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Supplementary Information

Supplementary Movie 1. Detected aftershocks within the first hour after the 2004

Mw6.0 Parkfield earthquake. (a) The cross-section view of the detected events along

the San Andreas Fault (SAF) color-coded by their occurrence times after the mainshock.

The star denotes the epicenter of the mainshock. The background shading denotes the

mainshock slip distribution from Murry and Langbein1. (b) 2-8 Hz band-pass-filtered

vertical seismogram recorded at station MMNB. The vertical red dashed lines and blue

lines mark the origin time of newly detected event and those listed in the NCSN catalog,

respectively. (c) Envelope function of the 2-8 Hz band-pass-filtered vertical seismogram

recorded at station MMNB in the first hour after the mainshock. The vertical red line

denotes the moving origin time, and the short blue line marks the origin time of event

listed in the NCSN catalog.

Supplementary Movie 2. All detected events after the 2004 Mw6.0 Parkfield

earthquake plotted as logarithmic time since the mainshock. (a) The cross-section

view of the detected events along the SAF color-coded by the logarithmic time after the

mainshock. The background shading denotes the slip distribution of the mainshock and

the first 60-day afterslip from Murry and Langbein1. (b) Envelope function of the 2-8 Hz

band-pass-filtered vertical seismogram recorded at station EADB after the mainshock.

Other symbols are the same as in Supplementary Movie 1.

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2

Supplementary Note 1: Comparisons Between the Detected and Catalog Events

Since some detected events are also listed in the Thurber et al.2 catalog, we compute

the inter-hypocentral distance between the template events and these detected events

listed in the catalog (Figure S1a). We find that 95% of the events are within the distance

of 2.7 km for CC values larger than 0.2, which roughly places an upper-limit of the

location uncertainty of the detected events relative to the templates. We also compare the

magnitude difference and the median amplitude ratios between the templates and those

detected events that are also listed in the Thurber et al.2 relocated catalog. The results are

roughly consistent with the relationship of tenfold increase in amplitude for one unit

increase in magnitude (Figure S1b). The amplitude-magnitude distribution shown in

Figure S1b also contains large scatter, most likely due to the frequency-band limitation of

the amplitude ratios, or unknown changes in instrument gains. We do not attempt to

apply any magnitude correction in this study.

As mentioned in the main text, a total of 543 events were listed in the Thurber et al.2

catalog from 09/28/2004 to 09/30/2004, and 933 events were listed in the NCSN catalog

in the same period. The difference between the Thurber et al.2 and the NCSN catalogs

mainly stems from the fact that the Thurber et al.2 catalog only contains events with high-

quality waveforms that correlate with other events, and hence is not as complete as the

NCSN catalog.

To further evaluate the quality of the detected events, we first identify those events

that are listed in the NCSN but not in the Thurber et al.2 catalog. Next, we match them

with our newly detected catalog by requiring their origin time difference to be less than 2





3

s, and the hypocentral separation distance to be less than 10 km. Figure S2 shows the

comparisons of the hypocentral depths and magnitudes of the 415 events that satisfy the

above matching criteria. The distributions generally follow the 1-1 relationship but also

contain some scatter. At least some of the scatter in the hypocentral depths reflects the

inherent difference between the standard NCSN and the Thurber et al.2 relocated

catalogs. In addition, we simply assign the location of the detected event as that of the

best template event in this study. In reality, they could be separated by certain distances,

which would result in scatter in the depths and magnitudes.

Figure S1. Comparisons of earthquake parameters between the template and

detected events. (a) Mean cross-correlation (CC) values versus hypocentral separations

between the template and detected events. The background shade shows the logarithmic

number of event pairs over a grid cell with the size 0.1 km x 0.01 CC value. The solid

triangles mark the corresponding CC values above which 95% of the data points are

within certain distances. (b) Difference in magnitude versus the median amplitude ratios

between the templates and those detected events that are also listed in the Thurber et al.2





4

relocated catalog. The red dashed line marks the relationship between tenfold increase in

amplitude and one unit increase in magnitude.

Figure S2. Comparisons of earthquake parameters between the 415 events.

Comparisons of hypocentral depths (a) and magnitudes (b) for 415 events that are listed

in the NCSN catalog and detected by the matched filter technique. The dashed line marks

the 1-1 relationship.

Supplementary Note 2: Statistical Properties of Detected Aftershocks

Next, we compare the statistical properties (i.e., frequency-magnitude relationship and

aftershock decay patterns) for aftershocks listed in the NCSN catalog and those detected

by the matched filter technique. To ensure that we compare events from the same region,

we select earthquakes along the strike of the SAF (139.2o) with a fault-normal distance

less than 2 km, and within −50 km (NW) to 20 km (SE) relative to the epicenter of the

2004 M6 earthquake (−120.3667o, 35.8155

o). The choice of the along-strike distance





5

takes into account potential aftershock migrations, which is described in details in the

main text and the following sections.

Figure S3a shows a comparison of the magnitudes versus logarithmic time since the

Parkfield mainshock for aftershocks listed in the NCSN catalog and those detected by the

matched filter technique. It is clear that our method have detected significant amount of

“missing” aftershocks, especially in the first few hundred seconds immediately after the

mainshock. In addition, many small-magnitude events in the range of –2 to 0 were

identified at latter times. We also compute the evolving magnitude of completeness Mc

with time using the goodness-of-fit test (GFT)3. Specifically, we select 100 aftershocks

each time, move forward by 20 events, and determine the Mc value as the magnitude at

which 90% of the data can be modeled by a power-law fit. We find that the Mc value

decrease systematically with time since the mainshock, indicating an increase of the

detection ability with time for our matched filter technique, similar those observed for

regular catalogs (e.g., ref. 4).

Figure S3b compares the frequency-magnitude relationships for events in both

catalogs. The cumulative magnitude-frequency distribution curves for both catalogs are

similar at larger magnitudes, and deviate from each other at smaller magnitudes. The Mc

values estimated from the GFT method are 1.1 and 0.9 for the NCSN and our detected

catalog, respectively. Figure S3c compares the aftershock decay rates for both catalogs.

To reduce the bias due to these missing aftershocks at smaller magnitudes, we only select

aftershocks with magnitude larger than 1.5, which is well above the Mc value for both

catalogs. We compute the seismicity rate by using moving overlapping windows (e.g.,

ref. 5). The initial window contains 2 data points. We then slide the window by 1 data





6

point and increase its window length by 1 data point. The maximum allowable length is

21 data points. The aftershock rates for both catalogs decay logarithmically with time

since the mainshock, with an Omori’s law decay slope p close to 0.8. For the detected

events, the aftershock rate in the first few hundred seconds shows clearly deviation from

the power-law decay with the slope of 0.8. This observation is similar to the seismicity

rate directly measured from high-pass-filtered seismograms in the same region6.

However, because the Mc value changes dramatically with time after the mainshock (e.g.,

refs 4, 7), it is quite possible that Mc value is larger than 1.5 immediately after the

mainshock. In addition, the HRSN short-period instruments were clipped during and in

the first 30 s after the Parkfield mainshock. Hence, some early aftershocks that occurred

during this period could be missing in our detected catalog. Finally, it is interesting to

note that the seismicity rate curve with m ≥ 1.5 for the detected events are still above that

of the NCSN catalog at 2-3 days after the mainshock, indicating that missing events from

a regular catalog could extend to a few days, larger than the first few hours as suggested

from previous studies (e.g., refs 4, 6-9).

To investigate this further, we count the numbers of events for both catalogs in three

magnitude bins, 0 ≤ m <1, 1 ≤ m < 2, and m ≥ 2, and compute the ratio between them in

each 0.2 logarithmic time bin. We then use the percentage of (1 – ratio) as a proxy for a

measure of missing aftershocks in the NCSN catalog (Figure S4). We find that more than

80% of intermediate-size events (1 ≤ m < 2), and 60% of the large events (m ≥ 2) is

missing in the NCSN catalog within the first hour after the mainshock. The detection

ability of the NCSN improves with time since the mainshock. By the second day, only

55% of the events in the magnitude range of 1 ≤ m < 2 are missing.





7

In comparison, the percentage of missing aftershocks for large events (i.e., m ≥ 2) is

nearly constant (50-70%) after the first few hundred seconds (Figure S4). A detailed

examination of waveforms of these newly detected aftershocks with m ≥ 2 at later times

reveals that some do correspond to newly detected events (e.g., Figure S5d). However, in

other cases, the magnitudes of the newly detected events were assigned erroneously. For

example, in Figure S5a, the template event 20041102102612 (CUSP ID 32416567) as

listed in the NCSN catalog has a local magnitude ML = 3.28. It was followed within 10 s

by another event (CUSP ID 30506546) with larger amplitude, but the coda duration

magnitude for this event listed in the NCSN catalog is only Md = 1.05. Because the

waveforms of the first event match best to those of the detected event 20040930152020,

the assigned magnitude is 2.48, which is based on the median amplitude ratio of 0.16. In

reality, the true magnitude of this newly detected event could be much smaller.

We note that Md is assigned to the majority of small events in the Thurber et al.2 and

the NCSN catalogs, while ML is assigned to some intermediate-size events (3 ≤ ML ≤ 5),

and the moment magnitude Mw is assigned to a few large events (Mw ≥ 4). Bakun10

found

that the USGS Md is consistent ML with in the magnitude range of 1.5 to 3.25, and Md is

slightly larger than ML for ML ≤ 1.5 and smaller than for ML ≥ 3.25. Because we do not

expect to see a large magnitude discrepancy (e.g., larger than 2) among different

magnitude scales, it is likely that small portions of magnitudes in the NCSN catalog are

not determined properly. Because some of the misdetermined magnitudes could be

transferred into the magnitudes estimated in our study, we suggest that the 60% missing

rate at later times for m ≥ 2 is probably an overestimate value, which likely reflects both

true missing events, and those with magnitude assigned erroneously.





8

Figure S3. Statistical properties of the detected aftershocks. (a) A comparison of

event magnitude versus time since the Parkfield mainshock for aftershocks detected by

the matched filter technique (red triangle) and those listed in the NCSN catalog (blue

circle) The green square shows the evolving Mc value computed using the goodness-of-

fit test3. (b) Cumulative (lines) and non-cumulative (triangles and circles) number of

aftershocks versus magnitude for events detected by the matched filter technique (red)





9

and those listed in the NCSN catalog (blue). The larger solid symbols mark the Mc values

for two different catalogs. (c) A comparison of the aftershock rate for the detected events

(red) and listed in the NCSN catalog (blue) with magnitude larger than 1.5. The green

dashed line corresponds to the seismicity rate before the mainshock (i.e., background

rate). The two horizontal lines correspond to the average background rate and the

maximum allowable detection rate of 0.5/s (1 event for every 2 s). The solid, dashed and

gray dashed lines show the reference rate with p = 1, 0.8, and 0.5, respectively.

Figure S4. Number of aftershocks since the mainshock. Number of events listed in the

detected catalog (a) and the NCSN catalog (b), and the ratio between them (c) plotted

with logarithmic time since the main shock in three magnitude bins.





10

Figure S5. Example waveforms recorded at the vertical component of station

MMNB. The waveforms for the template and detected events are shown in red and black,

respectively. The amplitudes of waveforms in each panel are plotted using the same scale

in counts. In panel (a), the template event 20041102102612 with ML = 3.28 was followed

by another event (CUSP ID 30506546) with larger amplitude but smaller magnitude Md =

1.05. In panel (b), the magnitude of the template event Md = 3.55 is probably much larger

than the true magnitude, given the amplitude of waveform and similarity with those

shown in (a). In (c), the estimated magnitude for the detected event is M = 2.6, while the

magnitude listed in the NCSN catalog is only Md = 1.07. Given the amplitude ratio

between the template and detected event, it is likely that the magnitude of the template

event Md = 1.98 is over estimated. Panel (d) represents a true detected event with

estimated M = 2.7.





11

Supplementary Note 3: Examples of Detections at Different Locations

Figure S6 shows the detections for 7 template events at various distances and depths

along the fault strike. The detection rates for the last two events around Gold Hill (GH)

near the mainshock epicenter are much larger than other events that are further away

around Middle Mountain (MM), suggesting different occurrence patterns of aftershocks

in distinct regions. In addition, events with shallow (Figure S6a) and deep (Figure

S6b,d,e) hypocentral depths generally have less detection as compared with those at

intermediate depths (Figures S6c,f,g). In particular, the template event 20031021090015

is the last event in the SAFOD LA targeting clusters before the 2004 Parkfield earthquake

(Robert Nadeau, per. comm., 2007). The first detected event occurred on 09/29/2004

00:26:55, about 7 hours after the mainshock. In comparison, the first repeating SAFOD

targeting event after the Parkfield mainshock as listed in the Thurber et al.2 relocated

catalog occurred at 9/30/2004 04:34:53, about 35 hours after the mainshock. A detailed

earthquake relocation based on waveform cross-correlation is needed to determine

whether these newly detected events belong to the SAFOD targeting events or not (e.g.,

ref 11), which is beyond the scope of this study. However, the similarities of waveforms

between these newly detected events and those listed in the SAFOD targeting events

indicate that they must occur very close to each other (Figure S7). In summary, within the

waveform detection ability, our result suggests that the SAFOD target regions did not

become active until 7 hours after the mainshock.





12

Figure S6. Examples of positive detections for 7 template events. The mean CC values

above the detection threshold of 9 times the MAD (red dashed line) are plotted with time





13

since the Parkfield mainshock. These 7 events occur at different along-strike distances

and hypocentral depths. The event ID, along-strike distance, depth, and number of

detections are marked on top of each panel.

Figure S7. 2-8 Hz band-pass-filtered vertical seismograms recorded at station

MMNB. The first event was used as the template. The red traces correspond to three

newly detected events. The black traces correspond to events listed in the Thurber et al.2

catalog and belong to the SAFOD LA repeating cluster (Robert Nadeau, per. comm.,

2007). The corresponding magnitude is also marked on the top right of each trace.





14

Supplementary Note 4: Detailed Investigations of Aftershock Migration

The aftershocks could potentially expand further north in the creeping section, and

south towards Cholame than shown in Figure 3. However, we cannot detect aftershocks

in those regions, which are outside the spatial distribution of our template events in the

Thurber et al.2 catalog (ranging from –49 to 19 km in the along-strike direction). To rule

out such possibility, we examine the along-strike distance versus logarithmical time

relative to the 2004 Parkfield mainshock for all events listed in the standard NCSN

catalog (Figure S8), which covers a broader region than the Thurber et al.2 catalog. The

general feature is similar, in that aftershocks expend along the SAF strike with

logarithmical time since the mainshock. The migration speed in the creeping section is

close to those shown in Figure 3, and the aftershock area merges with the background

seismicity at about –50 to –45 km near 107 s (~115 day) after the mainshock. However,

the migration pattern is clearer in Figure 3 because of the significant increase of events in

that region. In comparison, the migration speed as outlined by aftershocks listed in the

NCSN catalog SE of the mainshock epicenter is 2.8 km/decade, while the migration

pattern in the detected aftershocks is not clear (Figure 3). Such a difference could be

caused by missing aftershocks SE of the epicenter in the first few days after the

mainshock, as illustrated in Figure 3. Nevertheless, it is clear that few aftershocks occur

beyond 20 km SE of the Parkfield mainshock.





15

Figure S8. Migration of the aftershocks from the NCSN catalog. The occurrence

times relative to the 2004 Parkfield mainshock versus the along-strike distances for all

events listed in the NCSN catalog before (a) and after (b) the mainshock. The two black

lines mark the approximate slopes of migration of aftershocks along the fault strike. The

short bar marks the time scale of 1 hour, 1 day, 30 day, and 1000 day before or after the

mainshock.





16

Based on their depth distributions, we separate all aftershocks into the following

depth range: 0 – 3, 3 – 9, and 9 – 16 km, and compare their migration patterns (Figure

S9). The shallow event above 3 km depth mostly occurred north of MM in the creeping

section of the SAF. The apparent migration speed is ~6 km/decade. The majority of

aftershocks occurred at intermediate depths between 3 and 9 km. Aftershocks started

immediately along the mainshock rupture zone, and the apparent migration speed is ~3.4

km/decade. Most deep events larger than 9 km occurred beneath and SE of MM. The

apparent migration speed is between 2.8 and 3.7 km/decade. By the end of the detection

period (09/30/2004), the aftershocks at shallow and intermediate depth expanded to 38-40

km along the SAF strike NW of the epicenter. In comparison, the deep aftershocks only

expanded to the distance of 26-28 km.

Finally, we examine the temporal evolution of the hypocentral depths for the detected

aftershocks. Because the migration pattern might be different for events at different

along-strike locations, we divide the entire aftershocks into three segments according to

their seismicity distributions: creeping section northwest of MM, beneath MM, and

southeast of MM (Figure S10). Except for a few outliers, the shallow aftershocks (i.e.,

top 5 km) in the creeping section northwest of MM and beneath MM appear to migrate in

the up-dip direction. However, a lack of shallow seismicity southeast of MM prevents us

from investigating the up-dip migration pattern in that segment. Similarly, the down-dip

migration is best shown in segments beneath and southwest of MM. The fact that most

aftershocks deeper than 9 km northwest of MM occurred ~1 day since the mainshock is

consistent with a relatively slow along-strike migration of deep seismicity (Figure S9).





17

Figure S9. Along-strike Migration of aftershocks at different depths. The occurrence

times since the 2004 Parkfield mainshock versus the along-strike distances for events at

depth of 0 – 3 km (a), 3 – 9 km (b), and 9 – 16 km (c). Other symbols are the same as in

Figure 3b.





18

Figure S10. Migration of the early aftershocks with depth. The occurrence times since

the 2004 Parkfield mainshock versus their hypocentral depths for events at the following

along-strike distances: creeping section northwest of MM (−50 ∼ −22) km (a), beneath

MM (−22 ∼ −18) km (b), and southeast of MM (−18 ∼ 20) km (c). The blue circles and

the red triangles mark the events listed in the Thurber et al.2 catalog and detected by the

matched filter technique, respectively. The short bar marks the time scale of 1 hour, 1 day,

and 30 day after the mainshock.

Supplementary Note 5: Seismic Activity Immediately Before the Parkfield

Mainshock

Because our detection time to start on the midnight of 09/28/2004, we have detected

some seismic activity before the occurrence of the Parkfield mainshock. Out of the 19

detected events on 09/28/2004, only 4 events are listed in the Thurber et al.2 catalog

before the Parkfield mainshock. The seismicity spreads out in space and time (Figures

S11-S12), and do not show any clustering around the hypocenter of the Parkfield

mainshock. Hence, it is clear that within the detection ability, we found no foreshock





19

activity associated with the Parkfield mainshock. This is consistent with the lack of clear

preseismic strain signals during the weeks to seconds before the Parkfield mainshock12

.

Figure S11. Detected and catalog events before and after the Parkfield mainshock.

The occurrence times relative to the 2004 Parkfield mainshock versus the along-strike

distances for all events before (a) and after (b) the mainshock. The blue circles mark the

events listed in the Thurber et al.2 relocated catalog. The large green star marks the

location of the 2004 Parkfield mainshock, and the green dashed line denotes the

approximate fault length from the mainshock slip inversion1. The red small triangle mark

the event detected by the matched filter technique. The two black lines mark the





20

approximate slopes of migration of aftershocks along the fault strike. The short bar marks

the time scale of 1 hour, 1 day, and 30 day before or after the mainshock.

Figure S12. Detected and catalog events before and after the Parkfield mainshock.

The occurrence times relative to the 2004 Parkfield mainshock versus the hypocentral

depths for all events before (a) and after (b) the mainshock in linear time scale, and

before (c) and after (d) the mainshock in logarithmic time scale. The blue circles and the





21

red triangles mark the events listed in the Thurber et al.2 catalog and detected by the

matched filter technique. The two black lines mark the approximate slopes of migration

of aftershocks in up-dip and down-dip directions. The short bar marks the time scale of 1

hour, 1 day, and 30 day before or after the mainshock.

Supplementary Note 6: Apparent Migration Caused by Plotting the Time Axis as

Logarithmic

One potential cause of the apparent migration (Figures 3 and S8-S10) is an increase in

the number of samples by plotting the time axis in the logarithmic scale. Such bias does

exist if the seismicity rate is near constant. See for example Figure S11a and Figure S12c

for events before the mainshock. However, if the aftershocks follow the Omori’s law

decay with p = 1 immediately after the mainshock, we would expect equal number of

events in each logarithmic time bins and hence do not have such bias. In reality, the p

value for the Parkfield sequence is about 0.8-0.9 at later times, and we are still missing

events immediately after the mainshock (See Supplementary Note 2 and Figure S2). Both

would result an increase of the sample size with logarithmic time.

To further rule out such bias, we first generate plots similar to Figure 3 for

aftershocks with m ≥ 1.5 (Figure S13). This results in a significant reduction of the total

number of events, but with more uniform distribution of sample size with logarithmic

time. Next, we divide the whole catalog into 20 sub-catalogs with equal number of

aftershocks (Figure S14). In both cases, we find that similar migration patterns still exist.

We also generate synthetic catalogs by randomizing the origin times and the along-strike

distances (Figure S15). We find that randomizing the origin times could produce a pattern





22

that mimic the logarithmic-type migration. However, the numbers of aftershocks are not

enough to match with the observed ones in the first few hours after the mainshock due to

the time randomization.

Finally, we compare the linear, logarithmic, and √t migration patterns in both linear

and logarithmic time scales (Figure S16). The √t migration pattern is predicted for fluid

induced seismicity, where the distance r = √4πDt, and D is the hydraulic diffusivities13

.

As shown in Figure S16, it is relatively easy to distinguish linear expansion with the other

two types. The expansion with logarithmic time is characterized by very rapid expansion

at early time and virtually no expansion at later times. In comparison, the expansion with

the square root of time is somewhat between the linear and logarithmic expansion. It

expands less rapidly at early time, and more at latter times as compared with the

logarithmic time expansion. Figure S17 shows that with one free parameter D, it is

relatively difficult to fit both the start and end of the observed seismicity front with √t

function. In addition, the obtained D is much larger than the typical range of 1-10 m2s

-1 in

the crust14

. Hence, we suggest that the migration pattern is best characterized by

logarithmic, rather than √t or linear functions.





23

Figure S13. Migration of the Parkfield early aftershocks with m ≥ 1.5. (a) The cross-

section view of the all detected events with m ≥ 1.5 along the SAF color-coded by the

logarithmic time after the mainshock (green star). (b) The occurrence times of

aftershocks with m ≥ 1.5 since the 2004 Parkfield mainshock versus the along-strike

distances. Other symbols and notations are the same as in Figure 3.





24





25

Figure S14. Aftershock migration plotted with equal number of events. (top left) The

cross-section view of the all detected events along the SAF color-coded by the

logarithmic time after the mainshock. The green star denotes the hypocenter of the

mainshock. The background shading denotes the mainshock slip distribution from Murry

and Langbein1. (top right) The background seismicity before the Parkfield mainshock.

(panel 1-20) Parkfield early aftershocks plotted in equal number of events.

Figure S15. Aftershock migration before and after randomization. (a) The

logarithmic occurrence times of all aftershocks within 2 km of the SAF strike since the

2004 Parkfield mainshock versus the along-strike distances. (b) The randomized





26

occurrence times since the mainshock versus the along-strike distances. (c) The

occurrence times since the mainshock versus the randomized along-strike distances.

Figure S16. A comparison of different migration functions. A comparison of linear

(red), √t (green), and log10(t) (blue) functions in linear (a) and logarithmic scales. The

solid, dashed, and dotted lines correspond to slightly different parameters in each

function.





27

Figure S17. Aftershock migration plotted in linear time scale. The along-strike

distances versus the occurrence times of all aftershocks within 2 km of the SAF strike

since the 2004 Parkfield mainshock. The blue line marks the best-fitting logarithmic

function and the green lines marks three √t functions with different D values. The panel

(a) shows the entire 55 hours and panel (b) shows the first 5 hours after the mainshock.





28

Supplementary Note 7: Comparison with the Principle Component Analysis of

Savage and Langbein15

Many recent studies have focused on the comparison of the postseismic deformation

and cumulative number of aftershocks following several large earthquakes16-21

, including

the 2004 Parkfield earthquake15, 20-22

. In most cases, the postseismic deformation and the

cumulative number of aftershocks are linearly related. This led Perfettini and Avouac16

to

propose that both postseismic deformation and aftershocks are driven by reloading of the

seismogenic zone resulting from frictional afterslip.


performed a principal component analysis of the 12 continuous

GPS stations located close to the epicenter of the 2004 Parkfield earthquake, and found

that the first mode F1(t) alone provides an adequate description of the postseismic

deformation at all sites. In addition, they showed that after the first few days, the

temporal function F1(t) appears to be linearly related to the cumulative number of

aftershocks ΔN(t) with m > 1.5. However, the data within the first few days appears to

follow another linear relationship with different slope. Savage and Langbein15

suggested

that missing aftershocks immediately after the mainshock6 could not explain such change

in slope because the early aftershocks are already too many to match the linear

relationship established at later times.

To verify this, we compare the cumulative number of aftershocks with m > 1.5 obtained

from this study with the temporal function F1(t) used in Savage and Langbein15

. We use

the along-strike distance range of (−28.18 ~ 3.30) km, and distance range perpendicular

to the SAF strike of (−4.14 ~ 3.75) km to select aftershocks. Those numbers are chosen to

be close to the quadrilateral used in the study of Savage and Langbein15

. Aftershocks





29

occurred later than 2.35 day after the mainshock (the end of our catalog) are taken from

the NCSN catalog in the same space window. We also removed the background rate of

0.0925 per day following the work of Savage and Langbein15

. As shown in Figure S18,

we find a break in the slope at ΔN(t) = 300 (t = 3.16 day). The break point and the slope

shown in Figure S18c are slightly different as compared with those in Figure 8c of


, most likely due to the minor difference in space window used in

selecting aftershocks. Because the temporal function appears to be smooth (Figure S18b),

we suggest that the break in slope mainly comes from the cumulative aftershocks. Figure

S18d shows that the difference in the slope is even larger if we use the newly detected

catalog, consistent with the previous inference that the observed feature is not caused by

missing early aftershocks, but by too many early aftershocks15

.

It is still unclear what is main cause of such break in slope. An increase of the slope

between the cumulative number of aftershocks and postseismic deformation suggests that

the partition between seismic and aseismic slip, i.e., the seismic coupling coefficient χ, is

larger immediately after the mainshock than at later times. One possible mechanism is the

transient embrittlement and/or strengthening of patches at high strain rates that are

otherwise creeping or partially creeping at low strain rates23-25

. A time-dependent

variation in the strain rate could also result in temporary deepening of the brittle-ductile

transition zone after the mainshock26-27

, and diminishing seismic moment of repeating

aftershocks25

. An alternative explanation is that other mechanisms, such as dynamic

stresses from the seismic waves generated by the mainshock (e.g., ref. 28, and reference

therein), contributed to trigger aftershocks immediately after the mainshock, but not at

later times. The third possibility is missing m > 1.5 aftershocks in the NCSN a few days





30

after the mainshock (See also Supplementary Note 2 and Figures S3-S5). Although this is

in contradiction with the general view of increasing detection ability after the

mainshock4, we cannot completely rule it out at this stage. Applying the same matched

filter technique to the continuous data at later times after the mainshock could help to

resolve this issue.





31





32

Figure S18. Cumulative number of aftershocks and post-seismic deformation. (a)

The cumulative number of aftershocks with m > 1.5 from the NCSN catalog (red) and the

combined catalog (green) versus the logarithmic time since the mainshock. The blue line

marks the end time of the newly detected catalog. The magenta and cyan lines mark the

break point inferred from the NCSN catalog (panel c) and the combined catalog (panel

d), respectively. (b) The composite principle components of the first mode F1(t) versus

the logarithmic time since the mainshock. The green circle, blue plus, and black square

mark the 1-min, 30-min and daily data, respectively. (c) The first mode F1(t) versus the

cumulative number of aftershocks from the NCSN catalog. The solid and dash blue lines

are the best linear fit to the data for ΔN(t) > 300 and < 300, respectively. The cyan line

marks the break point of ΔN(t) = 300 (t = 3.16 day). (d) The first mode F1(t) versus the

cumulative number of aftershocks from the combined catalog. The solid and dash blue

lines are the best linear fit to the data for ΔN(t) > 600 and < 600, respectively. The

magenta line marks the break point of ΔN(t) = 600 (t = 2.35 day).

Supplementary Note 8: Comparison with the Numerical Simulations of Kato29

Kato29

performed 3D numerical simulations to study aftershock expansions triggered

by propagating postseismic sliding (i.e., afterslip) with varying frictional parameters a

and b of the laboratory-derived rate-state dependent friction law30

. He found that the

radius of the aftershock area expands logarithmically with time since the mainshock, and

the rate of aftershock expansion is inversely proportional to the value of A−B

(=(a−b)σeff), where σeff is the effective normal stress. The latter effect can be explained by





33

an increase of steady-state frictional stress (and hence resistance to postseismic sliding)

with increasing A−B value29

.

Here we compare the migration speed obtained in this study with the simulation results

of Kato29

. We first define the mainshock rupture area to be 28 km NW and 4 km SE of

the mainshock epicenter, based on the mainshock slip inversions (e.g., refs 1,31) and the

extent of the aftershock area in the first 100-200 s after the mainshock (Figure 3). Next,

we use a mainshock rupture radius Rs of 16 km and effective mainshock epicenter at 12

km NW of the true epicenter to convert the convert the along-strike distance into ratio

relative to the mainshock rupture radius (R/Rs). Figure S19 shows that the observed

migration speed is roughly consistent with the simulated migration speeds for A−B value

of 0.2–0.5 MPa. The simulation with A−B value of 0.1 MPa does not match the

observations well because all aftershocks occurred within the first month. In comparison,

there is a lack of early aftershocks in the first 500 s and very few events in the first day

for A−B value of 0.8 MPa, inconsistent with the general pattern shown in Figure S19a. As

noted in the main text, the corresponding value of a–b is in the range of 0.004–0.01,

assuming an effective normal stress of 50 MPa32

. Our value is close to the value of 0.007

obtained by geodetic inversion of Barbot et al.33

, and is an order of magnitude higher than

the value of 0.0001–0.002 obtained by Johnson et al.32

. By analyzing afterslip of the 2003

Mw8.0 Tokachi-Oki earthquake, Miyazaki et al.34

and Fukuda et al.35

obtained the A-B

value of 0.6 MPa and 0.214-0.220 MPa, respectively, close to the values inferred in this

study.

We note that the simulation done in Kato29

is not designed specifically for the Parkfield

region. While the rupture radius of the simulated mainshock is 15 km, which is close to





34

the true rupture length of ~32 km for the Parkfield mainshock, the average co-seismic

slip and the resulting seismic moment is 1-2 order larger than those for the Parkfield

mainshock. In addition, the simulated aftershock has a rupture radius of 3 km,

corresponding to a moment magnitude Mw = 5.5 (with the assumption 3 MPa stress drop

and the circular crack model of Eshelby36). In comparison, the largest aftershock of the

Parkfield mainshock has Mw = 5.0, and the majority of aftershocks has much smaller

magnitude. Finally, the simulated aftershocks only occur once within the 3-yr recurrence

interval, and they occur right at the time of the inferred seismicity propagation front. In

comparison, only a few aftershocks occur near the migration front, and the majority of

aftershocks occur behind the migration front. Hence, the above comparison needs to be

viewed with caution. A future simulation with parameters similar to the real Parkfield

environment would help to convert the obtained migration speeds into frictional

parameters along the SAF.

Figure S19. Comparison of aftershock migration with numerical simulations. (a) The

occurrence times of aftershocks from the NCSN (blue) and detected catalogs versus the





35

R/Rs since the Parkfield mainshock. The black dashed line marks the approximate

migration of the seismicity front, and the green dashed line mark the approximate

mainshock radius. (b) The occurrence times of simulated aftershocks versus the R/Rs for

Case 1-5 with varying A−B values shown in Figure 8 of Kato29

.

Supplementary Note 9: Limitations and Future Development of the Technique

While the matched filter technique developed in this study is effective in detecting

many missing aftershocks immediately after the mainshock, it has several limitations:

First, it requires the usage of waveforms of existing events as template. Hence, it can

only detect events around the region that have template events. Brown et al.37

have

developed a technique to search for low-frequency earthquakes within non-volcanic

tremor by performing running autocorrelation of the continuous waveforms. Such

technique could also be applied to detect and locate events without the requirement of

pre-existing templates.

Secondly, we choose the 20 samples/s data, rather than the 250 samples/s data

recorded by the HRSN in this study. This is mainly limited by the heavy computation

associated with the sliding-window cross-correlations. Because of this, we only applied a

2-8 Hz filter to the data. So the mainshock coda is longer and could mask some early

aftershocks in the first 100-200 s. In addition, many HRSN recordings clipped in the first

50 s. Hence, our catalog is likely missing some early aftershocks immediately after the

mainshock. As mentioned by Peng et al.6, the 2004 Parkfield earthquake and its

immediate aftershocks were recorded by many nearby instruments on scale. These

include the SAFOD pilot hole38

, the USGS GEOS Parkfield array39

, the CGS Parkfield





36

strong motion arrays40

, and the USGS Parkfield Dense Seismograph Array (UPSAR)41

.

Although most of these instruments are set in triggered mode, the rigorous aftershock

sequences result in continuous recordings in the first few hundred seconds or so. Figure

S20 shows an example of on-scale recording of the Parkfield mainshock and its

aftershocks within the first 1000 s by one of the SAFOD Pilot Hole instruments PH001 at

1096 m depth below surface. The numerous spikes in the spectrogram correspond to the

early aftershock signals, with only 16 of them listed in the NCSN catalog. As noted

before, our early aftershock catalog is still not complete in the first few hundred seconds.

We envision that the same matched filter technique could be applied to those on-scale

continuous recordings and higher frequency bands

to detect the missing events

immediately after the Parkfield mainshock.

Finally, depending on the mean CC value, the identified event could have a small but

distinguishable separation from the template event. In this study, we simply assign the

location of the template with the highest CC value to the detected event. A further

development of our matched filter technique is to integrate the information of waveform

similarity and relative arrival times between the template and detected events to relocate

these events using the double-difference algorithm (e.g., refs 42, 43). These studies will

be performed in a follow-up work.





37

Figure S20. Parkfield early aftershocks recorded by the SAFOD Pilot Hole station.

(a) The raw vertical-component seismogram recorded at the SAFOD Pilot Hole station

PH001 within the first 1000 s after the 2004 Mw6.0 Parkfield earthquake. (b) The

corresponding spectrogram of (a) showing the mainshock and numerous early

aftershocks. The think horizontal line at 40 Hz marks the corner of the high-pass filter,

and the thin bands around 60 and 184 Hz mark the continuous electronic noise. (c) The

envelope functions of the median-averaged spectrogram above 40 Hz. The vertical blue

and red lines mark the origin times of 16 and 130 aftershocks listed in the NCSN catalog

and detected by our technique, respectively.





38

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SUPPLEMENTARY INFORMATION - media. · PDF fileThe dashed line marks the 1-1 relationship. Supplementary Note 2: ... the percentage of missing ... the true magnitude of this newly detected