highest 199

PPD. Figure 4 shows examples of spectral ratios determined for selected events. The 200

calculated difference between the theoretical Brune’s spectrum and the NDCA for each event 201

was averaged for each sequence to determine the final site correction term as a function of 202

frequency, as shown in Figure 5 for three events in the GJ sequence. 203

If the site correction term is well-defined, we can expect the estimated source spectra of the 204

events involved in determining the site correction terms to be consistent with the site-205

corrected NDCA for the same event. In the case of the GJ sequence, we can see that the two 206

values are well-matched, as expected (Figure 6(a)). However, there are significant 207

discrepancies in the PH sequence (Figure 6(c)). The reason for these discrepancies appears to 208

be that the original estimates of fc obtained from the spectral ratio method for the PH 209

sequence are not accurate because the number of applicable earthquakes is insufficient. To 210

overcome this problem, we recalculated the site correction term for the PH sequence. First, 211

we determined the Brune spectra, which fit the corrected NDCA for each event, and then 212

recalculated the site correction terms by averaging the differences between the Brune spectra 213

and the NDCAs for the three events. The corrected NDCA using the recalculated site 214

correction term demonstrates a significantly improved fit to the theoretical Brune’s spectrum 215

(Figure 6(b)). 216

Using coda-based methods and Bayesian inversion, we estimated the PPD of Mw, fc, and 217

stress drop for 12 and 7 earthquakes in the GJ and PH sequences, respectively (Table 2). The 218

stress drop scaling for both the GJ and PH sequences show that stress drop increases with 219

increasing magnitude on the overall scale (Figure 7). The observed trends in stress drop 220

10

scaling cannot be explained by the self-similar model with a constant stress drop (Aki, 1967). 221

The estimates of the stress drop appear to be considerably scattered for smaller earthquakes 222

(Mw < ~3.5) in both sequences. This may indicate that estimates of stress drop for smaller 223

events are not stable because of the low signal-to-noise ratio. The stress drop of the smallest 224

PH event (PH01 in Table 2) is much smaller than that of other events with similar magnitudes. 225

For relatively larger events (Mw >= 4.0) in the GJ sequence, it is likely that the stress drop 226

increases with increasing Mw in a range between Mw 4.5 and 5.5. This observation is 227

consistent with other previous studies using similar coda-based methods (Mayeda and 228

Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; Yoo and Mayeda, 2013). For the 229

PH sequence, we do not observe an increasing trend in the given magnitude range because 230

the stress drop of the PH main shock (PH02) is smaller than those of the shocks of similar 231

magnitude in the GJ sequence. No significant increase in the stress drop for the specific 232

magnitude range was reported for the Parkfield sequence (Allman and Shearer, 2007). 233

Additionally, the stress drops of two other PH events (PH04 and PH07) with Mw larger than 234

4.0 are also smaller than the stress drops of similar-sized GJ events. 235

To summarize the characteristics of stress drop scaling for the two sequences, the stress drops 236

of the PH sequence appear to be smaller than those of the GJ sequence, and two PH events 237

(PH01 and PH02) have much smaller stress drops in comparison with those of events with 238

similar magnitudes in the GJ sequence. The stress drop of PH01 (Mw 3.3) is smaller than that 239

of GJ13 (Mw 3.3) by a factor of approximately 4. The stress drop of PH02 (Mw 5.5) is smaller 240

than that of GJ03 (Mw 5.6) and GJ01 (Mw 5.1) by a factor of 4.3 and 2.5, respectively. 241

Estimates of the stress drops for the GJ and PH main shocks reported by other studies show 242

similar results. Son et al. (2018) reported that the stress drop of GJ03 is 11.2 MPa based on 243

the analysis of the S-wave source spectrum. The mean stress drop of the same event derived 244

from finite fault inversion using the empirical Green’s function method is 23 MPa (Uchide 245

11

and Song, 2018). These values are somewhat larger than our estimate (8.29 MPa). For PH02, 246

Song and Lee (2019) estimated the mean stress drop of PH02 to be approximately 2 MPa 247

from finite fault inversion using InSAR data, and this value is consistent with our result (1.92 248

MPa). We note that PH02 and PH01 are considered anthropogenic earthquakes (Kim et al., 249

2018; Grigoli et al., 2018; Lee et al., 2019; Ellsworth et al., 2019; Woo et al., 2019b). PH01 250

was an induced earthquake, which occurred during a period when fluid injections for EGS 251

development were conducted. PH02 (the PH main shock) is considered a “runaway” 252

earthquake, which implies that its occurrence is affected by fluid injections even though it 253

releases strain energy accumulated through natural tectonic processes (Ellsworth et al., 2019). 254

Therefore, a question arises as to whether the low stress drops of PH02 and PH01 result from 255

the influence of fluid injections. There have been several studies reporting that stress drops of 256

induced earthquakes are smaller than those of tectonic earthquakes (Sumy et al., 2017; Boyd 257

et al., 2017; Hough, 2014). Hough (2014) argued that the stress drops of induced earthquakes 258

are smaller than those of tectonic earthquakes by a factor of 2–10 based on differences in 259

intensity between tectonic and induced earthquakes measured by a “Did You Feel It?” system. 260

Although the difference in the stress drop between the PH and GJ main shocks derived in this 261

study lies within the range proposed by Hough (2014), it is not sufficient to conclude that the 262

low stress drops observed in the PH sequence, especially for PH02 and PH01, are caused by 263

fluid injections. It is well known that the stress drop is controlled by many other factors, such 264

as focal depth, faulting type, and heat flow. Therefore, it is possible that the discrepancy in 265

the stress drop can be attributed to other factors. The PH and GJ main shocks differ in several 266

ways besides fluid injection. First, the focal depth of the PH main shock (4.27 km; Lee et al., 267

2019) is much shallower than that of the GJ main shock (14.5 km; Woo et al., 2019a). 268

Second, while the faulting type of the GJ main shock is nearly pure strike-slip, that of the PH 269

main shock is strike slip with considerable thrust-faulting components. 270

12

Although several studies have found that there is no clear depth dependence of stress drop 271

(Wu et al., 2018; Allmann and Shearer, 2009), most previous studies support the theory that 272

shallow earthquakes have lower stress drops than deep earthquakes (Huang et al., 2017; Oth, 273

2013). Huang et al. (2017) reported that induced earthquakes with deep focal depths (<5 km) 274

show similar stress drops as those of tectonic earthquakes in the central United States and 275

concluded that induced and tectonic earthquakes are not distinguishable based only on 276

differences in stress drop. Therefore, it is possible that the lower stress drop of the PH main 277

shock compared to the GJ main shock is caused only by the difference in focal depth. The 278

difference in focal depth can explain why the stress drops of the PH events are relatively 279

lower than those of the GJ events. Regarding the faulting style of earthquakes, the relations 280

between faulting style and stress drop reported by previous studies are not consistent. In 281

general, it is well-accepted that reverse-faulting earthquakes have higher stress drops (e.g., 282

McGarr, 1984; McGarr and Fletcher, 2002). However, Allmann and Shearer (2009) 283

suggested that the stress drop of strike-slip is higher than that of other faulting types. Our 284

observation shows that the stress drop of the GJ main shock, which has pure strike-slip 285

mechanism, is higher than that of the PH main shock, which has considerable reverse-faulting 286

components; this is consistent with the result presented by Allmann and Shearer (2009). Oth 287

(2013) suggested that stress drop variations are strongly correlated with heat flow variations 288

in crustal earthquakes in Japan. Therefore, heat flows can be another factor that affects stress 289

drop; however, we do not have sufficient information on whether there is a considerable 290

difference in heat flow between the epicentral regions of the GJ and PH sequences. 291

292

Conclusions 293

We analyzed the stress drop scaling of two moderate earthquake sequences that occurred in 294

the same tectonic regime. The stress drop seems to increase with an increasing magnitude in 295

13

both sequences. The observed magnitude dependence in stress drop scaling cannot be 296

explained by a self-similar model with a constant stress drop (Aki, 1967). The scaling of the 297

GJ sequence is similar to the results of other earthquake sequences studied using similar 298

coda-based methods (Mayeda and Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; 299

Yoo and Mayeda, 2013). The characteristic feature is that stress drop rapidly increases with 300

Mw in the range between Mw 4.5 and 5.5. This rapid increase in stress drop is not found in the 301

PH sequence. On average, stress drops of the PH sequence are lower than those of the GJ 302

sequence. Stress drops of PH02 and PH01 are much smaller than the events with similar 303

magnitudes in the GJ sequence. Considering previous studies on factors controlling the stress 304

drop, it is likely that differences in focal depth between the two sequences cause differences 305

in the stress drop. Although the focal depths of all PH events are similar, the stress drops for 306

the two PH events (PH01 and PH02) are particularly lower than those of the other PH events. 307

In addition, these two events are likely to be influenced by fluid injections. It may be inferred 308

that the much lower stress drops for the two events are caused by fluid injection. However, it 309

is not conclusive that the effect of fluid injection is adequate to explain the lower stress drops 310

based on only the observations in our study. 311

312

Data and Resources 313

Waveform data were acquired from seismograph networks and data centers in the region, 314

including those of the Korea Institute of Geology and Mineral Resources (KIGAM) and the 315

Korea Meteorological Administration (KMA) (the event catalog and data are available from 316

authors upon request). Geotectonic lines were obtained from KIGAM 317

(https://mgeo.kigam.re.kr, last accessed March 2017). The figures in this article were 318

generated using generic mapping tools (GMT; https://www.soest.hawaii.edu/gmt/, last 319

accessed March 2017). 320

14

321

Acknowledgments 322

We thank Vanessa Napoli (Applied Research Associates, Inc.) whose comments/suggestions 323

helped improve and clarify the original manuscript. This work was supported by the Nuclear 324

Safety Research Program through the Korea Foundation of Nuclear Safety (KoFONS) using 325

the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the 326

Republic of Korea (No. 1705010). Seung-Hoon Yoo received support under the Air Force 327

Research Laboratory contract FA9453-16-C-0022. And we appreciate to Cezar I. Trifu, 328

associate editor of Bulletin of the Seismological Society of America, and anonymous 329

reviewers for the revision comments/suggestions. 330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

15

References 346

Aki, K. (1967). Scaling law of seismic spectrum, J. Geophys. Res. 72(4) 1217-1231, doi: 347

10.1029/JZ072i004p01217. 348

349

Allmann, B. P., and P. M. Shearer (2009). Global variations of stress drop for moderate to 350

large earthquakes, J. Geophys. Res. Solid Earth 114(B1) B01310, doi: 351

10.1029/2008JB005821. 352

353

Allmann, B. P., and Shearer, P. M. (2007). Spatial and temporal stress drop variations in 354

small earthquakes near Parkfield, California, J. Geophys. Res.: Solid Earth 112(B4), doi: 355

https://doi.org/10.1029/2006JB004395. 356

357

Bodin, T., Sambridge, M., Rawlinson, N., and Arroucau, P. (2012). Transdimensional 358

tomography with unknown data noise, Geophys. J. Int. 189(3) 1536-1556, 359

doi.org/10.1111/j.1365-246x.2012.05414.x . 360

361

Boyd, O. S., D. E. McNamara, S. Hartzell, and G. Choy (2017). Influence of lithostatic stress 362

on earthquake stress drops in North America, Bull. Seismol. Soc. Am. 107(2) 856-868, doi: 363

10.1785/0120160219. 364

365

Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes, 366

J. Geophys. Res. 75(26) 4997-5009, doi: 10.1029/JB075i026p04997. 367

368

Brune, J. N. (1971). Correction to “Tectonic stress and the spectra of seismic shear waves 369

from earthquakes,” J. Geophys. Res. 76(20) 5002, doi: 10.1029/JB076i020p05002. 370

371

16

Ellsworth, W. L., D. Giardini, J. Townend, S. Ge, and T. Shimamoto (2019). Triggering of 372

the Pohang, Korea, Earthquake (Mw 5.5) by enhanced geothermal system stimulation, Seismol. 373

Res. Lett. 90(5) 1844-1858, doi: 10.1785/0220190102. 374

375

Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and 376

related problems, Proc. Roy. Soc. Lond. Math. Phys. Sci. 241(1226) 376-396, doi: 377

10.1098/rspa.1957.0133. 378

379

Grigoli, F., S. Cesca, A. P. Rinaldi, A. Manconi, J. A. López-Comino, J. F. Clinton, R. 380

Westaway, C. Cauzzi, T. Dahm, and S. Wiemer (2018). The November 2017 Mw 5.5 Pohang 381

earthquake: A possible case of induced seismicity in South Korea, Science 360(6392) 1003-382

1006, doi: 10.1126/science.aat2010. 383

384

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their 385

applications, Biometrika 57(1) 97–109, doi: 0.2307/2334940. 386

387

Hough, S. E. (2014). Shaking from injection‐induced earthquakes in the central and eastern 388

United States, Bull. Seismol. Soc. Am. 104(5) 2619-2626, doi: 10.1785/0120140099. 389

390

Huang, Y., W. L. Ellsworth, and G. C. Beroza (2017). Stress drops of induced and tectonic 391

earthquakes in the central United States are indistinguishable, Sci. Adv. 3(8) e1700772, doi: 392

10.1126/sciadv.1700772. 393

394

Kim, K. H., J. H. Ree, Y. Kim, S. Kim, S. Y. Kang, and W. Seo (2018). Assessing whether 395

the 2017 Mw 5.4 Pohang earthquake in South Korea was an induced event, Science 360(6392) 396

1007-1009, doi: 10.1126/science.aat6081. 397

398

17

Kim, S., J. Dettmer, J. Rhie, and H. Tkalčić (2016). Highly efficient Bayesian joint inversion 399

for receiver-based data and its application to lithospheric structure beneath the southern 400

Korean Peninsula, Geophys. J. Int. 206(1) 328-344, doi: 10.1093/gji/ggw149. 401

402

Lee, K.-K., W. L. Ellsworth, D. Giardini, J. Townend, S. Ge, T. Shimamoto, I.-W. Yeo, T.-S. 403

Kang, J. Rhie, D.-H. Sheen, C. Chang, J.-U. Woo, and C. Langenbruch (2019). Managing 404

injection-induced seismic risks, Science 364(6442) 730-732, doi: 10.1126/science.aax1878. 405

406

Malagnini, L., S. Nielsen, K. Mayeda, and E. Boschi (2010). Energy radiation from 407

intermediate‐ to large‐ magnitude earthquakes: Implications for dynamic fault weakening, J. 408

Geophys. Res. Solid Earth 115(B6) B06319, doi: 10.1029/2009JB006786. 409

410

Mayeda, K., A. Hofstetter, J. L. O’Boyle, and W. R. Walter (2003). Stable and transportable 411

regional magnitudes based on coda-derived moment-rate spectra, Bull. Seismol. Soc. Am. 412

93(1) 224-239, doi: 10.1785/0120020020. 413

414

Mayeda, K., L. Malagnini, and W. R. Walter (2007). A new spectral ratio method using 415

narrow band coda envelopes: Evidence for non‐ self‐ similarity in the Hector Mine sequence, 416

Geophys. Res. Lett. 34(11) L11303, doi: 10.1029/2007GL030041. 417

418

Mayeda, K., and L. Malagnini (2009). Apparent stress and corner frequency variations in the 419

1999 Taiwan (Chi‐ Chi) sequence: Evidence for a step‐ wise increase at Mw∼5.5, Geophys. 420

Res. Lett. 36(10) L10308, doi: 10.1029/2009GL037421. 421

422

McGarr, A. (1984). Scaling of ground motion parameters, state of stress, and focal depth, J. 423

Geophys. Res. Solid Earth 89(B8) 6969-6979, doi: 10.1029/JB089iB08p06969. 424

425

18

McGarr, A., and J. B. Fletcher (2002). Mapping apparent stress and energy radiation over 426

fault zones of major earthquakes, Bull. Seismol. Soc. Am. 92(5) 1633-1646, doi: 427

10.1785/0120010129. 428

429

Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, and A. H. Teller (1953). Equation of 430

state calculations by fast computing machines, J. Chem. Phys. 21(6) 1087-1092, doi: 431

10.1063/1.1699114. 432

433

Oth, A. (2013). On the characteristics of earthquake stress release variations in Japan. Earth 434

Planet. Sci. Lett. 377-378 132-141, doi: 10.1016/j.epsl.2013.06.037. 435

436

Park, J. C., Kim, W., Chung, T. W., Baag, C. E., and Ree, J. H. (2007). Focal mechanisms of 437

recent earthquakes in the Southern Korean Peninsula, Geophys. J. Int. 169(3) 1103-1114. 438

439

Rhie, J., & Kim, S. (2010). Regional moment tensor determination in the southern Korean 440

Peninsula. Geosci. J. 14(4) 329-333. 441

442

Soh, I., Chang, C., Lee, J., Hong, T. K., and Park, E. S. (2018). Tectonic stress orientations 443

and magnitudes, and friction of faults, deduced from earthquake focal mechanism inversions 444

over the Korean Peninsula. Geophys. J. Int. 213(2) 1360-1373. 445

446

Sokos, E. N., and J. Zahradnik (2008). ISOLA a Fortran code and a Matlab GUI to perform 447

multiple-point source inversion of seismic data, Comput. Geosci. 34(8) 967-977, doi: 448

0.1016/j.cageo.2007.07.005. 449

450

Son, M., C. S. Cho, J. S. Shin, H.-M. Rhee, and D.-H. Sheen (2018). Spatiotemporal 451

distribution of events during the first three months of the 2016 Gyeongju, Korea, earthquake 452

sequence, Bull. Seismol. Soc. Am. 108(1) 210-217, doi: 10.1785/0120170107. 453

19

454

Song, S. G., and H. Lee (2019). Static slip model of the 2017 Mw 5.4 Pohang, South Korea, 455

earthquake constrained by the InSAR data, Seismol. Res. Lett. 90(1) 140-148, doi: 456

10.1785/0220180156. 457

458

Sumy, D. F., C. J. Neighbors, E. S. Cochran, and K. M. Keranen (2017). Low stress drops 459

observed for aftershocks of the 2011 Mw 5.7 Prague, Oklahoma, earthquake, J. Geophys. Res. 460

Solid Earth 122(5) 3813-3834, doi: 10.1002/2016JB013153. 461

462

Uchide, T., and S. G. Song (2018). Fault rupture model of the 2016 Gyeongju, South Korea, 463

earthquake and its implication for the underground fault system, Geophys. Res. Lett. 45(5) 464

2257-2264, doi: 10.1002/2017GL076960. 465

466

Vackář, J., J. Burjánek, F. Gallovič, J. Zahradník, and J. Clinton (2017). Bayesian ISOLA: 467

New tool for automated centroid moment tensor inversion, Geophys. J. Int. 210(2) 693-705, 468

doi: 10.1093/gji/ggx158. 469

470

Woo, J.-U., M. Kim, D.-H. Sheen, T.-S. Kang, J. Rhie, F. Grigoli, W. L. Ellsworth, and D. 471

Giardini (2019a). An in‐ depth seismological analysis revealing a causal link between the 472

2017 Mw 5.5 Pohang earthquake and EGS project, J. Geophys. Res. Solid Earth in press, doi: 473

10.1029/2019JB018368. 474

475

Woo, J.-U., J. Rhie, S. Kim, T.-S. Kang, K.-H. Kim, and Y. Kim (2019b). The 2016 476

Gyeongju earthquake sequence revisited: aftershock interactions within a complex fault 477

system, Geophys. J. Int. 217(1) 58-74, doi: 10.1093/gji/ggz009. 478

479

20

Wu, Q., M. Chapman, and X. Chen (2018). Stress‐ drop variations of induced earthquakes in 480

Oklahoma, Bull. Seismol. Soc. Am. 108(3A) 1107-1123, doi: 10.1785/0120170335. 481

482

Yoo, S.-H. and K. Mayeda (2013). Validation of non‐self‐similar source scaling using ground 483

motions from the 2008 Wells, Nevada, earthquake sequence, Bull. Seismol. Soc. Am. 103(4) 484

2508-2519, doi: 10.1785/0120120327. 485

486

Yoo, S.-H., J. Rhie, H. Choi, and K. Mayeda (2010). Evidence for non‐ self‐ similarity and 487

transitional increment of scaled energy in the 2005 west off Fukuoka seismic sequence, J. 488

Geophys. Res. Solid Earth 115(B8) B08308, doi: 10.1029/2009JB007169. 489

490

Yoo, S.-H., J. Rhie, H. Choi, and K. Mayeda (2011). Coda-derived source parameters of 491

earthquakes and their scaling relationships in the Korean Peninsula, Bull. Seismol. Soc. Am. 492

101(5) 2388-2398, doi: 10.1785/0120100318. 493

494

495

Full mailing address of each author 496 497

498

Gyeongdon Chai1; cgd1605@gmail.com 499

Seung-Hoon Yoo2; syoo@ara.com 500

Junkee Rhie1* ; rhie@snu.ac.kr 501

Tae-Seob Kang3; tskang@pknu.ac.kr 502

503

504

505

506

507

508

509

510

511

21

Table 1. Consecutive 14 frequency bands used for making coda envelopes. 512

513

No. Frequency (Hz)

FREQ01 0.05 ~ 0.1

FREQ02 0.1 ~ 0.2

FREQ03 0.2 ~ 0.3

FREQ04 0.3 ~ 0.5

FREQ05 0.5 ~ 0.7

FREQ06 0.7 ~ 1.0

FREQ07 1.0 ~ 1.5

FREQ08 1.5 ~ 2.0

FREQ09 2.0 ~ 3.0

FREQ10 3.0 ~ 4.0

FREQ11 4.0 ~ 6.0

FREQ12 6.0 ~ 8.0

FREQ13 8.0 ~ 11.0

FREQ14 11.0 ~ 14.0

514

515

516

517

518

519

520

521

522

523

524

525

526

527

22

Table 2. Source parameters of the 2016 Gyeongju and 2017 Pohang earthquake sequences. 528

Seq. Event (No.) Lat Lon Dep Mw(1) Mw(2) fc(1) (Hz) fc(2) (Hz) Δσ(1) (MPa) Δσ(2) (MPa)

2016.256.104432 (GJ01) 35.77 129.20 14.96 5.14 5.13 0.71 ± (0.03) 0.73 ± (0.00) 4.73 ± (0.08) 4.75 ± (0.01)

2016.256.111050 (GJ02) 35.76 129.19 15.83

3.19

3.23 ± (0.01)

0.51 ± (0.03)

2016.256.113254 (GJ03) 35.75 129.19 14.46 5.57 5.58 0.57 ± (0.02) 0.52 ± (0.00) 10.55 ± (0.06) 8.27 ± (0.01)

2016.256.141827 (GJ04) 35.78 129.20 13.83 3.07 3.14 2.79 ± (0.03) 2.91 ± (0.01) 0.26 ± (0.08) 0.32 ± (0.02)

2016.256.145230 (GJ05) 35.76 129.19 13.52 3.21 3.26 3.73 ± (0.04) 2.55 ± (0.04) 0.98 ± (0.12) 0.32 ± (0.08)

2016.256.153710 (GJ06) 35.78 129.21 13.53

3.07

4.71 ± (0.01)

1.05 ± (0.03)

Gyeongju 2016.256.232447 (GJ07) 35.76 129.18 13.00 3.23 3.25 4.34 ± (0.03) 3.93 ± (0.01) 1.65 ± (0.09) 1.15 ± (0.03)

2016.257.053142 (GJ08) 35.76 129.19 13.96

3.03

3.81 ± (0.01)

0.47 ± (0.03)

2016.263.113358 (GJ09) 35.75 129.18 15.80 4.46 4.49 1.15 ± (0.03) 1.22 ± (0.01) 1.94 ± (0.09) 2.47 ± (0.02)

2016.265.025354 (GJ10) 35.76 129.19 13.79 3.43 3.42 4.84 ± (0.03) 4.45 ± (0.01) 4.38 ± (0.09) 2.95 ± (0.03)

2016.272.073430 (GJ11) 35.76 129.19 12.96

3.14

3.63 ± (0.02)

0.60 ± (0.03)

2016.276.115307 (GJ12) 35.75 129.20 15.42 2.98 2.94 6.41 ± (0.03) 5.41 ± (0.01) 2.14 ± (0.10) 1.01 ± (0.03)

2016.284.135910 (GJ13) 35.75 129.19 14.40 3.3 3.31 3.10 ± (0.03) 2.89 ± (0.01) 0.97 ± (0.10) 0.55 ± (0.03)

2017.105.023113 (PH01) 36.11 129.36 5.0 3.33 3.34 2.75 ± (0.05) 1.80 ± (0.03) 0.73 ± (0.16) 0.14 ± (0.05)

2017.319.052931 (PH02) 36.11 129.37 5.0 5.48 5.44 0.34 ± (0.03) 0.38 ± (0.01) 1.73 ± (0.08) 1.92 ± (0.01)

2017.319.060949 (PH03) 36.09 129.34 8.0(KMA) 3.45 3.10 ± (0.05) 0.89 ± (0.09)

Pohang 2017.319.074930 (PH04) 36.12 129.36 6.6 4.31 4.3 1.04 ± (0.02) 1.31 ± (0.01) 0.81 ± (0.07) 1.66 ± (0.01)

2017.323.144547 (PH05) 36.12 129.36 4.2 3.53 3.54 3.66 ± (0.04) 2.61 ± (0.02) 2.78 ± (0.13) 0.90 ± (0.04)

2017.323.210515 (PH06) 36.14 129.36 4.0 3.59 3.62 2.95 ± (0.03) 2.17 ± (0.02) 1.86 ± (0.08) 0.63 ± (0.03)

2018.041.200303 (PH07) 36.08 129.33 8.0 4.61 4.6 1.22 ± (0.04) 0.77 ± (0.01) 3.86 ± (0.11) 1.08 ± (0.01)

529

*hypoDD relocation data from Woo et al. (2019b) were used for Gyeongju, and Pohang 530

sequence location data were obtained from the KMA catalog; focal depths were computed by 531

ISOLA. (1) and (2) denote the results of coda spectral ratio and source calibration methods, 532

respectively. 533

534

535

536

23

List of Figure Captions 537

1) Map showing the seismic stations used in this study to create synthetic coda envelope 538

models and perform the coda-based spectral ratio and source calibration study. The white and 539

black triangles indicate the station networks operated by Korea Meteorological 540

Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 541

respectively. The area in the dashed square is shown in Figure 2. 542

2) Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 543

earthquake sequences occurred. The focal mechanisms determined by ISOLA software 544

(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 545

Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 546

aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 547

Pohang sequence has reverse and strike-slip faulting events. 548

3) Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, showing 549

the frequency-dependent decaying trends. The synthetic coda envelope models fit well with 550

the observed data envelopes (grey lines). 551

4) Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) main shock 552

and largest aftershock with the same EGF events in sequence. The focal mechanisms and 553

Pohang event depth information were determined using ISOLA, and the Gyeongju event 554

depth information was obtained from Woo et al. (2019b). Dashed lines (yellow) indicate the 555

use of posterior distribution to determine the corner frequency by full-Bayesian MCMC. The 556

black and white colors of triangles indicate the corner frequencies of the target and EGF 557

events. 558

5) To correct the site effect, we prepared the site-term with the GJ main shock (Mw 5.58), 559

foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). In 560

addition, we created the synthetic Brune model (the lines overlaying the squares) for the 561

events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 562

we determined the correction-term (grey dotted lines) for each event. The site-term (black 563

line) of this station was obtained by averaging all the correction-terms. The site-term of the 564

station was applied to obtain the site-corrected amplitudes for every recorded event. 565

6) Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) Pohang. 566

The symbols represent the mean values of the site-corrected amplitude data with one standard 567

deviation. Synthetic Brune curves (black lines) are the results of the source calibration. The 568

stars denote the corner frequencies on the Brune curve with posterior distributions (yellow 569

lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, MHS; Metropolis-570

Hastings Sampling method). The same colors as in Figure 2 are used here for the 571

corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using the 572

fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show the 573

NDCAs for stations after revision using the recalculated site correction terms. Blue lines are 574

the same as the black lines in (b). 575

7) Scaling relations of corner frequency and stress drop versus seismic moment for two 576

earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented by 577

grey dotted lines. Black vertical and horizontal lines with the symbols represent one standard 578

24

deviation. The source scaling trend of the Gyeongju sequence is consistent with the 579

previously reported trend (thick dotted lines) of coda-based source studies. Both source 580

scaling trends cannot be explained by a constant stress drop model. 581

25

582

Figure 1. Map showing the seismic stations used in this study to create synthetic coda 583

envelope models and perform the coda-based spectral ratio and source calibration study. The 584

white and black triangles indicate the station networks operated by Korea Meteorological 585

Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 586

respectively. The area in the dashed square is shown in Figure 2. 587

26

588 589

Figure 2. Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 590

earthquake sequences occurred. The focal mechanisms determined by ISOLA software 591

(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 592

Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 593

aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 594

Pohang sequence has reverse and strike-slip faulting events. 595

596

597

27

598

Figure 3. Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, 599

showing the frequency-dependent decaying trends. The synthetic coda envelope models fit 600

well with the observed data envelopes (grey lines). 601

602

603

604

605

28

606

Figure 4. Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) 607

main shock and largest aftershock with the same EGF events in sequence. The focal 608

mechanisms and Pohang event depth information were determined using ISOLA, and the 609

Gyeongju event depth information was obtained from Woo et al. (2019b). Dashed lines 610

(yellow) indicate the use of posterior distribution to determine corner frequency by full-611

Bayesian MCMC. The black and white colors of triangles indicate the corner frequencies of 612

the target and EGF events. 613

29

614

Figure 5. To correct the site effect, we prepared the site-term with the GJ main shock (Mw 615

5.58), foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). 616

In addition, we created the synthetic Brune model (the lines overlaying the squares) for the 617

events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 618

we determined the correction-term (grey dotted lines) for each event. The site-term (black 619

line) of this station was obtained by averaging all the correction-terms. The site-term of the 620

station was applied to obtain the site-corrected amplitudes for every recorded event. 621

30

622

623 624

625

626

31

Figure 6. Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) 627

Pohang. The symbols represent the mean values of the site-corrected amplitude data with one 628

standard deviation. Synthetic Brune curves (black lines) are the results of the source 629

calibration. The stars denote the corner frequencies on the Brune curve with posterior 630

distributions (yellow lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, 631

MHS; Metropolis-Hastings Sampling method). The same colors as in Figure 2 are used for 632

the corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using 633

the fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show 634

the NDCAs for stations after revision using the recalculated site correction terms. Blue lines 635

are the same as the black lines in (b). 636

32

637

Figure 7. Scaling relations of corner frequency and stress drop versus seismic moment for 638

two earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented 639

by grey dotted lines. Black vertical and horizontal lines with the symbols represent one 640

standard deviation. The source scaling trend of the Gyeongju sequence is consistent with the 641

previously reported trend (thick dotted lines) of coda-based source studies. Both source 642

scaling trends cannot be explained by a constant stress drop model. 643