retrieving impulse response function amplitudes from the · 2017-01-20 · 1 retrieving impulse...

submitted to Geophys. J. Int.

Retrieving impulse response function amplitudes from the1

ambient seismic field2

Loıc Viens1, Marine Denolle1, Hiroe Miyake2,3, Shin’ichi Sakai2 and Shigeki Nakagawa2

1 Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA

E-mail: [email protected]

2 Earthquake Research Institute, University of Tokyo, Tokyo, Japan.

3 Center for Integrated Disaster Information Research, Interfaculty Initiative in Information Studies,

University of Tokyo, Tokyo, Japan

3

Received ...; in original form ...4

Key words: Seismic interferometry; Seismic noise; Surface waves and free oscillations; Wave5

propagation; Body waves; Earthquake ground motions6

2 L. Viens et al.

SUMMARY7

8

Seismic interferometry is now widely used in passive seismology to retrieve the impulse re-9

sponse of the Earth between two distant seismometers. The phase information has been the fo-10

cus of most studies, as conventional seismic tomography uses travel-time measurements. The11

amplitude information, however, is harder to interpret because it has been argued to strongly12

depend on the distribution of ambient seismic field sources and on the multitude of processing13

methods. Our study focuses on the latter by comparing the amplitudes of the impulse responses14

calculated between seismic stations in the Kanto sedimentary basin, Japan, using several pro-15

cessing techniques. This region provides a unique natural laboratory to test the reliability of16

the amplitudes with dense instrumentation, notably the Metropolitan Seismic Observation net-17

work (MeSO-net), and complex wave propagation with strong attenuation and basin amplifi-18

cation. We compute the impulse response functions using the cross correlation, coherency and19

deconvolution techniques of the raw ambient seismic field and the cross correlation of 1-bit20

normalized data. To validate the amplitude of the impulse response functions, we use a shal-21

low Mw 5.8 earthquake which occurred on the eastern edge of Kanto Basin close to a station22

that is used as a virtual source. Both S and surface waves are retrieved in the causal part of the23

impulse responses computed with the different techniques, but their amplitudes agree better24

with those of the earthquake with the deconvolution method. The amplification related to the25

structure of the Kanto Basin, which overcomes the attenuation, is clearly retrieved from the26

ambient seismic field. To test whether or not the anticausal part of the impulse response from27

deconvolution also contains reliable amplitude information, we use a virtual source on the28

western edge of the basin and show that their surface-wave amplitudes agree well with those29

of a nearby shallow Mw 4.7 event. This study demonstrates that the deconvolution technique30

is the best strategy to retrieve reliable relative amplitudes from the ambient seismic field in the31

Kanto Basin and can be used to simulate earthquake ground motions.32

Retrieval of impulse response function amplitudes 3

1 INTRODUCTION33

Over the past decade, new opportunities have emerged in seismology through ambient seismic field34

seismic interferometry. Shapiro & Campillo (2004) empirically showed that the impulse response35

function (IRF) of the Earth can be retrieved by cross correlating ambient seismic field time series36

recorded by two distant seismometers. Under certain distribution of ambient seismic field sources,37

the IRF of the medium retrieved by cross correlation yields the true Green’s function (Snieder38

2004; Wapenaar 2004). The ambient seismic field on Earth is, however, mainly excited by the39

interaction of oceanic waves with the seafloor and the shores (Longuet-Higgins 1950), which leads40

to an uneven distribution of the ambient seismic field sources that potentially biases both phase41

and amplitude information of the IRFs.42

The travel-time information of the IRF has been, up to now, the primary focus of passive43

seismology. To reduce the biases caused by the non-uniform distribution of ambient seismic field44

sources, pre-processing of the raw ambient seismic field (1-bit normalisation, pre-whitening) is45

routinely performed before computing the cross correlations (Bensen et al. 2007). The travel-time46

measurements of the pre-processed IRFs have been used to image the Earth structure at local (Lin47

et al. 2013; Mordret et al. 2014; Roux et al. 2016), regional (Shapiro et al. 2005; Lin et al. 2008;48

Nishida et al. 2008), and global (Boue et al. 2013) scales, to estimate seismic anisotropy (Mordret49

et al. 2013; Takeo et al. 2013), monitor velocity changes in volcanoes (Brenguier et al. 2008b),50

and study the response of the crust after a large earthquake (Brenguier et al. 2008a, 2014).51

The amplitude information, in contrast, has attracted less attention because it appears to be52

more affected by the intensity and directionality of the ambient seismic field. Numerical (Cupil-53

lard & Capdeville 2010; Lawrence et al. 2013) and theoretical (Weaver 2011; Tsai 2011) studies54

predict a sensitivity of the amplitudes to the distribution of ambient seismic field sources as well55

as to the data processing. Despite this, several empirical studies demonstrated that the amplitude56

information seems to be preserved and can be used to simulate the long-period ground motions57

of moderate Mw 4–5 (Prieto & Beroza 2008; Denolle et al. 2013; Viens et al. 2015) and large58

Mw > 6.5 (Denolle et al. 2014a; Viens et al. 2016b) earthquakes, map site amplification (Denolle59

4 L. Viens et al.

et al. 2014b; Bowden et al. 2015) and infer seismic attenuation (Prieto et al. 2009; Lawrence &60

Prieto 2011).61

The amplitude of seismic waves can be affected by several effects: the elastic effects, which62

are the geometrical spreading, multipathing (focusing and defocusing) and scattering effects, and63

the anelastic effects, which are also called intrinsic attenuation. These processes are particularly64

efficient in complex shallow crustal structures, such as sedimentary basins. The low seismic-wave65

velocity of the soft sediments that compose basin and the shape of the basement both contribute66

to the trapping of seismic waves and thus their amplification. The Kanto Basin, Japan, is a sed-67

imentary basin that is locally deeper than 4 km and is located beneath the Tokyo Metropolitan68

area. The Japan Integrated Velocity Structure Model (JIVSM) (Koketsu et al. 2008, 2012) shows69

that the basin is constituted of sediments that have S-wave velocities ranging between 0.5 and 1.570

km/s and that lie over a stiff bedrock of S-wave velocity equal to 3.2 km/s. The contours of the71

basement are shown in Figure 1. This complex and deep structure has a resonance period of 6–1072

s (Kudo 1978, 1980; Furumura & Hayakawa 2007; Denolle et al. 2014b) and the seismic waves73

amplified by the basin are a potential threat to the large scale urban structures, such as high-rise74

buildings or long-span bridges, of the Tokyo Metropolitan area.75

The Tokyo Metropolitan area is extremely well instrumented. The dense Metropolitan Seis-76

mic Observation network (MeSO-net), which is composed of 296 accelerometer stations, was77

deployed in shallow 20-m deep boreholes (Kasahara et al. 2009; Sakai & Hirata 2009) to assess78

the seismic hazard in the region. There are also dozens of instruments of the Hi-net of the National79

Research Institute for Earth Science and Disaster Resilience (NIED) (Okada et al. 2004; Obara80

et al. 2005), University of Tokyo, and Japan Meteorological Agency (JMA) networks (Figure 1).81

All stations record continuous signals that contain the waveforms of several moderate Mw 4–582

earthquakes that occurred close to seismic stations (epicentral distances < 10 km). The ambient83

seismic field recorded by the stations has been used in several seismic interferometry studies to84

infer the complexity of the wave propagation and the seismic amplification in the basin (Denolle85

et al. 2014b; Viens et al. 2016a; Boue et al. 2016). Therefore, the combination of the large number86

of stations, the complexity of wave propagation, and the numerous shallow earthquakes makes the87


area the ideal natural laboratory to investigate the recovery of reliable amplitudes from the ambient88

seismic field.89

In this study, we aim to determine the best processing strategy to retrieve reliable IRF ampli-90

tudes from the ambient seismic field. After introducing the different processing techniques, we91

compare the waveforms of the vertical-to-vertical IRFs computed using one virtual source station92

located on the eastern edge of the basin. To validate the surface-wave amplitude of the IRFs, we93

compare their long-period peak ground velocities (PGVs) with the ones of a shallow earthquake94

that occurred in the vicinity of the virtual source. Finally, we discuss the effect of seasonal varia-95

tions, the retrieval of realistic S-wave amplitudes, and the possibility of using the anticausal part96

of the IRFs using one virtual source located on the western edge of the basin.97

2 METHODS: CROSS CORRELATION, COHERENCY, AND DECONVOLUTION98

We use the ambient seismic field data recorded in October 2014 by the seismic stations located99

close to the surface of the Kanto Basin. After instrumental response correction, the acceleration100

records of the MeSO-net stations are integrated once in time to retrieve the corresponding velocity101

waveforms and the data-set is divided into 1-hour time windows. Waveforms are band-pass filtered102

between 0.05 and 2 Hz (0.5–20 s) and down-sampled to 4 Hz to speed up the computation process.103

To reduce the bias that might be caused by earthquakes (Bensen et al. 2007), we remove the104

windows that have spikes larger than 10 times the standard deviation of each time window. We105

finally compute the Fourier transform of each 1-hour non-overlapping time series after using a106

zero-padding of 10 times the length of the window to increase the resolution when performing the107

computation in the frequency domain.108

For each pair of virtual source-receiver stations, we compute the IRFs using three different109

techniques. The first method is the cross correlation and can be written as110

CZZ(xr, xs, t) =⟨F−1 (vZ(xr, ω)v

∗Z(xs, ω))

⟩, (1)

where vZ(xr, ω) and v∗Z(xs, ω) are the Fourier transformed time series recorded by the vertical111

6 L. Viens et al.

component Z at the receiver station xr and the virtual source xs. The ∗ symbol is the complex112

conjugate and ω is the frequency. The inverse Fourier transform, denoted by F−1, of the cross113

correlation is computed for each 1-hour time window to retrieve the waveforms in the time domain114

t. We finally stack the cross correlations over 1 month, represented by the 〈〉 brackets, to increase115

the signal to noise ratio (i.e., equivalent to spatially averaging the effect of the ambient seismic116

field sources). For the cross correlation, we use both raw and 1-bit normalized ambient field data.117

The 1-bit normalization is a widely used technique (Campillo & Paul 2003; Shapiro & Campillo118

2004; Bensen et al. 2007) that only retains the sign of the data, setting the positive values to 1 and119

the negative ones to −1.120

The second technique is the coherency. It is similar to pre-whitening in the frequency do-121

main (Bensen et al. 2007), and consists of using the amplitude spectrum of the raw data from122

both stations as a denominator term when performing the cross correlation. This process can be123

summarized as124

CoZZ(xr, xs, t) =

⟨F−1

(vZ(xr, ω)v

∗Z(xs, ω)

{|vZ(xs, ω)|}{|vZ(xr, ω)|}

)⟩, (2)

where | | represents the absolute value and {} denotes a smoothing of the spectra using a moving125

average over 20 points to stabilize the denominator terms. All the other notations are the same as126

in Equation 1.127

The third method is the deconvolution, where only the amplitude spectrum of the data recorded128

by the virtual source is used in the denominator, and can be written as129

DZZ(xr, xs, t) =

⟨F−1

(vZ(xr, ω)v

∗Z(xs, ω)

{|vZ(xs, ω)|}2

)⟩, (3)

where all the notations are the same as in Equations 1 and 2.130

The travel-time (or phase) information is preserved through all three techniques as the denom-131

inator term in Equations 2 and 3 only affects the amplitude information. The regularization of the132

amplitude with the denominator term, however, prevents us from directly comparing the ampli-133


tudes from these three techniques without any scaling. In the following, we either normalize the134

amplitudes or calibrate them with earthquake records before comparing the waveforms.135

3 EFFECTS OF THE PROCESSING ON THE IMPULSE RESPONSE FUNCTIONS136

We use the techniques described in Section 2 to retrieve IRFs between the TENNOD station,137

which is the virtual source, and receivers in the basin. The virtual source station has been chosen138

because of its location close to the epicentre of a shallowMw 5.8 earthquake, which occurred in 14139

March 2012 at a depth of approximately 11 km (F-net/NIED catalog), that is used to validate the140

amplitude of the IRFs in Section 4. In the Kanto Basin, the primary source of the ambient seismic141

field is the Pacific Ocean. Such distribution of ambient seismic field sources and the location of142

the virtual source and receiver stations both lead to a strong asymmetry between the causal and143

anticausal parts of the IRFs. As the signal of the anticausal part is very weak, we only focus on the144

causal part of the IRFs for the TENNOD virtual source.145

Figure 2 shows the four waveforms, which are normalized to their respective peak absolute146

value, computed between the TENNOD station and the E.SRTM and E.YMMM receivers (lo-147

cations shown in Figure 1). In the 1–10 s period range, several groups of waves, which can be148

explained by the seismic wave propagation in the layered Kanto Basin (Boue et al. 2016; Viens149

et al. 2016a), can be observed. The earliest group of waves arriving at 15 and 25 s for the E.SRTM150

and E.YMMM stations, respectively, has been identified as S waves by Viens et al. (2016a) and151

is seen in the four waveforms. However, differences in the amplitudes are observed among the152

waveforms, with smaller amplitudes retrieved with the deconvolution method. Nevertheless, the153

recovery of clear body waves from seismic interferometry without any additional computation re-154

mains unusual and has only been observed in a few studies (Roux et al. 2005; Poli et al. 2012;155

Boue et al. 2013).156

The second and third wave packets in Figure 2 are likely surface waves. The first group is well157

retrieved by all the methods, but its duration is shorter for the IRFs retrieved with the raw cross158

correlation. The second group is very weak for the waveforms obtained from raw and 1-bit cross159

correlations compared to the two other techniques. To explain this weak signal, we compute the160

8 L. Viens et al.

Fourier spectra of the IRFs retrieved with the cross correlation and deconvolution techniques of161

raw data for 28 stations in Figure 3. These receivers are located within the azimuth range of 274±162

4◦, between 15 and 100 km from the virtual source. The IRFs obtained by cross correlation have163

a narrower frequency content (0.18 to 0.3 Hz), which corresponds to the frequency range of the164

secondary microseism peak, compared to that of the deconvolution (0.1 to 1 Hz). Vasconcelos &165

Snieder (2008) demonstrated that this discrepancy between the two techniques is expected because166

the dependence on the ambient seismic field sources is stronger for the cross correlation than167

for the deconvolution. Therefore, the last group of surface-wave arrivals, which has a dominant168

period content of 1 to 3 s (Viens et al. 2016a), can only be retrieved by both the coherency and169

deconvolution methods that generate a broader frequency content.170

To study the effect of the processing on the reliability of the amplitudes, we assume that the171

dominant amplitude in the waveforms in sedimentary basins comes from the surface wave. We172

band-pass filter the IRFs at the same stations as in Figure 3 between 3 and 10 s. The two main173

reasons of the narrower band-pass filter are the following: first, the cross correlation can only174

retrieve waveforms at periods longer than 3 s; and second, Viens et al. (2016a) demonstrated that175

both phases and amplitudes of the Z–Z (vertical-to-vertical) IRFs between 3 and 10 s are highly176

similar to those of theMw 5.8 earthquake. Then, we correct their relative amplitude for the surface-177

wave geometrical spreading (1/√xs, where xs is the virtual source–receiver distance) and compute178

the envelope of the signals using the Hilbert transform. Finally, the waves travelling faster than 5179

km/s are probably non-physical and are tapered out. Figure 4 shows the envelopes, which are180

normalized by a single calibration factor taken as the peak amplitude at the station the closest to181

the virtual source, against the distance from the virtual source TENNOD. Despite the geometrical182

spreading correction, the amplitudes of the first surface-wave group generally decays with the183

increasing distance, a likely signature of the attenuation in Kanto Basin. However, remarkable184

local amplifications can be observed at some stations, as for example, at the two stations located185

between 60 and 70 km from the virtual source. We can also note that the amplitude of S waves186

retrieved with the cross correlation of raw and 1-bit data is higher than that of the two other187

techniques for most of the stations. Despite the surface-wave geometrical spreading correction,188


the amplitude of S waves decreases faster than that of the surface waves, which validates that the189

long-period surface waves are dominant in the Kanto Basin.190

4 VALIDATION AGAINST EARTHQUAKE RECORDS: ATTENUATION AND191

AMPLIFICATION192

We showed in Section 3 that the dominant signal is contained by the first group of surface-wave193

arrivals. To validate the amplitude of this group of waves, we compare their long-period PGVs194

with those of the Mw 5.8 earthquake. However, only the relative amplitude is preserved by seismic195

interferometry techniques and the IRFs must be calibrated against the earthquake velocity records.196

To scale up the amplitude of the IRFs to that of the earthquake, we calculate the ratio of earthquake197

to IRFs long-period PGV at each selected station, compute the mean of the ratio, and correct the198

IRFs by this factor. This correction is the same for the selected stations but is different for the cross199

correlation, coherency and deconvolution techniques. We also account for the difference between200

the epicentre and virtual source locations, which leads to a difference in surface-wave geomet-201

rical spreading. We effectively shift the virtual source to the earthquake epicentre by correcting202

the amplitudes with the ratio of the geometrical spreading terms√xs/√x, where xs is the vir-203

tual source–receiver distance and x is the epicentre–receiver distance. This correction is relatively204

minor (mean value of 0.96) given the proximity of the virtual source to the real source epicentre205

(8.3 km), the period range of interest (3–10 s), and the fact that the virtual source and the earth-206

quake are located outside of the Kanto Basin (higher seismic wave velocity and therefore longer207

wavelengths).208

To reduce the azimuthal effects related to the non-uniform distribution of the ambient seismic209

field sources and to the surface-wave radiation pattern at the earthquake source (Denolle et al.210

2014a; Viens et al. 2016b), we only calibrate the IRFs within narrow azimuth ranges of 8◦. Finally,211

we select the stations located at distances greater than 30 km from the epicentre to ensure a similar212

path effect for the earthquake and IRF waveforms. The two corrections applied to the amplitudes213

and the station selection allow us to compare the simulated IRF PGVs with the observed, ground214

truth, earthquake PGVs.215

10 L. Viens et al.

For the stations located within the 264±4◦ azimuth angle from the epicentre, we plot the216

natural logarithm of the long-period PGVs as a function of the distance from the epicentre in Figure217

5. We also show the 1/√x and 1/

√x× e−αx theoretical curves, where x is the epicentre–receiver218

distance and α is an effective attenuation coefficient. We choose a constant value of α = 14×10−3219

km−1, which is close to the values found by Prieto et al. (2011) in the Los Angeles sedimentary220

basin (e.g., α = 2–5 × 10−3 km−1 in the 5 to 10 s period range). In Figure 5, we can observe221

that the amplitude decay of the IRF and earthquake PGVs follows the 1/√x × e−αx theoretical222

curve relatively well for distances smaller than 80 km and larger than 140 km from the epicentre.223

However, between 80 and 140 km, there is a large amplification for both predicted and observed224

values. This amplification correlates well with the deepest part of basin (Koketsu et al. 2008, 2012),225

which is also shown in Figure 5. Such amplification at large distance demonstrates that elastic 3-D226

effects of wave focusing overcome the attenuation in Kanto Basin.227

To further quantify the match between the observed and predicted amplitudes, we compute the228

root mean square error (RMS error) between the natural logarithm (ln) of the PGVs, which can be229

written as230

RMS error =

√∑Nn=1(ln(PGV

neq)− ln(PGV n

IRF ))2

N, (4)

231

where PGV nGF and PGV n

eq are the IRF and earthquake PGVs, respectively, and n is the nth sta-232

tion of a total number of stations N located within an azimuth range. For the 67 stations located233

within the 264±4◦ azimuth range, the RMS errors are equal to 0.239, 0.457, and 0.251 for the de-234

convolution, coherency, and cross correlation, respectively. The minimum RMS error is obtained235

for the IRFs retrieved with the deconvolution method. The RMS error computed from the PGVs236

retrieved with the cross correlation technique is comparable to that from the deconvolution and237

much smaller than the one from the coherency technique.238

To study the azimuthal dependence of the RMS error, we compute the RMS error for stations239

located within 8◦ azimuth ranges, every 2◦ between 254◦ and 290◦ from the epicentre. Results are240

shown for the raw and 1-bit cross correlation in Figure 6a and for the coherency and deconvolution241


in Figure 6b. The largest RMS error is obtained for the coherency technique at almost all azimuth242

angles and the smallest RMS errors are found with the raw cross correlation and deconvolution243

methods. We also find that the RMS error is higher for the azimuth angles larger than 284◦. To244

evaluate the consistency of the PGVs in the RMS estimates, we bootstrap Equation 4 by randomly245

resampling 1000 times the original PGV values and evaluating the 95% confidence interval of the246

RMS error of the new set of PGV values (Figure 6). As expected, fewer stations in the azimuth247

angles larger than 284◦ lead to a greater uncertainty in the RMS value, but the overall mean RMS248

value may arise from biases due to non-uniform source distribution.249

5 DISCUSSION250

5.1 Seasonal variations251

The IRFs studied in the previous sections are computed using 1 month of data recorded in Octo-252

ber 2014. To investigate the effect of possible seasonal variations, we compute the deconvolutions253

using Equation 3 for the months of April, June, August, and December 2014. The waveforms254

between the TENNOD virtual source and the E.SRTM and E.YMMM receivers, which are nor-255

malized with the maximum value of month of April, are shown in Figures 7a and 7b, respectively.256

The shape of the waveform slightly changes over the year, but the different wave arrivals are ob-257

served for each month. Moreover, the maximum amplitude is almost constant over the year and no258

clear seasonal pattern can be deduced for these two stations.259

We compute the maximum values of the waveforms normalized with the month of April for260

all the stations located in the 250–294◦ azimuth range from the epicentre, and summarize their261

mean and standard deviation values in Table 1. The amplitudes are the lowest in April, but weakly262

vary with the seasons (less than 10%) and the standard deviation is around 0.20 for each month.263

This shows that the peak value of the waveforms is stable throughout the year in the Kanto Basin.264

This contrasts with the study of Stehly et al. (2006) that noticed dramatic seasonal variations in265

the amplitudes with the seismic network in southern California.266

To verify whether or not the small amplitude variations observed over the year impact the267

retrieval of earthquake PGVs, we calibrate the IRF amplitudes for each month following the same268

12 L. Viens et al.

procedure as in Section 4. Figure 8 shows the RMS errors computed using Equation 4 for each269

month against the azimuth angle from the epicentre. Small variations can be observed over the270

different months, but the general trend remains the same throughout the year. One interesting271

feature is that the RMS error for the month of August is the highest for azimuth angles smaller than272

262◦, but the smallest for azimuth angles greater than 280◦. This can be interpreted that August273

experienced a more localized, or nearer noise source to influence the amplitude with the somewhat274

narrow azimuth coverage. December experiences the opposite trend, likely for a similar reason.275

The month of October allows to retrieve minimum RMS errors in the central part of the basin276

where strong and complex 3-D effects are observed. One possible explanation for the minimum277

RMS error for the data recorded in October 2014 is that two typhoons passed over the Kanto Basin278

during this month and might have excited the ambient seismic field more efficiently. However,279

further work is needed to understand the potential effect of strong meteorological events on our280

results.281

5.2 S-wave amplitudes282

Along the 274±4◦ azimuth angle, clear S waves can be retrieved. To investigate the reliability of283

their amplitudes, we perform the same kind of analysis as done for the surface waves. We first284

band-pass filter the data between 4 and 10 s and we select the phases traveling between 1.7 and285

5 km/s. We calibrate the amplitude of the S waves following the same procedure as in Section 4,286

but with the ratio of the virtual source–receiver and hypocentre–receiver distances to account for287

the geometrical spreading of body waves (xn/xh, where xn is the virtual source–receiver distance288

and xh is the hypocentre–receiver distance). The S-wave long-period PGVs of the earthquake and289

IRF are shown in Figure 9. The amplitude of the S waves are reliable with the coherency and290

deconvolution methods for distances larger than 60 km from the hypocentre. Similarly to surface291

waves, S waves are clearly amplified in the deepest part of the basin. The overestimation of the IRF292

PGVs for distances smaller than 60 km from the hypocentre might be explained by the fact that293

body waves travel directly from the hypocentre to the stations through the basement of the Kanto294

Basin. Therefore, body waves from the surface-to-surface instruments likely undertake a different295


ray path than from the deep source to the surface instrument. Nevertheless, reliable amplitudes296

of body waves can be extracted from the ambient seismic field at sufficient distance from the297

hypocentre using the deconvolution technique.298

5.3 Can the anticausal part of the deconvolution be used?299

So far, we have only studied the amplitude information of the causal part of the IRFs for seismic300

waves propagating westward, away from the coast. For earthquakes located on the west of the301

basin, however, seismic waves will propagate toward the East and most of the energy of IRFs will302

be contained in the anticausal part. Such configuration is, for example, similar to Southern Cali-303

fornia (Stehly et al. 2006) where earthquakes are expected along the San Andreas Fault and their304

seismic waves will radiate towards the coast where the Los Angeles Metropolitan area is located.305

Therefore, evaluating the reliability of the amplitude information contained in the anticausal part306

of IRFs is critical to predicting shaking from those earthquakes using the ambient seismic field.307

We retrieved the IRFs with the deconvolution method for the data recorded in October 2014308

by regarding the E.ZKUM station as the virtual source. This station is located close to a Mw 4.7309

earthquake (Figure 1), which occurred in 28 January 2012 at a depth of 20 km (F-net/NIED cata-310

log). We also use the same calibration procedure as in Section 4 for the surface waves propagating311

at velocities between 0.5 and 3 km/s, and show the results for two azimuth angles in Figure 10.312

We choose the 70±4◦ angle because of the large number of stations and the 90±4◦ to sample the313

deepest part of the Kanto Basin. For these two azimuths, the RMS errors (e.g., 0.412 and 0.476)314

are comparable to those of the causal part. Observed and simulated PGVs for the stations located315

above the deepest part of the basin, which reaches a depth of 4.1 km, are clearly amplified com-316

pared to the stations located above a basin depth of approximately 3 km. This demonstrates that317

the amplitude of the anticausal part of IRFs can also be trusted.318

6 CONCLUSIONS319

We retrieved IRFs from the ambient seismic field recorded in the Kanto Basin using three seismic320

interferometry techniques. We first showed that the waveforms retrieved with the cross correla-321

14 L. Viens et al.

tion technique have a narrower frequency content than the IRFs extracted with the coherency322

and deconvolution methods. To validate the surface-wave amplitudes of the amplitude calibrated323

IRFs, we compared their long-period PGVs to those of a shallow Mw 5.8 earthquake that occurred324

nearby the virtual source station. The long-period PGVs of the waveforms retrieved with the cross325

correlation and deconvolution techniques agree well with the ones of the earthquake and complex326

3-D effects, likely caused by the basin structure, are well captured by the ambient seismic field.327

We also investigated the sensitivity of the amplitudes to seasonal variations and showed that328

despite small variations, they remain relatively constant throughout the year for the deconvolution329

method. We also showed that the amplitudes of S waves are preserved for distances greater than330

60 km from the hypocentre with the deconvolution and coherency techniques. Finally, we con-331

ducted the same analysis on the surface-wave amplitude of the anticausal part of the IRFs from332

the deconvolution using an earthquake that occurred on the western part of the basin. The large333

amplification caused by the deepest part of the Kanto Basin is also well retrieved.334

This analysis demonstrates that the deconvolution technique produces broadband IRFs that335

contain both surface- and S-wave amplitudes that reproduce those of earthquakes in the complex336

Kanto Basin. Finally, IRFs obtained from deconvolution can be used to predict accurate seismic337

amplitudes of future earthquakes.338

ACKNOWLEDGMENTS339

We acknowledge Hi-net/NIED and JMA for providing the continuous data and F-net/NIED for the340

information about the earthquakes used in this study. We thank Naoshi Hirata and all the MeSO-341

net project members for the MeSO-net data. The MeSO-net project is supported by the Special342

Project for Reducing Vulnerability for Urban Mega Earthquake Disasters from the Ministry of343

Education, Culture, Sports, Science, and Technology (MEXT) of Japan.344

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Table 1. Mean and standard deviation of the peak values of the waveform for the months of April, June,

August, October, December 2014, normalized to peak value of the month of April 2014. For each month,

we use the deconvolution method between the TENNOD virtual source and 239 receiver stations located

within the 250–294◦ angle from the epicentre.

Normalized peak value April June August October December

Mean 1.00 1.06 1.06 1.04 1.11

Standard deviation 0.00 0.19 0.22 0.20 0.20

20 L. Viens et al.

290 °

254°

TENNOD

E.ZKUM

E.SRTM

E.YMMM

25 km

Mw 5.8

Mw 4.7

139.0° E 139.5

° E 140.0

° E 140.5

° E 141.0

° E

35.0° N

35.5° N

36.0° N

36.5° N

MeSO−net Hi−net JMA Univ. Tokyo Earthquakes

Basin depth (km)

4

2

0

PhilippineSea Plate

Pacific Plate

Figure 1. Map of the Kanto Basin, Japan, including stations of the MeSO-net (purple triangles), Hi-net

(black triangles), JMA (blue triangles), and University of Tokyo (green triangles) networks. Coastlines are

represented by the black lines and five hundred meter spaced basin depth contours derived from the JIVSM

(Koketsu et al. 2008, 2012) are shown by the coloured lines. The names of the TENNOD and E.ZKUM

virtual sources and the two receivers for which the waveforms are shown in Figures 2 and 7 are also showed.

The epicentre of theMw 5.8 and 4.7 earthquakes are represented by the red stars and their focal mechanisms

are plotted. The two azimuth angles of 254◦ and 290◦ that are used in the following are represented by the

two black lines departing from the Mw 5.8 earthquake epicentre. The upper right insert shows the Japanese

Islands (black lines), plate boundaries (grey lines), and the zoomed region (red square).


0 50 100 150 200 250

Time (s)

-1

0

1

2

3

4

5

6

7

8

No

rma

lize

d a

mp

litu

de

TENNOD - E.SRTM (44 km), BP: 1-10 s

Vertical component

Deconvolution

Coherency

1-bit

cross correlation

Raw

cross correlation

(a)

S wave

Surface waves

1st arrivals 2nd arrivals

0 50 100 150 200 250

Time (s)

-1

0

1

2

3

4

5

6

7

8

No

rma

lize

d a

mp

litu

de

TENNOD - E.YMMM (67 km), BP: 1-10 s

Vertical component

Deconvolution

Coherency

1-bit

cross correlation

Raw

cross correlation

(b)

S wave

Surface waves

1st arrivals 2nd arrivals

Figure 2. Impulse response functions retrieved from the raw cross correlation (red), 1-bit cross correlation

(orange), coherency (green), and deconvolution (blue) techniques between the virtual source (TENNOD)

and the (a) E.SRTM and (b) E.YMMM stations, which are located at 44 and 67 km from the virtual source,

respectively. The location of these two stations is shown in Figure 1. All the waveforms are shown for the

Z–Z component and are bandpass filtered between 1 and 10 s. The name of each group of arrivals is also

indicated.

22 L. Viens et al.

0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0

Frequency (Hz)

10-4

10-2

100

102

Norm

aliz

ed a

mplit

ude

Fourier spectra

Vertical component

Deconvolution

Raw cross correlation

Figure 3. Fourier spectra of the impulse response functions extracted using the deconvolution (black) and

the cross correlation (red) techniques between the TENNOD virtual source and 28 receiver stations. The

thick lines represent the geometric mean of the 28 Fourier spectra. The waveforms are normalized with the

peak value of the closest station to the virtual source (18 km) before being Fourier transformed.


0 50 100 150 200 250 300 350

Time (s)

20

30

40

50

60

70

80

90

100

110

Dis

tan

ce

fro

m t

he

TE

NN

OD

sta

tio

n

Band-pass filter 3 - 10 s

Vertical component

1st arrival of

surface waveS wave


1-bit cross correlation

Coherency

Deconvolution

Figure 4. Envelope of the Z–Z impulse response functions retrieved from the raw cross correlation (red),

1-bit cross correlation (orange), coherency (green), and deconvolution (black) techniques as a function of

the distance from the virtual source. All the impulse response functions are normalized with the maximum

value of the waveform at the closest station from the virtual source, corrected for the geometrical spreading

of surface waves (1/√xs, where xs is the virtual source–receiver distance), and band-pass filtered in the

period range of 3 to 10 s.

24 L. Viens et al.

TENNOD

25 km

264 ± 4°

Mw 5.8

139° E 140

° E 141

° E

35° N

36° N

Basin depth (km)

4

2

0

-4

-3

-2

-1

Ve

rtic

al co

mp

on

en

t

ln o

f lo

ng

-pe

rio

d P

GV

(ln

(cm

/s))

Deconvolution

RMS error: 0.239

50 100 150 200

Distance from epicentre (km)

3

2

1

0

-1

Ba

sin

de

pth

(km

)

Vs = 3.2 km/s

1.5

0.9

0.5

Coherency

RMS error: 0.457

Earthquake

IRF

50 100 150 200


3

2

1

0

-1

Vs = 3.2 km/s

1.5

0.9

0.5

-4

-3

-2

-1


RMS error: 0.251

50 100 150 200


3

2

1

0

-1

Vs = 3.2 km/s

1.5

0.9

0.5

Figure 5. (Upper panel) Map of the Kanto Basin including the basin depth contours from the JIVSM and

all the seismic stations. The receiver stations included in the 264±4◦ azimuth range, which is represented

by the two black lines, are used in this figure. (Middle panels) Natural logarithm of the long-period PGVs

of the earthquake (red) and impulse response functions (IRFs) after amplitude calibration (blue) waveforms

for the three different techniques. The black curves are the theoretical curves 1/√x and 1/

√xe−αx, where

x is the epicentre–receiver distance and α is an attenuation coefficient taken as 14 × 10−3 km−1. For each

panel, the RMS error computed using Equation 4 is also shown. (Bottom panels) Velocity profile extracted

from the JIVSM (Koketsu et al. 2008, 2012) for an azimuth angle of 264◦ from the epicentre. The S-wave

velocity of each layer is indicated and the thick line represents the basin depth.


252 256 260 264 268 272 276 280 284 288 292

Azimuth angle (° )

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

RM

S e

rror

(a)


1-bit cross correlation

252 256 260 264 268 272 276 280 284 288 292

Azimuth angle (° )

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

RM

S e

rror

(b)

Coherency

Deconvolution

Figure 6. (a) Mean of the RMS error computed from the long-period PGVs of the earthquake and the

impulse response functions retrieved with the raw cross correlation (red squares) and 1-bit cross correlation

(orange squares) techniques as a function of the azimuth angle from the epicentre. For each azimuth angle,

the 95% confidence interval of the bootstrap is indicated by the error bars. (b) Same as Figure 6a for the

RMS errors computed from the long-period PGVs of the earthquake and the impulse response functions

computed with the coherency (green) and deconvolution (black) methods.

26 L. Viens et al.

0 50 100 150 200−1

0

1

2

3

4

5

6

7

8

9

Norm

aliz

ed a

mplit

ude

TENNOD − E.SRTM (44 km), BP: 3−10 sVertical component

April (1)

June (1.18)

August (0.99)

October (1.09)

December (1.19)

Time (s)

(a)

0 50 100 150 200−1

0

1

2

3

4

5

6

7

8

9

Norm

aliz

ed a

mplit

ude

TENNOD − E.YMMM (67 km), BP: 3−10 sVertical component

April (1)

June (0.87)

August (0.88)

October (0.93)

December (1.03)

Time (s)

(b)

Figure 7. Impulse response functions retrieved with the deconvolution method between the virtual source

(TENNOD) and the (a) E.SRTM and (b) E.YMMM stations from the raw data recorded in April (black),

June (blue), August (orange), October (red) and December (green) 2014. The waveforms are normalized

with the peak amplitude of the impulse response retrieved for the month of April and the maximum value

of each waveform is indicated between parenthesis. All the waveforms are shown for the Z–Z component

and are bandpass filtered between 3 and 10 s.


252 256 260 264 268 272 276 280 284 288 292

Azimuth angle (° )

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

RM

S e

rror

April

June

August

October

December

Figure 8. Mean of the RMS error computed from the long-period PGVs of the earthquake and impulse

response functions extracted with the deconvolution technique using the data recorded in April (black),

June (blue), August (orange), October (red), and December (green) 2014 as a function of the azimuth angle

from the epicentre.

28 L. Viens et al.

TENNOD

25 km

274 ± 4°

Mw 5.8

139° E 140

° E 141

° E

35° N

36° N

Basin depth (km)

4

2

0

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

Ve

rtic

al co

mp

on

en

t

ln o

f L

on

g-p

erio

d P

GV

(ln

(cm

/s))

Deconvolution

RMS error: 0.392

50 100 150 200

Distance from hypocentre (km)

3

2

1

0

-1

-2

Ba

sin

de

pth

(km

)

Vs = 3.2 km/s

1.5

0.9

0.5

Coherency

RMS error: 0.401

Earthquake

IRF

50 100 150 200


3

2

1

0

-1

-2

Vs = 3.2 km/s

1.5

0.9

0.5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1


RMS error: 0.464

50 100 150 200


3

2

1

0

-1

-2

Vs = 3.2 km/s

1.5

0.9

0.5

Figure 9. (Upper panel) Map of the Kanto Basin including the basin depth contours from the JIVSM and all

the seismic stations. The receiver stations included in the 274±4◦ azimuth range, which is represented by the

two black lines, are used in this figure. (Middle panels) Natural logarithm of the S-wave long-period PGVs

of the earthquake (red) and impulse response functions (IRFs) after amplitude calibration (blue) waveforms

for the three different techniques as a function of the distance from the hypocentre. For each panel, the RMS

error computed using Equation 4 is also shown. (Bottom panels) Velocity profile extracted from the JIVSM

(Koketsu et al. 2008, 2012) for an azimuth angle of 274◦ from the hypocentre. The S-wave velocity of each

layer is indicated and the thick line represents the basin depth.


E.ZKUM

25 km

Mw 4.7

70 ± 4°

90 ± 4°

139° E 140

° E 141

° E

35° N

36° N

Basin depth (km)

4

2

0

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5

Ve

rtic

al co

mp

on

en

t

ln o

f L

on

g-p

erio

d P

GV

(ln

(cm

/s))

Azimuth: 70 4°

RMS error: 0.412

Earthquake

IRF

30 50 100 150


4

3

2

1

0

Ba

sin

de

pth

(km

)

Vs = 3.2 km/s

1.5

0.9

0.5

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

-2.5V

ert

ica

l co

mp

on

en

t

ln o

f L

on

g-p

erio

d P

GV

(ln

(cm

/s))

Azimuth: 90 4°

RMS error: 0.476

30 50 100 150


4

3

2

1

0

Ba

sin

de

pth

(km

)

Vs = 3.2 km/s

1.5

0.9

0.5

Figure 10. (Upper panel) Map of the Kanto Basin including the basin depth contours from the JIVSM and

all the seismic stations. The receiver stations included in the 70 ±4◦ and 90 ±4◦ azimuth ranges, which

are represented by the black lines, are used in this figure. (Middle panels) Natural logarithm of the long-

period PGVs of the surface waves of the Mw 4.7 earthquake (red) and that of the anticausal IRF from

deconvolution after amplitude calibration (blue) waveforms as a function of the distance from the epicentre.

For each panel, the RMS error computed using Equation 4 is also shown. (Bottom panels) Velocity profile

extracted from the JIVSM (Koketsu et al. 2008, 2012) for the 70 and 90◦ azimuth angles from the epicentre.

The S-wave velocity of each layer is indicated and the thick line represents the basin depth.

retrieving impulse response function amplitudes from the · 2017-01-20 · 1 retrieving impulse...

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