Engineering Geology 200 (2016) 104–113

Contents lists available at ScienceDirect

Engineering Geology

j ourna l homepage: www.e lsev ie r .com/ locate /enggeo

A modified HVSR method to evaluate site effect in NorthernMississippi considering ocean wave climate

Zhen Guo, Adnan Aydin ⁎Department of Geology and Geological Engineering, The University of Mississippi, University, MS 38677, United States

⁎ Corresponding author.

http://dx.doi.org/10.1016/j.enggeo.2015.12.0120013-7952/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 July 2015Received in revised form 4 December 2015Accepted 10 December 2015Available online 11 December 2015

This paper presents the time history maps of horizontal-to-vertical spectral ratio (HVSR) of 12 long-termmicrotremor recordings (LTRs) in Northern Mississippi and the coastal area of Gulf of Mexico. These mapsshow that a stable predominant frequency (f0) value can be estimated across most of Northern Mississippiwhere the unconsolidated sediment thickness (UST) is larger than 300m. On the other hand, estimates of ampli-fication factor, taken as HVSR values at f0 (HVSR@f0), display a strong time-dependency, potentially caused byvariations of source location and energy level of microseism, i.e. ocean wave activities in Atlantic Ocean andGulf of Mexico. Validity of this observation is examined by calculating transfer functions between HVSR@f0 andocean data (ocean wave height, ocean wind speed and atmospheric pressure above ocean). Additionally, 3Dmicrotremor spectra of each LTR and those of all STRs within each 100 m-UST group are converted into spatialspectral vectors and projected on stereographic nets. Patterns of the clusters formed by these projections showthat theHVSR@f0 values are related to bothUST and vibration source location and energy level. Finally, amodifiedHVSR method based on stereographic projection is proposed to determine the average spectral vector of eachcluster, which enables a more accurate estimation of amplification factor.

© 2015 Elsevier B.V. All rights reserved.

Keywords:HVSR methodOcean wave climateSite effectNorth Mississippi

1. Introduction

The horizontal to vertical spectral ratio (HVSR)method presented byNakamura (1989) is widely used for estimating site effect parameters(predominant frequency f0 and amplification factor (HVSR value at f0or HVSR@f0)) based on microtremor recordings. However, the proce-dures to improve identification of f0 and its harmonics are relativelyrecently established (Bard and SESAME Team, 2005). Increasingnumber of studies utilizing these sets of guidelines shows that valuesof f0 and HVSR@f0 may significantly vary with time (as local wind,ocean wave climate and other ambient noise sources vary). For exam-ple, Haghshenas et al. (2008) reported that HVSR@fi (i = 0, 1, and2) values determined from earthquake recordings were higher andmore stable than those obtained from microtremor recordings. Moro(2014) stated with an illustration of wind-modified HVSR spectra thatthe HVSR values are affected to some degree by the nature and ampli-tude of dominant sources. Guo et al. (2014) attempted to find correla-tions between HVSR@f0 and local atmospheric pressure as well aslocal wind speed, and demonstrated that good correlations occuroccasionally only between HVSR@f0 and local atmospheric pressure.These observations show that modification of the HVSR@f0 values bychanges in environmental conditions or vibration source(s) is aninevitable process and needs to be considered when estimating

amplification factor in site effect evaluation. Therefore, this paperpresents a modified procedure to improve HVSR's estimate of site effectparameters (f0 and HVSR@f0) based on the observations by Guo et al.(2014) and Guo and Aydin (2015) (briefly summarized below) as wellas further correlation analyses between HVSR and ocean wave climate.This modified procedure improves the current understanding of thevariability and dependencies of the HVSR estimates (in any frequencyband), and helps determine the most representative or stable valuesfor different ocean climate scenarios. The analysis described in thispaper makes use of the datasets described in Guo et al. (2014) andGuo and Aydin (2015), with frequent references to their figures andtables. To avoid overcrowding the text, these figures and tables will bereferred to using the following format: Fig. #-year and Table #-year,e.g., Fig. 1 of Guo et al. (2014) abbreviated as Fig. 1-2014.

As mentioned above, the key observations reported in our recentpapers that guided this study are outlined in the following. Guo et al.(2014) demonstrated that f0 estimated by the HVSR method in North-ern Mississippi, where unconsolidated sediment thickness (UST) ismostly above 300 m, varies between 0.16 Hz and 0.5 Hz as a functionof UST. This frequency range coincides with that (0.085–0.5 Hz) ofDouble-Frequency (DF) microseisms (Peterson, 1993; Webb, 1998;McNamara and Buland, 2004) which are closely related to the oceanwave activities (Bromirski et al., 1999, 2005; Cessaro, 1994; Chevrotet al., 2007). As presented in Fig. 8(a)-2015 and 8(c)-2015, DF valuesin horizontal direction coincide very well with the HVSR estimates off0 within UST range N500 m. On the contrary, DF values in vertical

105Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

direction are almost constant across thewhole UST range. Furthermore,Fig. 3-2014 shows that the values of HVSR@f0 for all long-term record-ings (LTRs) are all function of time, which can also be seen in Fig. 3(this paper). At the same time, Guo and Aydin (2015) confirmed thatvariations of spectral amplitudes of DF microseisms are correlatedwith the ocean wave climate in Atlantic Ocean and Gulf of Mexico.

In order to reexamine the relationship between variation of HVSR@f0 and oceanwave climate, this study involves (a) establishing the trans-fer functions between HVSR@f0 and wave climate (significant oceanwave height, significant wind speed above ocean and atmosphericpressure above ocean) using regression analysis, (b) analyzing time-and frequency-dependent variations of vibration directions and HVSRvalues by visualizing microtremor spectra as resultant spatial spectralvectors projected onto a stereographic net, and (c) modification of theHVSR method based on the resulting projection patterns (revealingsource variations), which enables better estimates of amplification factor.

2. Study area

Fig. 1 presents the location and geological map of the study area.As shown in the regional scale map on the bottom, the study area is lo-cated in Mississippi Embayment, a broad and gently southwestwardplunging trough filled by weak to unconsolidated sediments underlainby Paleozoic bedrocks (Cushing et al., 1964). A description of generalstratigraphic sequence can be found in Table 1-2014. In Fig. 1, the USTcontours in Northern Mississippi are based on Bodin et al. (2001). Thethick dash-dot lines marked as A–A′ and B–B′ are two geologicalcross-sections across the embayment, which can be found in Bodinet al. (2001) and Seed et al. (2006) respectively. InNorthernMississippi,where all short-term recordings (STR) were made, the UST valuesgradually increase from 0 m at eastern boundary to as large as 1400 mat western boundary, near Mississippi River. Similarly, the UST valuesincrease parallel to the river along B–B′ from 1067m (3500 ft) inMem-phis, TN to 4267 m (14,000 ft) in the coastal area of Gulf of Mexico,where several LTRs were made. Such wide UST ranges provide uniqueopportunities to explore possible scenarios on HVSR and UST relation-ships. Besides, comparable distances from Northern Mississippi to Gulfof Mexico and to Atlantic Ocean (500–600 km and 700–800 km respec-tively) facilitate observations of combined influences of these twopotential sources on DF microseisms (Guo and Aydin, 2015), and offersa unique opportunity to evaluate influence of this competition on f0 andHVSR@f0 values. Thus, the geographical and geological settings ofthe area make it ideal for a systematic reexamination of the statedproblems.

3. Methodology

3.1.1. Data acquisition

This reexamination studywas conducted on12 LTRs and234 STRs, thelocations of which are shown in Fig. 1. For LTRs, the locations and USTvalues are summarized in Table 1, where details about data acquisitionconditions can be found in Table 1-2015. STRs are all located in NorthernMississippi and are divided into 100 m-UST groups according to the USTvalue at each recording station. All recordings were made by an LE-3D/20s seismometer with eigenfrequency of 0.05 Hz and a RefTek 130-01/3data logger with a sampling rate of 100 Hz.

3.1.2. Data processing

3.1.2.1. Color gradient map of HVSR in time–frequency domain for LTRsAs outlined in Guo et al. (2014), the HVSR spectra of 20-min time

series segments of LTRs are calculated for 100 narrow frequencybands of equally divided logarithmic intervals within 0.02–15.0 Hzrange by Geopsy, a free software suite developed for the analysis ofambient noise (www.geopsy.com). Then the calculated HVSR spectra

are plotted in time–frequency (t–f) domain to create the HVSR(t,f )maps. The HVSR value for each band is calculated from:

HVSR fð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNS fð Þ2 þ EW fð Þ2

2V fð Þ2

vuut ð1Þ

where NS(f), EW(f) and V(f) are amplitude spectra in N–S, E–W andvertical directions of each LTR segment or STR.

3.1.2.2. Transfer function between HVSR value and ocean dataTo investigate correlation between HVSR and ocean wave climate at

any given frequency, a transfer function is defined as:

Tr tð Þ ¼ HVSR@ f tð ÞX tð Þ ð2Þ

where HVSR@f(t) in this study is specified at f0 or f1 the first harmonicsof f0 (Guo et al., 2014), and X(t) is time-series ocean data (significantocean wave height, significant wind speed and atmospheric pressureabove ocean).

3.1.2.3. Stereographic projection of vibration vectorA single pick of microtremor time series in three directions (vertical,

N–S and E–W) defines a spatial vector M�!

, which can be projected as apoint onto a stereographic net as shown in Fig. 2a. The projectionrequires two angles,φe and δ, defined from the resultant horizontal vec-

tor H!

to the East and to the spatial vector M�!

, respectively. The angleφe,which is defined as estimated vibration angle in Guo and Aydin (2015),may be used to delineate general vibration directions in two or moreequal sectors of the first quadrant depending on the possible sourcesvibrationswithin a frequency band of interest. In this study, consideringE–W and N–S alignments of the Atlantic Ocean and the Gulf of Mexico,respectively, these sectors are selected as: 1) N–S (±45° from N or S) if45° ≤ φe b 90°; and 2) E–W (±45° from E or W) if 0° ≤ φe b 45°. Thereliability of estimating vibration directions with these sectors hasbeen discussed in Guo and Aydin (2015) and will be further discussedlater in this text. The angle δ reflects the HVSR values, e.g. for δ b 45°,HVSR N 1, and vice versa. In order to show frequency dependentvariations of vibration directions and HVSR values, average spectralamplitudes in three directions (V(f), NS(f) and EW(f)) of each LTR seg-ment and STR are used for stereographic projection. Therefore, the twoangles of each LTR segment and STR at each frequency can be estimatedby Eqs. (3) and (4) respectively:

φe fð Þ ¼ atanNS fð ÞEW fð Þ ð3Þ

δ fð Þ ¼ atan1

HVSR fð Þ� �

: ð4Þ

For each segment of LTR and complete STR in every 100 m-USTgroup, the spatial spectral vectors calculated for each frequency bandare projected as blue dots forming a cluster. The two angles (φeR andδR) representing averages of these clusters are calculated and projectedas a red dot. As the spectral amplitudes are all positive values, theprojected dots are all located in the first quadrant of a compass asexemplified in Fig. 2b. In this figure, the thick solid gray circles areHVSR and δ contours with dual scales, and the dashed circles representtheir mid-values. The dashed circle representing a greater value thanHVSR of 10 has a value of 20.

In order to calculate the angles φeR and δR of a spatial vector inCartesian coordinates (Goodman, 1989), firstly calculate the three

106 Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

107Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

transform factors l, m and n by Eq. (5) along each axis:

l ¼ cos δ cosφe m ¼ cos δ sinφe n ¼ sin δ: ð5Þ

Then find the resultant transform factors lR, mR and nR:

lR ¼X

liR�� �� mR ¼

Xmi

R�� �� nR ¼

Xni

R�� �� ð6Þ

where the summation is carried over Ns segments of a LTR, and theresultant vector magnitude jRj is:

R�� �� ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXli

� �2þ

Xmi

� �2þ

Xni

� �2r

: ð7Þ

Finally, the angles φeR and δR are given by:

δR ¼ asin nRð Þ 0 ≤ δR ≤ 90� ð8Þ

φeR ¼ acoslR

cos δR

� �: ð9Þ

The standard deviation of the vectors of a LTR or a STR group can befound from:

SD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNs− R

�� ��Ns

sð10Þ

where Ns is the total number of divided segments of a LTR or STRs in a100 m-UST group.

4. Results

4.1. HVSR color gradient map of LTRs

The HVSR(t,f) maps of T-1, T-2, OC-4, OC-6, NM 29 and LA 1 areshown in Fig. 3. From these maps, the predominant frequency (f0)peak of each recording is identified according to the criteria suggestedby Bard and SESAME Team (2005) and summarized in Guo et al. (2014).

4.1.1. T-1 and T-2The HVSR(t,f) maps of T-1 and T-2 show broad f0 peaks over a

frequency range of 1–4Hz, which is about an order ofmagnitude higherthan that of the DF peaks, as can be seen on the gradient maps of powerspectral density in time–frequency domain (PSD(t,f)) (Fig. 3a-2015).Within the DF range (0.1–0.6 Hz), the PSD energy levels in bothhorizontal and vertical directions correlate well with the ocean waveclimate, whereas the HVSR values are almost constant around 1 overthe whole recording periods. Within the local f0 range (1-4 Hz), timedependent variation of HVSR values is obvious, but showsno correlationwith ocean wave climate.

4.1.2. OC-4 and OC-6The PSD(t,f) maps of LTRs at OC-4 (Fig. 3b-2015) and OC-6 (Fig. 3c-

2015) reveal two distinct DF peaks (1st-DF shifting around 0.20 Hz and2nd-DF at 0.36 Hz, Table 2-2015), while the HVSR(t,f) maps (Fig. 3)show that both OC-4 and OC-6 have only one (sharp and narrow)predominant frequency peak at f0 = 0.29 Hz, which falls within theDF ranges. However, their HVSR@f0 values significantly vary with time(Fig. 3), between 6.4 and 11.7 at OC-4 and 4.6 and 12.2 at OC-6. At

Fig. 1. (Top)Geologymap (based onUSGS andDavid, 2011) of the study area and locations of lonthickness (UST) contours are based on Bodin et al. (2001). The geologic cross sections of A–A′1) study area indicated by the box (left); 2)wave climate (oceanwave height, oceanwind speedOcean and Gulf of Mexico (from National Data Buoy Center, NDBC at http://www.ndbc.noaa.go

OC-6, the DF peaks are occasionally broad (Fig. 3c-2015) but the HVSRpeak at f0 is always very sharp and narrow (Fig. 3).

4.1.3. NM 29 and LA 1The HVSR(t,f) maps of NM 29 and LA 1 share several similar

characteristics: 1) the f0 peaks are both at low frequency range, at NM29 f0 = 0.17 Hz and at LA 1 f0 = 0.13 Hz; 2) the f0 peaks are bothmore identifiable during 0:00–7:00; 3) the average HVSR@f0 values atNM 29 and LA 1 are 4.4 and 3.3 respectively, which are both lowerthan that at OC; and 4) a second peak (considered as f1) can also identi-fied at 0.52 Hz at NM 29 and at 0.24 Hz at LA 1.

4.2. Transfer function between HVSR and ocean data

A comparison of the HVSR(t,f) maps of OC-4, OC-6 and LA 1 (Fig. 3)to the wave climate histories (Fig. 3-2015) portrays the obviouscorrelation between HVSR@f0 and ocean wave climate. This meansthat estimation of amplification factor from HVSR values can be signifi-cantly improved by establishing transfer functions between thesesystem variables. For this reason, Fig. 4 is made to present the transferfunctions of HVSR values (at f0 at OC-4, OC-6 and LA 1, and at f1 at LA1) and wave climate data observed at eight ocean observation stations(National Data Buoy Center (NDBC); http://www.ndbc.noaa.gov/).Locations of these stations can be found in Fig. 1, where the AtlanticOcean and Gulf of Mexico stations are labeled using their originalnumbers, 41XXX and 42XXX respectively.

If HVSR@f is perfectly correlated with ocean data, the transferfunctions are expected to show no time variation. Otherwise, timevariations can be simulated by numericalmodels, fromwhich the trans-fer functions are derived. As shown in Fig. 4, the transfer functions are allwithin relatively narrow bands, which differ with respect to the types ofocean data, and recording locations of microtremor and ocean data. Forexample, at OC-4, values of the transfer functions of HVSR@f0 and1) ocean wave height (Fig. 4a-1) are within 2–10; 2) wind speed(Fig. 4a-2) are within 0.5–2; and 3) pressure (Fig. 4a-3) are within0.2–0.4. Similar observations can be made for recordings at OC-6(Fig. 4b) and LA 1 (Fig. 4c and d). The transfer functions show time var-iations to different degrees, some of which are very low, e.g. for HVSR@f0 of OC-4 vs. wind speed at station 41010 in Atlantic Ocean and forHVSR@f0 as well as HVSR@f1 of LA 1 vs. ocean wave height at station41008 in Atlantic Ocean. Meanwhile, the transfer functions betweenHVSR@f0 and wave height at ocean data station 42360 in Gulf ofMexico (Fig. 1-2015) are very similar for OC-4 and OC-6.

To compare the variations of transfer functions among the threemea-sured parameters of ocean wave climate (wave height, wind speed andpressure), coefficient of variation (CV) of transfer functions is calculatedfor each HVSR@fi (i = 0 or 1) versus each parameter of ocean wave cli-mate from all available observation stations, as shown in Fig. 4. Amongthe three parameters, pressure is the one for which the transfer functionsshow the least variation (i.e. the values of CVs are all lowest) with the lo-cation of ocean stations (Fig. 3a-3, b-3, c-3 and d-3). Since the oceanwindand wave originate from changes in atmospheric pressure and its spatialvariation, it is not surprising that the transfer functions between HVSR@f0and pressure form narrower bands and smaller variations. Consideringthat for a certain type of ocean data, e.g. wave height, the transfer func-tions are more concentrated during quiet periods as shown in Fig. 4-aand -b as well as the time zone in Fig. 3c-2015, regardless of ocean datalocation, differences between the transfer functions must be larger dueto noisy (high ocean activities) period as shown in Fig. 4 and other timezones at Fig. 3c-2015.

g-term recordings (LTRs) and short-term recordings (STRs). Theunconsolidated sedimentand B–B′ can be found in Bodin et al. (2001) and Seed et al. (2006). (Bottom) Location of, and pressure) observation stations (marked as “ocean data” in the legend) in the Atlanticv/). Color zoning represents changes in the relief over the continent and the sea-floor.

Table 1Summary of locations, unconsolidated sediment thickness (UST), predominant frequency(f0) and amplification factors calculated by modified HVSR method of long-term record-ings (LTRs).

LTRs Location UST (m)a f0φeR

(°)δR(°)

HVSR@f0R SD

T-1 Tishomingo statepark, MS

10.22.018 43.6 11.5 4.92 0.085

T-2 2.466 42.6 17.1 3.25 0.107NM 14 Corinth, MS 133.7 0.967 44.7 16.6 3.35 0.076

OC

−1

Oxford campus ofUniversity ofMississippi, MS

726.0

0.290 48.5 5.9 9.68 0.056−2 0.290 37.9 7.1 8.03 0.026−3 0.290 51.3 7.7 7.40 0.051−4 0.290 49.9 7.1 8.03 0.029−5 0.290 51.6 6.0 9.51 0.040−6 0.290 51.0 7.1 8.03 0.052

NM 29 Clarksdale, MS 1334.5 0.170 45.3 13.3 4.23 0.068SM 1 Collins, MS Unknown 0.130 44.5 8.4 6.77 0.096SM 2 Biloxi, MS 2000–3000b

LA 1 New Orleans, LA10,000b

1097c0.130 51.9 16.1 3.46 0.046

a UST values down to Paleozoic rocks at T-1, T-2, OC and NM 29 are read from thecontours based on Bodin et al. (2001) as shown in Fig. 1.

b UST values down to Mesozoic rocks at SM 2 and LA 1 are read from Hardin (1962).c Thickness of Quaternary age deposits at Houma, LA, around 70 km southwest of LA 1

(Seed et al., 2006).

108 Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

4.3. Stereographic projections

Stereographic projections of microtremor spectral vectors arecarried out at 100 discrete frequencies logarithmically evenly distribut-ed within 0.02–15 Hz range for all LTRs and all STRs in each 100m-USTinterval. Examples of these projections at several selected frequencies(covering low, medium and high frequency ranges) of LTRs and STRsare presented in Figs. 5 and 6 respectively.

4.3.1. LTRsAs shown in Fig. 5, for each recording, the clusters formed by the

projected points differ in shape and position in different frequencyranges:

• In the low frequency range (b0.1 Hz), both φe and δ angles formwideranges.

• Within the DF range (blue dashed box in Fig. 5), and especially at thepredominant frequency f0 (red box in Fig. 5), the clusters are moreconcentrated than the low frequency range, which suggest thepresence of a specific energy source. At OC (Fig. 5b and c), NM 29

Fig. 2. Stereographic projection of a spatial vector and definition of the relevant terms (a);

(Fig. 5d) and LA 1 (Fig. 5f), where UST N 300 m, the clusters showwider ranges in φe dimension than in δ dimension.

• Within the “holu” frequency range (around 0.6Hz), the clustersmost-ly vary in δ dimension, which suggests that the specified vibrationsources change in their energy level.

• Within the high frequency range (N1.0 Hz), a) for T-2 recorded onbedrock and only during day time, location and energy of vibrationsource vary with time, which produces a scattered cluster; b) for theothers recorded during night time or during a quiet period of daytime, the clusters are mostly very concentrated, probably varying inδ dimension; and c) the vertical amplitude is larger than the horizon-tal amplitude at most recordings since δ angles are mostly larger than45°.

4.3.2. STRsStereographic projections of spectral vectors for STRs at the same

frequency ranges as LTRs are presented in Fig. 6. The projections aregrouped by the locations of STRs in 100 m UST intervals. The followingobservations are made:

• Within the low frequency range (b0.1Hz), similar to LTRs, the clustersform wide ranges in both φe and δ dimensions.

• Within the DF ranges, patterns of the clusters vary with UST values. Inthe low UST range, the clusters are more scattered in δ dimension. AsUST increases, the clusters cover a wider range in φe dimension whilebecoming narrower in δ dimension.

• Within the high frequency range, except in the lowest UST ranges(Fig. 6a and b) where the f0 is located at the high frequency range,the clusters display random patterns.

5. Discussion

5.1. Vibration source, unconsolidated sediment thickness and HVSR values

FromFigs. 3 and 4, it can be stated that theHVSR values are related toboth unconsolidated sediment thickness and oceanwave climatewithin0.1–0.6Hz. Themodifications ofmicrotremor over the bedrock (T-1 andT-2) are almost identical in horizontal and vertical directions, makingHVSR a stable quantity regardless of variations in vibration sources.On the other hand, over the areas underlain by moderately thicksequence of unconsolidated sediments (as at OC), horizontal andvertical vibrations are modified most differently within a very narrow

and a cluster of projected vectors calculated along an LTR at a specified frequency (b).

Fig. 3. Color gradient maps of HVSR in time–frequency (t–f) space at T-1, T-2, OC-4, OC-6, LA 1 and NM 29.

109Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

frequency band around f0, where the time variation of dominantvibration source energy level presents itself as fluctuations of HVSR@f0. The thick sequence of unconsolidated sediments (at NM 29 and LA1)modify the horizontal and vertical vibrations in a complex way lead-ing to a relatively small f0 peak appearing at lower f0 values than otherareas such as OC. One possible explanation is that lack of a distinctboundary between unconsolidated sediment and “bedrock” results inthe impedance contrast lower than the threshold (shear wave velocitycontrast of 2.5) to produce a clear f0 peak (Konno and Ohmachi,1998). Because this is the first reported microtremor recording onsuch thick sediments, a more systematic research is needed to establishprevalence and causative mechanisms of the observed HVSR patternover thick sediment sequences. It is also worth noting that these smallpeaks are more identifiable during night time, when local noise isreduced dim. This enhances the visibility of the small f0 peaks (at NM29 and LA 1) that fall into a frequency band that is influenced by localwind and other noise sources as explained in Guo et al. (2014). Despitethis limitation over thick sequences, the presented analyses clearlyshow that at large distances from the source(s), changes in HVSR@f0can be directly related to variations in the energy of the vibration source,oceanwave activities in this case. It follows that the HVSR@f0 as a proxyof site amplification factor primarily varies with the source energy levelat large distances.

The stereographic projections of LTRs (Fig. 5) not only strengthensthe conclusion above, but also indicates that in low frequency, the

vibration source (estimated according to φe angle) and HVSR values(suggested by δ angle) vary significantly with time without an obviouscorrelation.

The stereographic projections of STRs (Fig. 6) also indicate relation-ships among vibration source, sediment thickness and HVSR values. Inlow frequency range (b0.1 Hz), the scattered clusters point to theuncertainty of the vibration source in this range. In the DF range, withincreasing UST, concentrating clusters in δ dimension suggest that themodification by sediments of HVSR values is dominant. In the highfrequency range, thick sediments (UST N 300m)have very limitedmod-ifying effects on the energy components. Furthermore, from thesestereographic projections for selected frequency bands, the f0 value foreach UST range can be identified easily by comparing the locations ofthese clusters. If these projections are produced on a denser array ofdiscrete frequencies, the estimation of f0 would be more accurate.

5.2. Reliability of estimated vibration angle (φe)

The estimated vibration angle φe calculated following the procedurein Guo and Aydin (2015) and Eq. (3) enablesmuch faster determinationof the vibration directions and thus creation of color gradient maps ofvibration direction as a function of both time and frequency (Figs. 5-2014 and 3-2015). However, its accuracy and reliability are questionedbecause of the complexity of the composition and propagation ofmicrotremor. Theoretically, this method would be perfectly valid if the

Fig 4.Transfer functions between HVSR@f0 at (a) OC-4, (b) OC-6, (c) LA 1, and HVSR@f1 of (d) LA 1 and ocean data. Coefficient of variation (CV) of transfer functions is indicated ineach figure.

110 Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

111Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

microtremor within a narrow frequency bandwas excited from a singlesource and propagated as a single wave type (e.g. Rayleigh waves) onhorizontal plane. In spite of the fact that the microtremor is a mixtureof all kinds of body and surface waves generated from various sources,the possibility of multiple sources can be limited by taking a verynarrow frequency band and a short recording period. The resulting esti-mate of the vibration direction can be considered to represent one dom-inant vibration source.

Fig. 7 demonstrates consistency of estimates of the main vibrationdirection of a 20-min recording within a narrow frequency band usingthe three methods: a) direct plot of the time series in NS vs. EW direc-tions forming a vibration cluster (Guo et al., 2014); b) particle motionplot of ratio of radial to transverse components vs. back-azimuth angle(Guo and Aydin, 2015); and c) stereographic projection of estimatedvibration angle (φe) by Eq. (3). If a relatively strong signal is dominantwithin a short recording period, the consistency between φe and φm isstronger, e.g. Fig. 5(b)-2015 (noisy time) and (a)-2015 (quiet time).Analyses of other 20-min recording segments at OC-6 show that themethods (b) and (c) provided consistent estimates for around 52% of129 segments during the quiet period, and for as high as 68% of 80segments during the noisy period.

Fig. 5. Stereographic projection of LTRs of (a) T-2, (b) OC-4, (c) OC-6, (d) NM 29, and (e) LA 1

5.3. A modified HVSR method

As an easy and fast method, the HVSR method proved to bereliable in estimating some of the site effects parameters, especiallypredominant frequency f0, by numerous researchers all over theworld. However, this method's estimate of amplification factor is stillbeing questioned and the cause of inconsistencies is not well known.This study reveals that the amplification factor's estimates are time-dependent which explain variable degree of success of the HVSRmethod with this site effect parameter.

As displayed by the transfer function between HVSR@f0 and waveclimate data, values of HVSR@f0 is related to the energy level of thevibration source (ocean activities) within the area where UST N 300 min Northern Mississippi. However, as shown in Figs. 5 and 6, shape ofthe clusters reflects both time and frequency dependent variation inboth vibration direction and the HVSR values, which is uniquely helpfulin understanding how the vibration source influence the HVSR values,especially HVSR@f0.

As depicted on the stereographic projections for LTRs (Fig. 5),even thoughmost clusters at f0 (indicated by red box) have very narrowranges in δ dimension, values of δ is still obviously time-dependent,

. The DF range is indicated by dashed blue box and f0 of each LTR is indicated by red box.

Fig. 6. Stereographic projections of STRs grouped by UST ranges: (a) 0–100 m, (b) 200–300 m, (c) 400–500 m, (d) 600–700 m, (e) 800–900 m, (f) 1000–1100 m, and (g) 1200–1300 m.

112 Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

reflecting fluctuations in energy level of the vibration sources.Therefore, in order to obtain amore accurate estimation of amplificationfactor, variations of HVSRs related to source energy level changes has to

be minimized. Inside each of these clusters, position of the averagespatial vector are calculated and plotted as a red dot, which presentsthe source location or direction as well as time-variation of the energy

Fig. 7. Vibration frequencymap (a), particle motion path (b), and projection of estimated vibration angle (at 0.222 Hz) (c) for a 20-min segment (2014:076:07:40–08:00) of LTR at OC-6.

113Z. Guo, A. Aydin / Engineering Geology 200 (2016) 104–113

level. Therefore, the HVSR value estimated by the position of this pointis a more reliable and accurate estimation of the amplification factor,given by:

HVSRR ¼ 1tan δR

ð11Þ

where δR is the angle between the resultant horizontal vector and theaverage spatial vector, calculated by Eq. (8). Applying this method, theamplification factors (HVSRR) for LTRswith identified f0 values are listedin Table 1, together with the two angles (φeR and δR) defining averagespatial spectral vectors and the standard deviations (SD) of thesevectors.

It should be noted, however, that the particle motion (Guo andAydin, 2015) is a more accurate though a considerably more time-consuming method for estimating the vibration direction, and wherepossible, one can replace φe with φm to obtain a more reliable calcula-tion of δR and HVSRR.

6. Conclusions

This study explored the potential causes of time-dependentvariations in estimated values of site effect parameters using HVSRmethod in Northern Mississippi and coastal area of Gulf of Mexico.The following conclusions can be drawn:

1) The analyses confirm that the HVSR method can provide stableestimates of the predominant frequency f0 across most of NorthernMississippi where UST is larger than 300 m.

2) The amplification factors taken to be HVSR@f0 show significant timevariation in this area, potentially caused by changes in energy levelsof microseism sources, i.e. ocean activities in Atlantic Ocean andGulf of Mexico. Time-trends of the transfer function betweenHVSR@f0 and ocean data (ocean wave height, ocean wind speedand atmospheric pressure above ocean) strengthen this conclusion.These observations also imply that it is highly plausible to monitorvariations in energy level of the vibration source(s) by continuousand real-time analysis of HVSR spectra.

3) The stereographic projections of microtremor spectral vectors areshown to effectively depict the time- and frequency-variation ofamplification factors of long-term microtremor recordings. Thisapproach enables determination of average spectral vectors andthus a more accurate estimation of amplification factor.

4) In order to reduce the uncertainties in estimating amplificationfactor, long-term recordings are recommended to capture possiblevariations of vibration source, particularly during noisy periods.

References

Bard, P.-Y., SESAME Team, 2005. Guidelines for the implementation of the H/V spectralratio technique on ambient vibrations—measurements, processing and interpreta-tions. SESAME European Research Project EVG1-GT-2000-00026, DeliverableNumber D23.12 (http://sesame.geopsy.org/index.htm (last accessed April 2015)).

Bodin, P., Smith, K., Horton, S., et al., 2001. Microtremor observation of deep sedimentresonance in metropolitan Memphis, Tennessee. Eng. Geol. 62, 159–168.

Bromirski, P.D., Duennebier, F.K., Stephen, R.A., 2005. Mid-ocean microseisms. Geochem.Geophys. Geosyst. 6, Q04009. http://dx.doi.org/10.1029/2004GC000768.

Bromirski, P.D., Flick, R.E., Graham, N., 1999. Ocean wave height determined from inlandseismometer data: implications for investigating wave climate changes in the NEPacific. J. Geophys. Res. 104 (20), 753–20,776.

Cessaro, R.K., 1994. Sources of primary and secondarymicroseisms. Bull. Seismol. Soc. Am.84, 142–148.

Chevrot, S., Sylvander, M., Benahmed, S., Ponsolles, C., Lefèvre, J.M., Paradis, D., 2007.Source locations of secondary microseisms in western Europe: evidence for bothcoastal and pelagic sources. J. Geophys. Res. 112 (B11301), 19.

Cushing, E.M., Boswell, E.H., Hosman, R.L., 1964. General Geology of the MississippiEmbayment, USGS Profess. Paper 448-B, Department of the Interior, United StatesGovernment Printing Office, Washington, D.C.

David, E.T., 2011. Geologic map of Mississippi, Mississippi Department of EnvironmentalQuality (MDEQ), http://deq.state.ms.us/MDEQ.nsf/page/Geology_surface, (lastaccessed Sep. 20, 2015).

Goodman, R.E., 1989. Introduction to Rock Mechanics. second ed. Wiley, New York, U.S.A.(562 pp.).

Guo, Z., Aydin, A., 2015. Double-frequency microseisms in ambient noise recorded inMississippi. Bull. Seismol. Soc. Am. 105 (3), 1691–1710.

Guo, Z., Aydin, A., Kuszmaul, J., 2014. Microtremor recordings in Northern Mississippi.Eng. Geol. 179, 146–157.

Haghshenas, E., Bard, P.-Y., Theodulidis, N., SESAME WP04 Team, 2008. Empiricalevaluation of microtremor H/V spectral ratio. Bull. Earthq. Eng. 6, 75–108. http://dx.doi.org/10.1007/s10518-007-9058-x.

Hardin Jr., G.C., 1962. Notes on Cenozoic sedimentation in the Gulf Coast geosyncline,USA, in Geology of the Gulf Coast and central Texas and guidebook of excursions.Geological Society America Annual Meeting and Houston Geological Society,pp. 1–15.

Konno, K., Ohmachi, T., 1998. Ground-motion characteristics estimated from spectral ratiobetween horizontal and vertical components of microtremor. Bull. Seismol. Soc. Am.88 (1), 228–241.

McNamara, D.E., Buland, R.P., 2004. Ambient noise levels in the continental United States.Bull. Seismol. Soc. Am. 94 (4), 1517–1527.

Moro, G.D., 2014. Surface Wave Analysis for Near Surface Applications. first ed. Elsevier,Oxford, U.K. (252 pp.).

Nakamura, Y., 1989. A method for dynamic characteristics estimation of subsurface usingmicrotremor on the ground surface. Q. Rep. Railw. Technol. Res. Inst. 30, 25–33.

Peterson, J., 1993. Observation and modeling of seismic background noise. U.S.Department of Interior Geological Survey, Open-file Report, 93–322, Albuquerque,New Mexico.

Seed, R.B., Bea, R.G., Abbelmalak, R.I., et al., 2006. Investigation of the Performance of theNew Orleans Flood Protection Systems, in Hurricane Katrina on August 29, 2005,Volume I: Main Text and Executive Summary, Final Report (690 pp.).

USGS, Geologic maps of US states, http://mrdata.usgs.gov/geology/state/ (last accessedSep. 20. 2015).

Webb, S.C., 1998. Broadband seismology and noise under the ocean. Rev. Geophys. 36,105–142.