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Soil Dynamics and Earthquake Engineering

journal homepage: www.elsevier.com/locate/soildyn

Site amplification within the Mississippi embayment of the central UnitedStates: Investigation of possible differences among various phases of seismicwaves and presence of basin waves

Farhad Sedaghatia, Shahram Pezeshkb,⁎, Nima Nazemib

a AON Benfield, Analytics, Impact Forecasting, 200 E Randolph, 10th floor, Chicago, IL 60601, United StatesbDepartment of Civil Engineering, The University of Memphis, 3815 Central Avenue, Memphis, TN 38152, United States

A R T I C L E I N F O

Keywords:Mississippi embaymentUnconsolidated sedimentary basinNew Madrid seismic zoneSite amplificationBasin-induced surface waves

A B S T R A C T

The impact of unconsolidated sedimentary basins on ground motion amplification is of particular interest forearthquake engineers and seismologists. The Mississippi embayment (ME) of the New Madrid seismic zone,located in the central United States, is covered with a thick layer of unconsolidated soil deposits. Thus, theestimation of site response in this region is vital to simulate site-specific ground motions and to conduct site-specific probabilistic seismic hazard analysis. We evaluated site amplification at 11 stations within the ME,employing the horizontal-to-vertical spectral ratio (HVSR) technique.

Regarding the results obtained from this study, weak ground motions recorded by stations on the un-consolidated ME sediments are amplified 3–7 times for frequencies less than 5 Hz compared to stations locatedon bedrock. The fundamental resonant frequencies vary from 0.2 to 0.4 Hz within the ME. We investigateddifferences between the HVSRs obtained from P-waves, S-waves, coda, and pre-event noise. All fundamentalfrequencies obtained from different seismic phases are in good agreement with a less than 10% difference. Thefundamental frequencies of the P-wave and S-wave are relatively higher due to higher velocity of the P-wave andS-wave compared to other phases since the velocity of seismic waves and fundamental frequencies are pro-portional. There is a good correlation between the HVSR of the S-wave, coda, and pre-event noise portions forfrequencies more than 4 Hz. For the frequencies less than 4 Hz, the HVSR of the S-wave is higher than the HVSRof coda by a factor of 3. Reflections of S-waves from the edges of the unconsolidated sedimentary basin of the MEproduce surface waves. The presence of basin-induced surface waves in the coda portion for frequencies less than3 Hz results in increased amplitude of coda, and as a result, slower decay rate with time implying higher Qvalues. These basin-induced surface waves have a period of 0.5–4.0 s.

1. Introduction

Local site conditions associated with the low-velocity layers near thesurface have significant impacts on ground motions by changing theamplitude, frequency content, and duration of seismic waves.Furthermore, evaluation of the site response is one of the main factorsto simulate site-specific ground motions and to perform local or site-specific seismic hazard analysis [1,30,33,55]. Several ground motionprediction equations such as those developed for eastern North America(e.g., [5,48,61]) predict the median ground motion intensity measures(GMIMs) for generic rock sites. Then, employing appropriate site-spe-cific amplification factors for the site under study, the GMIM of interestis transferred to the surface from the underneath older, harder, andmore competent soil or bedrock. It is assumed that the bedrock would

not amplify ground motions. According to the National EarthquakeHazards Reduction Program (NEHRP), the bedrock is defined as theuppermost layer with an average shear wave velocity (VS) of more than760m/s.

To perform site response analyses at different frequencies, we needto have a good understanding of surface geology and dynamic char-acteristics of the surface layers over the bedrock. The dynamic char-acteristics of the soil layers are typically correlated with VS (corre-sponding to the stiffness), density, and damping ratio of the soil layers,which are characterized by the thickness of different soil layers, degreeof compaction, shear modulus, and the age of soil deposits [57].

The site response in sedimentary basins indicates the effect of soilcolumns and sediments with a low VS as well as the influence of thebasin and underlying bedrock topography [40,70]. Evaluation of site

https://doi.org/10.1016/j.soildyn.2018.04.017Received 6 July 2017; Received in revised form 6 December 2017; Accepted 16 April 2018

⁎ Corresponding author.E-mail addresses: farhad.sedaghati@aonbenfield.com (F. Sedaghati), spezeshk@memphis.edu (S. Pezeshk), nnazemi@memphis.edu (N. Nazemi).

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response in regions with deep unconsolidated soil layers or sedimentarybasins is of particular interest since ground motions can be significantlyamplified due to strong impedance contrasts between the surface layersand the bedrock or basement rock at certain frequencies and can causeintense structural damage [7]. Basement rock is defined as a site withno amplification.

There are various approaches to determine site amplification and/orde-amplification factors. The site amplification/de-amplification termin the frequency domain can be numerically estimated using the theo-retical methods accounting for the dynamic behavior of soil layers orthe shear-wave velocity gradient. These techniques require accurateinformation about the mechanical and geological features of soil layers.Furthermore, the site transfer function can be experimentally estimatedusing borehole data, microtremors (background ambient noises), orearthquake recordings. Although analyzing borehole data is one of themost accurate techniques to evaluate the site response, it is not eco-nomically justifiable to employ this technique on every site, especiallyfor deep sites. The soil transfer function can be obtained employing thegeneralized inversion technique, which aids at estimating the source,path, and site responses simultaneously [4,11]. The soil transfer func-tion at a desired site can also be acquired using the spectral ratio of aparticular earthquake at that site to a nearby reference rock site char-acterized as a site free of amplification [15], known as the soil/rockspectral ratio (SRSR) technique. It is worth mentioning that the desiredsite and the reference rock site should be close enough to share similarpath characteristics including the geometrical spreading and attenua-tion. The main difficulty of this method is to find an appropriate surfaceoutcropping rock site as the reference site that has characteristics of thebedrock below the soil layers at the desired site [59]. As an empiricalalternative method, the spectral ratio of the horizontal to the verticalcomponent of a specific event recorded at the desired site can provide areasonable approximation of the site response, since the near-surfacesite effects on the vertical component is negligible compared to thehorizontal component [5,19,37,45,55,60,63].

The horizontal-to-vertical component spectral ratio (HVSR) tech-nique was first introduced by Nakamura [45] to analyze the char-acteristics of microtremors which mostly consist of Rayleigh waves.Microtremors are ambient noise composed of high-frequency man-made noise such as those produced by traffic and low-frequency naturalnoise, for instance, vibrations generated by wind [16]. Then, Lermo andChávez-García [37] generalized this technique for shear waves tocompute the site response deploying earthquake ground motions. TheHVSR depicts a suite of peaks corresponding to the shear-wave re-sonance in a layered velocity structure [36]. Lermo and Chávez-García[37] observed that the site responses obtained from the HVSR tech-nique are in good agreement with the site responses acquired from theSRSR technique. Therefore, they used the peak of the spectrum ratio ofthe horizontal to the vertical component as an estimation of the firstresonant frequency of the site and its amplitude.

By comparing HVSRs with theoretical approximations or numericalsimulations, many investigators concluded that the HVSR technique canbe used as a first estimate of the site response even at sedimentarybasins and extreme local site conditions (e.g.,[6,9,10,16,21,23,28,39,44,56]). Note that since the HVSR technique isa first approximation, the accuracy of the higher-mode resonant fre-quencies and their amplifications has been a challenge. Therefore, thistechnique is often employed to estimate the first resonant frequency. Inaddition, comparing the HVSR and the site amplification factor de-termined from the linear 1-D approximation, several authors concludedthat although the location of the peaks representing the resonant fre-quencies are in fairly good agreement, the peaks’ amplitudes are dif-ferent (e.g., [13,25,32]). Furthermore, a few investigators observedfailure of the HVSR technique to estimate the site amplification (e.g.,[70]).

In this study, we evaluate the site amplification factor to investigatethe effects of unconsolidated sediment with a depth of approximately

1 km within the ME. In this regard, we use the HVSR instead of usingthe SRSR technique due to the following reasons. First, the basin shapecan change the characteristic of ray paths by focusing and defocusing ata site located inside the ME compared to a rock site outside of the basin.Second, the distance between desired stations located in the ME and thenearest reference rock site is relatively long, and thus the assumption ofhaving similar path characteristics for the reference rock site and thedesired station may be compromised. Furthermore, the HVSR is an ef-ficient and useful procedure for estimating the fundamental period andsite amplification factors of soft soils with a large impedance contrastcompared to the underlying bedrock such as is in the ME [8,12,58]. Itshould be mentioned that the total site response is the combined effectsof the site amplification and near-site attenuation, κ0 [3,14]. However,the purpose of this study is to determine the site amplification not thenear-site attenuation.

2. Geology and tectonics of the Mississippi embayment

The ME is an unconsolidated sedimentary basin overlying the NewMadrid seismic zone (NMSZ) that is seismically considered as the mostactive region in the central and eastern United States. The ME is asyncline oriented southward, spreading out from its apex in southernIllinois toward the lower coastal plain of the Gulf of Mexico. Riftingprocesses have resulted in the synclinal structure [18]. Following that, arelatively large depth of sediments was amassed by erosion of upliftedareas. However, different layers of sediments with different materials(e.g., marine and non-marine sand, silt, clay, etc.) may have been de-posited due to different geological processes. From north to south, thedepth of the sediments reaches up to 2 km and is about 1 km nearMemphis, Tennessee [65,67]. As another result of the rifting processes,reduced thickness of the crust created a zone of weakness that is ac-companied by an increased temperature of the crust [62]. This chain ofevents has been associated with seismic activity in the area, such as1811–1812 earthquakes ([24]; Brail et al., 1986).

Regarding the geologic-age of near-surface deposits, the ME is di-vided into two major geological features, uplands and lowlands (seeFig. 1), bounded by the Ozark uplift from the west and the NashvilleDome from the east. The boundaries of these zones are demarcated bysignificant differences in site responses, which is correlated with thevariations in VS. Large impedance contrast between the Paleozoicbedrocks and the unconsolidated soil deposits result in large P to Sconversions [42].

3. Database and data processing

We first collected 2894 three-component broadband seismogramsfrom 274 earthquakes with magnitudes more than 2.5 and hypocentraldistances up to 500 km within the NMSZ as the initial database. Theseevents occurred during the period of 2013–2017. Waveforms were re-corded by the Cooperative New Madrid Seismic Network (CNMSN) andcan be found on the Incorporated Research Institutions for Seismology(IRIS) website. The seismograms were downloaded starting from 85 sbefore the P-wave arrival until 400 s after the S-wave onset. All re-cordings were captured at 11 stations equipped with broadband GüralpCMG-40T triaxial broadband seismometers. The data are sampled at100 samples/sec. All seismometers have a flat velocity transfer functionin the frequency range of 0.033–50 Hz. We disregarded any recordswith hypocentral distances less than 16 km to ensure having enough P-wave window length for analysis. All collected data are visually in-spected to discard data with any amplitude anomalies or glitchescaused by the instrument. It is worth mentioning that it is not necessaryto deconvolve the instrument response from the time series for theHVSR analysis since the instrument transfer function is the same for allthree components, and thus it is canceled out by division of the hor-izontal to the vertical spectra. We selected a high-quality (with a dis-tinguishable P phase from the pre-event noise) subset of the initial

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database, including 336 triaxial recordings from 68 earthquakes withmagnitudes ranging from 2.5 to 4.4, hypocentral distances between16.81 and 442 km, and focal depths of 1–26 km, recorded by at leastthree stations. Fig. 2 depicts the distribution of the data in the magni-tude-distance space and Fig. 3 shows a map with the locations of theselected events as well as the Center for Earthquake Research and In-formation (CERI) stations. Stations GLAT, HALT, HICK, and LNXT aresituated on uplands and stations GNAR, HBAR, HENM, LPAR, PARM,PEBM, and PENM are located on lowlands. Table 1 lists the CERI'sstations, their locations, and the number of records captured at eachstation.

All traces are first baseline-corrected by removing the mean andlinear trend to avoid any bias in our analyses at very low frequencies.Then, we selected short windows over P-, S-, early coda, and late codawave as well as pre-event noise portions of waveforms. Since one ob-jective of this study is to assess the differences between the site am-plifications of P-, S- and coda waves, we chose short windows for P- and

Fig. 1. The geologic features of the ME.

Fig. 2. Distribution of the selected data in the magnitude-distance space (68earthquakes recorded at the CNMSN from 2013–2017). Circles are scaled basedon the depth of the event.

Fig. 3. Location map of the considered events and CERI's broadband stations.For each earthquake, the star size is scaled to its magnitude.

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S-waves to have a minimum impact from other phases such as scatteredand surface waves. The P-wave window begins from the first P-wavearrival and ends 1 s before the first S-wave arrival. For longer distances,the P-wave window length is restricted to 5 s. We used a minimumhypocentral distance of 16.81 km to ensure having at least a 2-sec P-wave window. The S-wave window starts from the first S-wave arrivaland has a length of 5 s. The early coda window begins from 1.5tS andthe late coda window starts from 2tS where tS is the direct shear wavearrival [2] and both have a length of 5 s. The 5 s pre-event noisewindow starts 7 s before the P-wave arrival. To compare the site am-plifications from different phases with the site amplification from thewhole record, a long window beginning 10 s before the P-wave arrivaland ending 150 s after the P-wave onset is employed. The whole seis-mogram is important since it is usually utilized for the structural re-sponse analysis [64]. Next, each selected window is cosine-tapered with5% at the beginning and 5% at the end to reduce truncation effects(Gibbs phenomena). The Fourier amplitude spectrum (FAS) of eachwindow is obtained using the Fast Fourier transform algorithm with16,384 (214) points. We zero-padded all windows to have consistentlengths. Therefore, the resolution in the frequency domain is 0.0061 Hz.The estimated FASs should be smoothed to reduce large scale fluctua-tions. On the other hand, heavy smoothing can obscure resonance peaksparticularly at low frequencies. Thus, we lightly smoothed all FASsapplying a running 21-point weighted average which resulted insmoothed FASs with a bandwidth of 0.1221 Hz. The final FAS of thehorizontal component is computed by the geometric mean of the N-Sand E-W components [17].

Since we used low-to-moderate magnitude earthquakes, which areenriched in high frequency energy, the low frequency part is usuallysituated below the noise [17,53]. Therefore, the analysis is done for thefrequency range of 0.15–20 Hz. In this frequency range, we estimatedthe HVSR for reliable frequencies at which the signal to noise ratio(SNR) exceeded 3. At each frequency, signal is obtained from the FAS ofthe P-, S-, or coda wave window and noise is picked from the FAS of thepre-event noise window. Fig. 4 demonstrates the smoothed FASs andthe HVSRs of the different time windows for the 25 Aug 2015 earth-quake with magnitude of 3.5 recorded at station HICK with a hypo-central distance of 106 km. In this figure, comparing the FAS from thewhole signal with the FAS from the S-wave portion reveals that themost energy of the seismic waves comes from the shear window al-though this window has a very short length.

The ratio of the FAS of the horizontal to the vertical component forvarious phases of seismic waves are used to explore the effects of thesedimentary basin on those phases and their discrepancies. Atkinsonand Cassidy [6] and Chen and Atkinson [22] found that averaging theHVSRs over many different events at a given site yields a better andmore stable indication of the site response. Thus, all HVSRs are log-averaged and then the standard deviation is estimated at each

frequency point for each station. Fig. 5 shows the average and standarddeviation of the HVSR for the whole signal at station GLAT obtainedfrom all 40 records captured at this station.

4. Results and discussion

4.1. HVSR analysis

Regarding the procedure explained in the previous section, we de-termined the frequency-dependent amplification for all the consideredstations. Fig. 6 presents the average HVSR as well as its standard de-viation obtained from the whole window containing all seismic phasesof seismograms. As can be seen, weak ground motions are amplified3–7 times for frequencies less than 5 Hz due to the unconsolidated MEsediments, while the amplification factor approaches to 1 for fre-quencies greater than 10 Hz. Significant site amplification particularlyat the low frequency range implies a strong impedance contrast be-tween the bedrock and the overlying soft sediment [33]. Furthermore,it can be observed that the scatter of site amplification estimated fromthe HVSR approach significantly increases around the peak frequencies,since the site amplification at peak frequencies is a function of incidentangle which is different for each record [37]. It is worth mentioningthat this scatter increases for lower peak frequencies compared tohigher peak frequencies due to the disparity of spectral amplitude atlow frequencies [51]. In essence, following the SESAME [58] proce-dure, two clear peaks in the frequency ranges of 0.2–0.4 Hz and0.5–1.5 Hz can be observed in all HVSRs. In addition to those low fre-quency peaks, a clear peak around 5 Hz is observed for HVSRs of sta-tions PEBM and PENM. Station GLAT also has a clear peak at around15 Hz. Other stations have closely spaced peaks (multiple peaks) in thefrequency range of 2–5 Hz. Bodin et al. [12] used the HVSR method formicrotremors captured at Shelby County, TN, and observed three peaks,the largest at about 4–5 s, and the other two at about 1–2 s, and at0.20–0.25 s. They referred to the largest peak between 4 and 5 s as thefundamental resonant period for sites considered in their study. Zan-dieh and Pezeshk [71] investigated the site amplification inside theNMSZ using the HVSR technique. They deployed 500 broadband seis-mograms out of 63 earthquakes with moment magnitudes ranging from2.5 to 5.2 and hypocentral distances less than 400 km recorded at sta-tions located inside the ME. They used a shear wave window containingdifferent shear wave phases such as S, SmS, Lg, and Sn. To obtain theFourier amplitude of the signal, they used the square root of the powerspectral density calculated by the Welch's method [68]. Zandieh andPezeshk [71] observed HVSRs varying from 2 to 4 for stations locatedon lowlands deposits and ranging from 1.5 to 3 for station located onuplands deposits in the low frequency range (≤5 Hz).

The main assumption of the HVSR method is that the site amplifi-cation is caused by a single soft soil layer overlying an elastic half-space[38]. The site amplification is characterized by the maximum amplifi-cation level, indicating the impedance ratio of the soft soil layer to thebedrock, and the predominant or fundamental frequency, fpeak, atwhich the maximum amplification occurs [27,34,38]. We chose the firstclear peak of the HVSR as the fundamental resonant frequency [58]which occurs in the frequency range of 0.2–0.4 Hz for all stations. Wepicked the exact frequency of the peak amplitudes by fitting a smoothGaussian distribution function to the HVSR curve. Table 2 tabulates thepicked fundamental resonant frequencies from the window containingthe whole ground motion. We also estimated VS for sediments with athickness of h using [29,35]

=V f h4S peak (1)

According to Eq. (1), for a layer with a constant thickness, thepredominant frequency increases with increasing stiffness (increasingshear-wave velocity). Note that the fundamental frequencies decreasewith increasing sediment thickness, as expected. Table 2 also compares

Table 1Locations of CERI's broadband stations.

Station Location Longitude Latitude Number ofRecords

GLAT Glass, Tennessee 89.288°W 36.269° N 40GNAR Gosnell, Arkansas 90.018°W 35.965°N 23HALT Halls, Tennessee 89.340°W 35.911°N 25HBAR Harrisburg, Arkansas 90.657°W 35.555°N 14HENM Henderson Mound,

Missouri89.472°W 36.716°N 43

HICK Hickman, Kentucky 89.229°W 36.541°N 48LNXT Lenox, Tennessee 89.491°W 36.101°N 35LPAR Lepanto, Arkansas 90.300°W 35.602°N 33PARM Stahl Farm, Missouri 89.752°W 36.664°N 42PEBM Pemiscot Bayou, Missouri 89.862°W 36.113°N 8PENM Penman Portageville,

Missouri89.628°W 36.450°N 25

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the average shear-wave velocities obtained in this study with the esti-mated shear-wave velocities from Langston and Horton [36] andMostafanejad and Langston [43]. Langston and Horton [36] used thehorizontal to vertical power spectral ratio analysis of ambient noisedata to evaluate the average shear wave velocities for the stations in theME. Mostafanejad and Langston [43] determined the velocity structure

of the ME using simultaneous inversion of vertical and radial tele-seismic transfer functions for broadband stations located within the ME.The comparison among the estimated average shear wave velocitiesindicates that there is a good correlation between the results obtainedfrom our study using local earthquake data, and results acquired fromLangston and Horton [36] employing ambient background noise. Theestimated shear wave velocities from Mostafanejad and Langston [43]also show a fairly good correlation; however, their velocities are gen-erally smaller than ours at all stations. This difference may be attributedto the difference between the nature of local and teleseismic earthquakerecordings or the difference between the HVSR and transfer functiontechniques.

4.2. Comparison between site amplifications and fundamental frequenciesobtained from different seismic phases

The degree of correlation between different seismic phases has beenalways a controversial topic. Tsujiura [66] showed that the site am-plification resulting from the coda wave agrees well with the site am-plification caused by the S-wave at rock sites. Castro et al. [20] ob-served that the P- and S-wave site responses generally have similartrends with shifting the maximum S-wave amplification toward lowerfrequencies compared to the maximum P-wave amplification. Seekinset al. [56] employed both HVSR and SRSR techniques and estimated thefrequency-dependent site amplification for five sites in San Francisco,CA. They selected 22 events mostly from the Loma Prieta aftershockswith magnitudes between 2.5 and 4.5 and chose 20 s S-wave and codawindows if it was possible. The coda window begins from the twiceshear wave arrival. They found that the HVSR and the SRSR estimated

Fig. 4. FASs and the HVSRs for different time windows of the three-component seismogram trigged by the 25 Aug 2015 earthquake (35.66°N; 89.68°W; magnitude of3.5, 12.7 km depth; 106 km hypocentral distance) captured by station HICK.

Fig. 5. HVSRs for the whole signal from 40 records captured at station GLAT.The solid thick line shows the average, μ, and the dashed lines represent ± onestandard deviation, σ, from the average.

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Fig. 6. Empirical frequency-dependent amplifications for different sites within the ME, determined from the whole signal window. The solid thick line shows theaverage and the dashed lines represent ± one standard deviation from the average.

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from coda waves are different than the HVSR and the SRSR obtainedfrom the S-waves at low frequencies and concluded that the low fre-quency part of coda waves might be contaminated with surface waves.Bonilla et al. [13] concluded that even though the site amplificationsfor the coda and shear wave are similar for rock sites, site amplifica-tions can be different by a factor of greater than 2 for stations locatedon basins and soft soils. Konno and Ohmachi [34] used an analyticalprocedure and showed that the fundamental periods of the S-wavecorrelate well with the fundamental periods of Rayleigh waves. Satohet al. [52] investigated the differences of site amplifications amongst S-waves and coda waves using the HVSR technique, deploying three-component velocity waveforms from 43 earthquakes captured at 19stations within the Sendai basin, Japan. In their study, the S-wave andcoda windows have a length of 10 s. They concluded that the HVSR ofthe coda portion is very small and similar to the HVSR of the S-waveportion for stations on rock. On the other hand, they found that there isa systematic difference between the HVSR of the S-wave portion andthe HVSR of the coda portion for soft sites. For such soft sites, theamplification of coda is greater by a factor of 2–4 at low frequencies(< 3Hz).

Fig. 7 compares the empirical frequency-dependent amplificationsobtained from various seismic phases with the amplification estimatedfrom the whole part of earthquake recordings as well as the amplifi-cation determined from the pre-event noise. Interestingly, spectralpeaks occur around the same frequencies for different phases; however,the level of amplification is different. Table 3 reports the picked fun-damental frequencies for all considered windows. It is interesting tonote that the difference between these fundamental frequencies is about15%. It is worth mentioning that in some cases the fundamental peaksare obscured when a small portion of seismograms are used even for thenoise window, but all these peaks can be observed from the HVSRs fromthe window including the whole signal. Therefore, a long windowcontaining all different seismic phases may better capture the funda-mental frequency of a given site. Amplification factors from the P-wavewindow are generally lower compared to other phases particularly inthe frequency range of 1–5 Hz. Furthermore, as expected, the peakfrequencies for the P-wave and S-wave window slightly shift towardshigher frequencies compared to the other phases due to higher velocityof the P-wave and S-wave relative to the velocity of those phases. FromFig. 7, it can be observed that the HVSRs obtained from the S-wavewindow are in a good correlation with the HVSRs of the early and latecoda portions as well as the pre-event noise windows for frequenciesmore than 4 Hz. For frequencies less than 4 Hz, S-wave, early coda, latecoda, and pre-event noise windows show similar peak frequencies;however, there is a systematic difference between the amplification

factors for these phases. In frequencies less than 4 Hz, particularly forfrequencies between 0.5 and 3 Hz, the S-wave amplification is generallythe highest, the pre-event noise amplification is usually the lowest, andthe early and late coda amplifications are in-between. The averagedHVSRs at different sites indicate that amplifications for the S-wave isgreater than amplifications of the coda up to a factor of 3 at the fre-quency range of 0.5–3 Hz. Horike [31], Nakamura [45], and Lermo andChávez-García [37] showed that microtremors are mostly composed ofsurface waves. The intermediate level of HVSRs of the early and latecoda in comparison to the HVSRs of S-wave and pre-event noise mayimply the contamination of coda waves, which consist of backscatteredbody waves, with surface waves. It is interesting to note that there is ananomalous peak at station HALT for the noise window (see Fig. 7).According to SESAME, although larger HVSR peak values represent asharper velocity contrast, sometimes no firm decision can be made re-garding the HVSR peak amplitude. We checked all HVSRs from thenoise window for this station and found that 5 HVSRs have very highvalues that increase the average HVSR peak amplitude. Therefore, thisanomalous high amplitude peak probably is an artifact of wind.

4.3. Basin-induced surface waves

Phillips and Aki [50] analyzed data from central California to obtainsite response and found that there is a poor agreement between thecoda and S-wave site amplification factors at low frequencies. Theyexplained this difference by the presence of trapped energy near thesurface. Frankel [26] also observed that there is contamination of codawaves with surface waves (T≈ 1–3 s where T is the period of surfacewaves) for deep-soil sites. He simulated synthetic seismograms usingthe 3D finite difference method for the San Bernardino valley andconcluded that the site amplification for coda waves is different from S-waves for the frequencies less than 2 Hz due to the presence of surfacewaves created by reflections and conversions of S-waves to surface-waves occurring at the edges of the basin. The different behavior of siteamplification for coda and S-waves in sedimentary basins were alsoobserved by other investigators and they attributed that to the presenceof basin-induced surface waves or the scattered energy trapped in thebasin (e.g., [25,41,52,56]).

We employ a zero-phase (non-causal) eight-pole Butterworth filterto explore whether the contamination of coda waves with surface wavesoccurs. 3 different passbands are used to bandpass-filter traces:0.2–1 Hz, 1–3 Hz, and 3–7 Hz. Fig. 8 depicts the N-S seismogram com-ponent for the 24 May 2013 event with a magnitude of 4.4 recorded atstation HBAR with a hypocentral distance of 190 km. This figure de-monstrates site reverberations for station HBAR due to the thick un-consolidated sediments of the ME in the frequency range of 0.2–1 Hz.Fig. 9 illustrates the N-S seismogram component for the 25 Nov 2015event with magnitude of 3.0 recorded at station GLAT with a hypo-central distance of 42 km. This figure reveals that site reverberations forthis site occur not only in the frequency range of 0.2–1 Hz, but also inthe frequency range of 1–3 Hz. These bandpass-filtered seismogramsshow that the amplitude of coda increases compared to the amplitude ofP- and S-waves for frequency bands less than 3 Hz. The increased am-plitude of coda is caused by the energy trapped in the basin [33,50,54].This increased amplitude of coda explains the importance of conversionof S-waves to surface waves near the edges of basins. These late-arrival,large amplitude, basin-induced surface waves are also important interms of structure response since they make the duration of groundmotions longer, and consequently, affect the seismic vulnerability oflong bridges and tall buildings.

The amplitude of seismic waves decreases with distance because ofattenuation. The inverse of attenuation is defined as quality factor (Q).Thus, higher attenuation means faster decay of amplitude with time. Ascan be seen from Figs. 8 and 9, site reverberations result in increasingcoda amplitudes, and consequently, cause higher Q values or lowerattenuation (slower decay rate of coda with time) [33,46,47,50], or

Table 2Results obtained from the HVSR analysis from a window over the whole lengthof ground motions.

Station Sedimentthickness h (m)a

Picked fundamentalfrequency (Hz)

VS (m/sec)b

VS (m/sec)c

VS (m/sec)d

GLAT 789 0.28 884 900 750GNAR 762 0.24 744 796 700HALT 768 0.28 863 878 640HBAR 722 0.26 758 811 570HENM 476 0.37 709 747 570HICK 576 0.31 717 715 560LNXT 816 0.26 837 888 750LPAR 853 0.24 812 830 760PARM 410 0.40 651 – 490PEBM 749 0.26 786 858 660PENM 551 0.31 686 700 540

a From Bodin et al. [12].b The results of the present study obtained from Eq. (1).c From Langston and Horton [36].d From Mostafanejad and Langston [42].

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sometimes negative coda Q values compared to the case where there isno site reverberation [53,69]. Therefore, using the coda portion in se-dimentary basins is not a reliable estimation of the S-wave

amplification at low frequencies if the contamination with surfacewaves occurs [26,46,47,49].

A continuous wavelet transform (CWT) is employed to investigate

Fig. 7. Comparison between amplifications obtained from different seismic phases and the whole record for different sites within the ME.

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the characteristics of basin-induced surface waves. The CWT is a time-frequency representation of seismic signals. In CWT, a signal is studiedunder various resolutions at different frequencies, and therefore, theCWT has a better resolution in comparison to a short-time Fouriertransform. Fig. 10 shows the time-frequency plot for the event used inFig. 8. The frequency of peak energy decreases with time from about5–10 Hz for body waves to about 1 Hz for surface waves. Around 142 s,the surface waves have peak energy at about 0.6–1 Hz. These surfacewaves appear as a wavelet having a period of around 0.5–4.0 s (seeFig. 8). This is in good agreement with the results obtained by Jemberieand Langston [33], who observed surface waves with a period of about3.5 s in the coda portion of seismograms within the ME. It is interestingto note that if seismic waves with frequencies less than 1 Hz are

ignored, the duration of the 24 May 2013 event with magnitude of 4.4recorded at station HBAR ends at around 150 s; while if basin-inducedsurface waves are considered the duration of the event ends around170 s (see Fig. 10). Therefore, basin-induced surface waves increase theduration of this earthquake at station HBAR up to 20 s.

5. Summary and conclusions

Paleoseismological evidence and historical earthquake activities aswell as frequently occurring moderate earthquakes in the NMSZ si-tuated in the central United States indicate the high level of seismichazard in this region. This region also deals with the impact of theunconsolidated sedimentary basin of the ME on the ground motionamplification. We carried out the analysis using the HVSR technique toquantify the site effects in the ME with a deep sedimentary structure

Table 3Comparison between the fundamental frequencies picked from different seismic phases and their estimated shear wave velocities.

Station h (m) Fundamental frequency Velocity (m/sec)

whole record P-wave S-wave Early coda Late coda Noise whole record P-wave S-wave Early coda Late coda Noise

GLAT 789 0.28 0.26 0.34 0.24 0.22 0.31 884 821 1073 757 694 978GNAR 762 0.24 – – 0.32 – 0.29 732 – – 975 – 884HALT 768 0.28 0.27 0.29 – – 0.34 860 829 891 – – 1044HBAR 722 0.26 – 0.24 0.23 – 0.24 751 – 693 664 – 693HENM 476 0.37 0.43 0.41 0.38 0.41 0.38 704 819 781 724 781 724HICK 576 0.31 0.33 0.37 0.33 0.27 0.35 714 760 852 760 622 806LNXT 816 0.26 – 0.31 – 0.27 – 849 – 1012 – 881 –LPAR 853 0.24 – 0.23 0.27 – – 819 – 785 921 – –PARM 410 0.40 – 0.44 0.38 0.46 0.45 656 – 722 623 754 738PEBM 749 0.26 0.36 0.40 – – – 779 1079 1198 – – –PENM 551 0.31 0.40 0.48 0.33 0.33 0.34 683 882 1058 727 727 749

Fig. 8. Bandpass filtered seismograms (N-S component) for the 24 May 2013earthquake (35.31°N; 92.72°W; magnitude of 4.4; 10 km depth; 190 km hypo-central distance) recorded at station HBAR.

Fig. 9. Bandpass filtered seismograms (N-S component) for the 25 Nov 2015earthquake (36.54°N; 89.60°W; magnitude of 3.0; 8.7 km depth; 42 km hypo-central distance) recorded at station GLAT.

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overlaid on the bedrock in the NMSZ. In this regard, we analyzed 336three-component seismograms from 68 earthquakes whose magnitudesvary from 2.5 to 4.4 and hypocentral distances are less than 450 km.

We computed the ratio of the FAS of the horizontal component tothe vertical component for various phases of seismic waves, to explorethe effects of the ME sedimentary basin on those phases and to assessthe degree of correlation between different phases of seismic waves andpre-event noise. We used a window containing the whole ground mo-tion as well as short windows over the P-, S-, early coda, late codawaves, and pre-event noise to compare the results.

The unconsolidated sediments of the ME significantly amplify weakground motions up to a factor of 7 for frequencies less than 5 Hz. Twoclear peaks between 0.2 and 0.4 Hz and between 0.5 and 1.5 Hz, as wellas significant site amplifications at all stations, indicate the strong im-pedance contrast between the bedrock with a depth varying from 200to 1600m and the overlying soft sediments. We observed that there aresystematic differences between site amplifications of different phases ofearthquake ground motions within the ME sedimentary basin attributedto the geological settings of the site and characteristics of the seismicphases. There is good agreement (less than 15% difference) betweenfundamental resonant frequencies obtained from different seismicphases. Although the HVSR estimated from S-wave and coda have si-milar peak frequencies, peak amplitudes systematically increase withdecreasing frequency for the S-wave. The ratio of the peak amplitudesof S-wave to coda reaches a factor of 3 at frequencies in the range of0.5–3 Hz. This different behavior of S-wave and coda occurs becausethe coda portion primarily consists of low-frequency surface waves inthe sedimentary basin of the ME which results in different peak am-plitudes for S-wave and coda.

Basin-induced surface waves are produced by reflection and con-version of S-waves from the edges of the basin. These basin-induced

surface waves cause reverberations at sites located within the ME, andthus result in increasing coda amplitudes for frequencies less than 3 Hz.Thus, the decay rate of coda wave cannot be observed at these fre-quencies in sedimentary basins. We found that observed surface waveshave a period of 0.5–4.0 s. One of the critical and important parameterscontrolling building damage during earthquakes is the duration ofground motions. Surface waves increase the shaking duration.Therefore, they should be considered in ground motion simulations forthe NMSZ and in structural analysis and design.

Of course, the HVSRs should be accompanied by the results fromnumerical or theoretical approaches to more accurately evaluate thesite amplification term in a given location. Moreover, note that theseamplifications are determined for weak to moderate events in which thesite response is supposed to be linear. In case of strong ground motions,the effects of nonlinearity may result in changing shear modulus,changing damping ratio, decreasing amplification factors, and changingthe fundamental frequency.

Acknowledgments

Waveform data for 2009 to 2016 were obtained from IncorporatedResearch Institutions for Seismology (IRIS; ds.iris.edu/ds/nodes/dmc,last accessed February 2017). The authors would also like to thank HadiGhofrani and an anonymous reviewer for their thoughtful reviews andconstructive suggestions.

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