retrieval of local surface wave velocities from tra c noise - an … · 2019. 8. 31. · cwp-773...

CWP-773

Retrieval of local surface wave velocities from trafficnoise - an example from the La Barge basin (Wyoming)

Michael Behm1, Roel Snieder1 & Garrett M. Leahy2

1Center for Wave Phenomena, Geophysics Department, Colorado School of Mines, Golden, CO2Deptartment of Geology and Geophysics, Yale University, New Haven, CT

ABSTRACTIn regions where active source seismic exploration is constrained by limitationsof energy penetration and recovery, cost and logistical concerns, or regulatory re-strictions, analysis of natural source seismic data may provide an alternative. Inthis study, we investigate the feasibility of using locally-generated seismic noisein the 2 - 6 Hz band to obtain a subsurface model via interferometric analy-sis. We apply this technique to 3-component data recorded during the La BargePassive Seismic Experiment, a local deployment in south-western Wyoming thatrecorded continuous seismic data between November 2008 and June 2009. Wefind traffic noise from a nearby state road to be the dominant source of surfacewaves recorded on the array, and observe surface wave arrivals associated withthis source up to distances of 5 kilometres. The orientation of the road withrespect to the deployment ensures a large number of stationary points, leadingto clear observations on both inline and cross-line virtual source - receiver pairs.This results in a large number of usable interferograms, which in turn enablesthe application of standard active source processing methods like signal pro-cessing, common offset stacking and travel time inversion. We investigate thedependency of the interferograms on the amount of data, on a range of process-ing parameters, and on the choice of the interferometry algorithm. The obtainedinterferograms exhibit a high signal to noise ratio on all three components. Ro-tation of the horizontal components to the radial/transverse direction facilitatesthe separation of Rayleigh and Love waves. Though the narrow frequency spec-trum of the surface waves prevents the inversion for depth-dependent shear wavevelocities, we are able to map the arrival times of the surface waves to later-ally varying group and phase velocities for both Rayleigh and Love waves. Ourresults correlate well with the geologic structure. We outline a scheme for obtain-ing localized surface wave velocities from local noise sources, and show how theprocessing of passive data benefits from the combination with well-establishedexploration seismology methods. We highlight the differences to interferometryapplied to crustal scale data and conclude with recommendations for similardeployments.

Key words: seismic interferometry, surface waves, three-component, near sur-face

1 INTRODUCTION

Passive seismology is gaining increased interest in thesubsurface imaging community. Applications range frommonitoring subsurface fluid injection and fault map-ping to imaging basin-scale tectonic features. For imag-ing problems, the methodologies used so far typicallydraw heavily from methods established in the field ofcrustal seismology (e.g., teleseimic inversion, interfer-

ometry, receiver functions), and there is a natural fo-cus on medium- to large-scale structures. In terms ofscale and geologic variability, the different settings oflocal targets require modified processing schemes andmay require choices of parameters that deviate stronglyfrom the standards in global and regional studies. Inparticular, there is much interest in ambient noise, ordaylight imaging techniques, in which local structure

280 M. Behm, R. Snieder & G. Leahy

Figure 1. Location of the deployment within the investigated area. Blue circles: Stations L01 L15 (segment 1); red circles:

Stations L19 L41 (segment 2); yellow circles: Stations L42 L55 (segment 3). White circles denote virtual sources for whichdata and interferogram examples are shown in the following figures. Labels of map axes are UTM coordinates in kilometres.

is recovered via interferometric processing. These tech-niques are enticing in that no active sources are re-quired, and a deployment of only a few days may besufficient to obtain a detailed subsurface image. Mostcommonly, frequency-dependant surface wave velocitiesare obtained and are inverted for the vertical shear wavevelocity structure. While there is vast literature on theapplication of so-called ambient noise tomography oncontinental scale (e.g., see the overview given by Bensenet al. (2007), the number of studies related to local tar-gets is relatively limited. Ridder and Dellinger (2011)obtain Scholte-wave velocity maps from ocean bottommeasurements at the Valhall field in Norway on a spatialscale comparable to our study. Bussat and Kugler (2009)investigate an approximately 100 km wide offshore areain the North Sea and derive depth-dependant shearwave velocities from surface waves. In contrast, Picozziet al. (2009) analyze a higher frequency range and subse-quently obtain a three-dimensional shear wave velocityimage at a 100 by 100 meters sized test site. Forghani

and Snieder (2010) outline why it is more difficult to re-trieve body waves from interferometry, although severalpapers demonstrate the applicability on a local scale(e.g. O’Connell (2007); Draganov et al. (2009)). In gen-eral, these and similar studies suggest potential, but ingeneral there are few high quality datasets available totest and benchmark these concepts against other imag-ing techniques. One such dataset was collected over theLa Barge Field in western Wyoming ( Figure 1). The LaBarge Passive Seismic Experiment (LPSE; Saltzer et al.(2011)) was a collaboration between ExxonMobil Up-stream Research Co. and researchers at the Universityof Arizona. In this experiment, instruments from theNational Science Foundations PASSCAL facility weredeployed for a period of approximately 8 months overa producing hydrocarbon basin. From November 2008to May 2009, 55 three-component broadband seismome-ters (Guralp CMG-3T) were continuously recording ata sample rate of 100 Hz. The station spacing in thisexperiment (250 m) is much narrower than the typi-

Surface wave velocities from traffic noise 281

Figure 2. Geologic map of the investigated area. Coloured circles show the averaged and normalized power spectral densities(PSD) at each station. See text for details. Labels of map axes are UTM coordinates in kilometres.

cal configuration for such sensitive instruments, and theconsistency and the high-quality of the dataset make itan ideal test ground to determine the value of ambi-ent noise techniques.Crustal structure beneath the ex-periment is constrained by local well control, and otheractive and passive studies. The dominant structural fea-ture is the Hogsback Thrust, where paleozoic carbonatesoverly clastic sediments. The thrust reaches the surfaceat the eastern edge of Cretaceous Mountain, and is pre-dominantly oriented north-south. East of the thrust theclastic sediments (clay stone and silt stone) are exposed.The Wyoming state highway 235 runs parallel and westof a prominent mesa, which comprises oil shale and sandstone. A schematic of the surface geology is provided inFigure 2. The major goal of our study is the evalua-

tion of the applicability of seismic interferometry fromlocally generated ambient noise for shallow subsurfacecharacterization. We test and adapt different algorithmswhich are routinely used in global and regional surfacewave studies, and aim at defining differences in appli-cation and parameter selection. Although we addressthe entire seismic exploration community, in particularpractitioners of passive seismology and interferometryshould find useful information in this case study. Sec-tion 2 introduces the data set. In Section 3, we reviewthe basic concepts of seismic interferometry, outline ourprocessing approach, and analyse the effect of differentprocessing parameters. The optimum algorithms andparameters are then applied to the entire data set toderive a substantial set of interferograms, which also


allow identifying the noise source. The interferogramsare inverted for shallow surface wave velocities in sec-tion 4, and section 5 concludes with the most importantinsights and recommendations for further deploymentsand studies.

2 DATA

Analysis of the raw data focuses on the calculation ofthe power spectral densities (PSD) to get an initial esti-mate of the exploitable frequency content. We find sig-nals over a wide frequency range, sometimes up to theNyquist frequency (50 Hz). Figure 3 gives an exampleof the two stations L11 and L29 where the latter one isat a close proximity to the road. L11 shows the onsetof an unknown noise activity at 12:30 local time. Thepronounced noise bursts at station L29 are attributed topassing cars or trucks, but their high-frequency contri-butions decay quickly with the distance to the road. Theearths microseism, peaking between 0.05-0.5 Hz (e.g.,Webb 1998) can be clearly seen on all stations. Thesesignals are excited by interactions between ocean wavesand the ocean floor. Our investigation shows a broadvariation on both spatial and temporal scales, thougha complete and detailed analysis of the spectral charac-teristics of the entire data set is beyond the scope of thispaper. The uniform instrumentation allows for a directcomparison of the PSD (Figure 2) for the entire observa-tion period of 7 months. The coloured circles in Figure2 represent the average PSD of the vertical componentof each station. These values are obtained as follows: Atfirst, the averages of the PSD within certain frequencybins (0.001 0.1, 0.1 0.3, 0.3 1, 1 5, 5 10, 10 20, 20 40Hz) are calculated for each 24 hour interval within theentire observation period. In each frequency bin, averag-ing is performed a second time over all 24 hour intervalsand these double-averaged PSDs are then normalized tothe maximum and minimum of all stations. Finally, theshown values in Figure 2 are calculated by averagingthese normalized values over all frequency bins. Lowvalues indicate a weak surface response, and we find aclear large-scale correlation with surface geology sincestations east of the Hogsback thrust show higher val-ues. Outliers like the high values at two stations west ofthe thrust can be correlated with local machinery (e.g.pumping pads). Similar results are obtained for the hor-izontal components. If we further restrict the data totime windows which include surface and body wavesfrom regional and global earthquakes only, we derivethe same pattern. We therefore interpret these values asindicators for local attenuation due to the near-surfacegeological structure. A detailed treatment is beyond thescope of this study, but we conclude that some stationswill be more affected by attenuation and thus mightanticipate interferograms of lower quality west of theHogsback thrust.

3 PROCESSING

3.1 The virtual source method and thestationary phase principle

In seismology, Greens function represents the impulseresponse of the earth. The virtual source method(Bakulin and Calvert, 2006) aims to derive Greens func-tion between two receiver stations by transforming onestation into a (virtual) seismic source. It is assumed thatone or more (real) sources radiate seismic energy whichis recorded by a set of receivers. As our study is basedon seismic noise of initially unknown origin, we referto those real sources as noise sources in the following.The noise sources are assumed to be located outsidethe deployment. In case of ambient noise studies (e.g.Wapenaar and Fokkema (2006)) and continuous record-ing, the timing and location of the noise sources donthave to be known. By correlating the trace yA(t) at re-ceiver A (the virtual source) with the trace yB(t) atreceiver B, the interferogram gAB(t) between the twoinstruments is obtained:

gAB(t) = yB(t) ? yA(−t) (1)

Note that we consider the traces, and thus the Greensfunction, as time series of discrete samples which arerepresented as vectors. In equation (1), the star signdenotes convolution which is equivalent to correlationwith the reversed time series. For many reasons (e.g.source signature, instrument noise, attenuation, scatter-ing phenomena, measurement of displacement insteadof stress; Snieder (2007); Halliday and Curtis (2008);Tsai (2011)), the obtained interferogram gAB(t) is onlyan approximation to the actual Green’s function, andtherefore an estimate of the impulse response of theearth. Thus Greens functions recovered by interferome-try might be considered as empirical Green’s functions.Correlation results in both positive (causal) and neg-ative (acausal) time lags. The character of the causaland acausal parts of the interferogram gives evidenceon the noise sources: symmetry hints towards evenlydistributed noise sources, while a stronger causal (oracausal) part indicates a dominance of noise sourcescloser to receiver A (or B) (Paul, 2005; Stehly et al.,2006).

As correlation in the time domain is equivalent toconvolution with the reversed time-series, equation (1)can be stated in the Fourier domain as

gAB(f) = yB(f) · yA(f) (2)

Interferometry can also be approached in theFourier domain by deconvolution (Snieder and Safak,2006; Vasconcelos and Snieder, 2008; Wapenaar et al.,2010b)

gAB(f) =yB(f)

yA(f)(3)


which transforms to

gAB(f) =yB(f) · yA(f)

‖yA(f)‖2(4)

A modification to equation (4) leads to interfer-ometry by cross-coherence (Aki, 1957; Wapenaar et al.,2010b; Prieto et al., 2009):

gAB(f) =yB(f) · yA(f)

‖yA(f)‖ · ‖yB(f)‖ (5)

Equations (2), (4), (5) are, apart from the denom-inator, identical, which in the two latter cases comprisethe amplitude spectra of the seismic data. If the ampli-tude spectra are flat (unlikely in practice), the interfer-ograms obtained by all three methods are of identicalshape and recover identical empirical Greens functions.If not, each of the different Greens function recoverymethods will result in different estimates of the impulseresponse of the earth. The performance of these threetechniques is examined in more detail in section 3.3.The stationary phase principle (Snieder, 2004; Sniederet al., 2006) is of great importance to seismic interfer-ometry. Translated to ray theory, it states that the dom-inant contribution to the reconstructed Greens functioncomes from ray paths which are identical prior to thearrival at the receivers. Wapenaar et al. (2010a) showthat these paths are equivalent to rays which are parallelat the source. In case of a homogeneous half space, thestationary phase region (location of the noise sourceswhich satisfy the stationary phase principle) for sur-face waves is simply the outward extension of the linewhich connects the receiver and the virtual source. Inpractice, seismic waves comprise finite frequencies andthe ray path is replaced by the Fresnel zone (or finite-frequency kernel). Further, we may expect a multitudeof noise sources distributed all over and around the in-vestigated area. In this case, the stationary phase prin-ciple ensures a kinematically correct empirical Greensfunction if the noise sources are of equal strength, andare distributed evenly around the virtual source - re-ceiver pair. Only then will contributions from noisesources outside the stationary phase region cancel. Thedominant contribution from oscillatory integrals wherethe phase varies much more rapidly than the amplitudecomes from the integration points where the phase isstationary (section 6.5 of Bender and Orszag (1978) orsection 2.7 of Bleistein (1984)). For interferometric ap-plications this implies that the dominant sources arethose at the stationary phase points, provided the sourcestrength varies over distance much more slowly than thephase of the interferometric integral does. The station-ary phase principle is usually valid in global seismol-ogy because the dominant noise sources (ocean waves,strong earthquakes) are ubiquitous. At smaller scales,the noise sources may be concentrated at certain lo-cations (e.g., cultural noise, roads, trees) and thus theresults must be evaluated carefully with respect to a

possible violation of the requirement that noise sourcesare evenly distributed. Coherent signals of noise sourcesmay be expected to be of very small amplitude. Stack-ing of individual interferograms is commonly appliedto enhance information from ambient noise data. Thisincreases the signal-to-noise (S/N) ratio of the inter-ferograms by down-weighting non-coherent seismic en-ergy. Alternatively, correlation of the entire time seriesat once would be possible, but computation is more effi-cient and practical when the continuous recordings arecut into short time windows. Correlation is then per-formed for each time window, and the resulting indi-vidual interferograms are stacked into a final interfero-gram. The total amount of input data and the lengthof the time windows depend on the virtual source - re-ceiver distance, the sub-surface structure (attenuation),the location, type and strength of the noise sources, andon computational considerations. For the testing of pro-cessing parameters and methods (sections 3.2 and 3.3),we use 5 days of vertical component data (December 1stto December 5th of 2008) and cut them into 10 s timewindows. A more exhaustive analysis of the time win-dow length and the overall amount of data is presentedin section 3.4.

(Note that the term noise is used throughout withtwo different meanings: Prior to interferometry, it de-scribes the ambient seismic energy which is radiated bythe actual (real) sources. This noise is turned into a sig-nal by interferometry, which creates a virtual seismictrace. Consequently, the S/N ratio of this trace (the in-terferogram) is high when the amount of ambient noiseis high.)

3.2 Pre-Processing

Prior to correlation, the data are subjected to a sequenceof processing steps. Bensen et al. (2007) describe thedata processing which is commonly applied to global-scale data (frequency filtering, temporal normalization,spectral whitening). We essentially follow their method-ology, but with some minor modifications as discussedbelow. The raw data indicate a broad spectrum (Fig-ure 3) which ranges from below the Earths microseism(0.07 and 0.13 Hz, respectively) to the Nyquyist fre-quency (50 Hz), but only spatially coherent signals willprovide useful interferograms.

Exploration industry is interested in broadening thefrequency content of seismic data towards the lowerend of the spectrum to obtain improved starting mod-els for full waveform inversion. For interferometric ap-plications, the low frequency threshold depends on thenoise source, on the local subsurface structure, and onthe receiver spacing and aperture of the array. If thewavelength is large in comparison to the virtual source-receiver distance (e.g. earthquake surface waves), thecorrelation resembles a zero-lag peak. The same ac-counts for waves which arrive simultaneously at the re-


Figure 3. Data, spectrograms and power spectral densities (PSD) of the stations L11 and L29. The 24 h long data series start

at November 29th, 2008 at 18:00 local time. The red curve in the PSD plots is a running average over 10 samples.

ceivers, e.g. vertical-incidence body waves from teleseis-mic earthquakes. Thus we exclude data which comprisesurface and body waves from regional and global earth-quakes, based on a catalogue by C. Byriol (pers. comm.2011). Tests with different high-pass filters showed thata strong zero-lag arrival emerges if frequencies lowerthan 2 Hz are included. This may indicate that someearthquake energy is still remnant in the data set. Low-frequency oscillations of the basin, possibly excited byearthquake originated waves (Rial, 1989), may also con-tribute. Because of their consideration we conclude thata high-pass filter of 2 Hz is required for further pro-cessing. With respect to the expected velocities of sur-face waves, 2 Hz are roughly equivalent to a wavelengthrange from 750 to 2000 meters. The high-frequency endof the spectral component that can be used is exam-ined by different low-pass filters applied to the inputdata. Figures 4a,c show interferograms obtained fromcorrelation in the time domain applied to data bandpass-filtered with different upper corner frequencies (20Hz, 40 Hz). Both results appear noisy and do not givemuch additional insight into subsurface structure. Wefurther detect spurious energy over the entire frequencyband (e.g. the zero-lag peak). This results from spec-tral whitening (see below) which, though applied after

band pass filtering, is automatically performed from thelowest to the Nyquist frequency. Analogously to active-source processing, we thus apply a band pass filter af-ter interferometry (post-stack filtering, Figures 4b,d).It shows that the interferograms do not comprise coher-ent signals with frequencies higher than 5 Hz, no mat-ter which low-pass filter is applied to the data. Notethat the post-stack band pass filter becomes obsoleteif spectral whitening is performed over the same fre-quency range only as the pre-stack band pass filter. Thisdepends however on the actual implementation of thewhitening algorithm. In our case, all shown interfero-grams are band pass-filtered from 2 to 6 Hz.

Though the stationary phase principle requiresnoise sources of equal strength, this is not generallythe case; we therefore apply temporal normalizationto the input data. Bensen et al. (2007) compare dif-ferent algorithms, and we additionally test the perfor-mance of automatic gain control (AGC). The running-mean normalization by Bensen et al. (2007) is similarto AGC, but is based on the absolute amplitudes in-stead of the squared amplitudes. We find the differenceof one-bit normalization, running-mean normalization,and AGC to be minor. We chose the AGC with a win-dow length of 0.1 s. One-bit normalization has the dis-


Figure 4. Comparison of different pre- and post-processing band pass filters for virtual source L22 and receivers along segment

3. The broken lines indicate linear move-outs for a velocity of 1500 m/s. NW and SE refer to the geographic directions. Seetext for details.

advantage of not being commutative with respect to ro-tation of the horizontal components, which is needed forthe transformation to radial and transverse components(cf. section 3.5). Spectral whitening aims at normalizingthe amplitude spectrum of the input data, thus boost-ing low-amplitude frequency components and collaps-ing monochromatic signals. The latter is of importancein industrial settings, since industrial machinery (e.g.,drill rigs, pumps) operate at discrete frequencies (e.g.Poletto and Miranda (2004). Total whitening may beperformed by normalizing the amplitude spectra at allfrequencies. User-controlled whitening is achieved whenthe amplitude spectra is divided by a smoothed version

of itself (Bensen et al., 2007). A strong smoothing filter(smoothing over large frequency intervals) has little ef-fect compared to weak smoothing (smoothing over smallfrequency intervals). We prefer user-controlled smooth-ing since total whitening results in slightly more spikyinterferograms. Tests show that the optimum smooth-ing length with regard to the S/N ratio of the inter-ferograms is 0.1 Hz. Like one-bit normalization, totalwhitening is also not compatible with the transforma-tion to radial and transverse components (section 3.5).Because spectral whitening introduces incoherent high-frequency artefacts, post-processing (after interferome-try) always included a band-pass filter of 2 to 6 Hz and


weighted smoothing in the time domain with a windowlength of 0.3 s. The linear move-out of the arrivals is aprominent feature and an indication for surface waves(Figure 4d).

3.3 Comparison of different algorithms

As outlined in section 3.1, the three different inter-ferometry algorithms (correlation, deconvolution, cross-coherence) are identical if the amplitude spectra ofthe input data are flat. The flatness depends on thewhitening operator (section 3.2), and as we chose user-controlled whitening, different results are expected. Itis noted that both deconvolution and cross-coherenceintrinsically whiten the data by spectral division, al-though the whitening operator (the denominator inequations 3-5) varies with virtual source and receiverstations. E.g., spectral notches which are stronger atthe receiver station than at the virtual source will not becompletely removed. For these reasons, and for simplic-ity and consistency, we apply all three methods on a uni-form, pre-whitened data set. The comparison is shown inFigures 5 and 6. For short offsets (less than 2 km; Figure5), the results are similar. At medium offsets (2 to 4 km;Figure 6), the correlation interferograms are generallymore noisy, in particular if whitening is weak. This dif-ference to deconvolution and cross-coherence might beexplained by the additional spectral division (equations3-5), which additionally equalizes the receiver and vir-tual source amplitude spectrum. Cross-coherence, andin particular deconvolution, exhibit a pronounced zero-lag peak at medium offsets, which is slightly enhancedin the case of weak whitening. A similar behaviour isobserved at offsets larger than 4 km. In case of weakwhitening and correlation, monochromatic signals per-sist in the interferograms. Ultimately, theoretical equiv-alence results in the fact that the choice of method willbe determined by the character of the dataset of in-terest, and the preference and expertise of the analyst.In this case, we find that the best results are achievedwith strong whitening (smoothing over 0.1 Hz wide fre-quency intervals) and by the use of cross-coherence.Consequently, all following computations are performedwith this combination.

3.4 Influence of the window length andnumber of input data

In case of continuous recordings and unknown noisesources, the choice for the amount of input data is im-portant. Depending on the available data and comput-ing resources, different strategies can be imagined. Inthe case of a short, temporary deployment, overlappingtime windows may be used to increase the probabilityof correlating signals from noise sources (Seats et al.,2012). For our data set, we regard the 7 months of datato be sufficiently long and therefore use adjacent time

windows, and restrict the analysis to the number andlength of the time windows. The wave forms in Figures4 6 are based on 10 s long time windows from a 5day period. In a first test, the 5 day period is extendedto 10 days, 15 days, 20 days, and 35 days, and also isdecreased to one day. In case of short to medium off-sets and low attenuation, there is no direct correlationof the S/N ratio of the interferogram with the lengthof the observation period. Instead it turns out that theinterferograms from the individual 5 day periods dif-fer significantly which indicates varying strength of thenoise source within these time frames. The same effectis observed at large offsets and/or stations located inregions of stronger geological attenuation (e.g., section1). In order to improve the S/N ratio, a possible strat-egy would be the selection and stacking of interfero-grams from periods with higher S/N ratio. The secondtest is a variation of the length of the time windows(10 s, 20 s, 60 s, 120 s). Longer time windows provideclearer surface wave arrivals, and in particular the zero-lag peak (section 3.3) is minimized. A possible expla-nation for both observations is the dissection of longcoherent signals by cutting the input data into shorttime windows. The zero-lag peaks, which are consideredas artefacts from remnant unwanted energy (e.g., high-frequency body waves of earthquakes not included inthe used catalogue, section 3.2), are down weighted byimproved correlation of longer time series. With regardto these tests, all following computations are performedfor 120 s long time windows from a 5 day period (De-cember 1st to December 5th, 2008).

3.5 Horizontal component processing

As the horizontal component data (east E, north N) areof similar quality as the vertical (Z) component data, wealso calculate interferograms for the horizontal compo-nents. On average, initial tests show clear arrivals at the(N)-interferograms, and a lower S/N ratio at the (E)-interferograms. Further, most of the (N)-interferogramsexhibit significantly higher apparent velocities whichmight indicate the presence of faster Love waves. We an-alyze this by the transformation of the horizontal (E,N)components into the radial and transverse (R,T) com-ponents. The radial direction is defined as the virtualsource - receiver azimuth , and the transverse directionpoints 90 degrees clockwise to the radial direction. Incase of a layered structure, the radial component (R)and the vertical component (Z) should highlight theRayleigh wave, while the Love wave should be presenton the transverse (T) component only. Surface wavesreconstructed by interferometry suffer the loss of theiroriginal particle motion due to the correlation process,thus the 90 phase shift between the vertical and horizon-tal components of the Rayleigh wave cannot be observedon. Nonetheless, Rayleigh and Love waves can be sepa-rated by their different velocities. Lin et al. (2008) ana-


Figure 5. Comparison of different pre- and post-processing band pass filters for virtual source L22 and receivers along segment

3. The broken lines indicate linear move-outs for a velocity of 1500 m/s. NW and SE refer to the geographic directions. Seetext for details.


Figure 6. Comparison of correlation (a,d), deconvolution (b,e), and cross-coherence (c,f) for virtual source L22 and receivers

along segment 3 (short to medium offsets). The left/right columns (a-c/d-e) are based on strongly/weakly whitened data(smoothing interval 0.1 Hz / 1 Hz). The broken lines indicate linear move-outs for a velocity of 1500 m/s.


Figure 7. Transformation of the east (b) and north (c) components to radial (e) and transverse (f) components for virtual

source L16 (star in (a)) and receivers along segment 3 (black dots in (a)). Trace spacing is proportional to the virtual sourcereceiver azimuth. The broken lines indicate linear move-outs for different velocities. The azimuth is counted positive in clockwise

direction starting from the north axis.


Figure 8. Transformation of the east (b) and north (c) components to radial (e) and transverse (f) components for virtual

source L30 (star in (a)) and receivers along segment 3 (black dots in (a)). Trace spacing is proportional to the source receiverazimuth. The broken lines indicate linear move-outs for different velocities.


lyzed the radial and transverse parts of crustal seismol-ogy interferograms and were able to demonstrate thatthe T-component has a higher S/N ratio than the R-component, and that the Love wave is clearly present onthe T-component. Subsequently they derived Rayleighwave velocities from Z-component readings, and Lovewave velocities from the T-components. We might ex-pect the same, but have to consider that the scale oflocal velocity variations with respect to the wavelengthis different than in crustal seismology. Local wave frontcurvatures at the stations will be larger, and Love andRayleigh waves will be partially projected on both the(R) and (T) components. Consequently, the wave sep-aration by (R,T) transformation is less effective. Ad-ditionally, due to the short offsets Rayleigh and Lovewaves are more likely to interfere which hampers theirseparation. Pre-processing becomes an issue in case of(R,T) transformation. Ideally, one would perform therotation of the raw data first, and then do the pre-processing and finally applying interferometry. This isnot practical with a 3D deployment because for eachvirtual source the azimuth depends on the receiver inquestion and pre-processing must be performed for eachvirtual source - receiver combination with an accord-ing multiplicative effect on the computational expense.Like Lin et al. (2008), we overcome this by choosingpre-processing operators which are commutative withthe rotation operator such that pre-processing has tobe applied to the horizontal component raw data (e(t),n(t)) only once. Band-pass filtering and whitening canbe regarded as convolution operators in the time do-main. Commutativity is achieved if the convolution op-erators for both components are identical, which is thecase for a band-pass filter with constant corner fre-quencies. In case of user-controlled whitening (section3.2), a practical solution is achieved by averaging thesmoothed amplitude spectra of both components. Tem-poral normalization (AGC) is approached in a similarway. AGC can be formulated as an element-wise multi-plication of the raw data series (e(t), n(t)) with seriesof normalizing factors (ge(t), gn(t)). Again, commuta-tivity is satisfied when ge(t) and gn(t) are identical. Asthe normalizing factors depend on the data, we calcu-late both ge(t) and gn(t), and chose the smaller onefor each sample. 1-bit normalization cannot be adaptedin a similar fashion, and thus it is not commutativewith rotation. With regard to their subsequent work-flow, Lin et al. (2008) applied interferometry on thepre-processed data, and finally rotated the interfero-grams. For reasons related to data handling, we switchthis order and perform the rotation of the pre-processeddata before applying interferometry. The parameters forthe pre-processing steps (band-pass corner frequencies,AGC window length, and whitening smoothing length)for the horizontal components are identical to the onesused for vertical-component processing. A comparisonof all five components (Z,N,E,R,T) is shown in Figures

Figure 9. Stacked power spectral density of all obtained

interferograms. See text for details.

7 and 8, where the spacing of the traces is propor-tional to their virtual source-receiver azimuth. Figure7 gives an example where the virtual source is west ofthe receivers, and the state road is east of the receivers.We expect that this road is the dominant noise source(cf. section 3.6) which is also illustrated by the appear-ance of waves in the acausal part only. Therefore thefaster Love waves would not only be expected on theT-component (Figure 7f), but also mainly on the N-component (Figure 7c) at W-E oriented azimuths. Dueto the sine and cosine functions in the rotation opera-tor, the contribution of the N-component still is twiceas large as from the E-component (Figure 7b) at an az-imuth of 115, which explains the overall similarity of theT- and N-components (Figures 7c,f). Comparing the Z-,R- and T-components, the latter ones feature a higherapparent velocity which is interpreted as the Love wave.Figure 8 shows that Love and Rayleigh waves might alsobe associated with different excitations. As the virtualsource and the southernmost receivers are located closeto the road, both causal and acausal signals may be ex-pected at these receivers. This is the case for the Z- andR-components (Figures 8d,e), but the causal signals aremissing at the T-component (Figure 8f). We thereforeconclude that stronger Love waves are generated at thesouthern part of the road.

3.6 Results

Splitting the 5-day interval (December 1st to Decem-ber 5th, 2008) into 120 s long windows at 50 Hz re-sults in 3600 data sections for each of the three com-ponents. For 2,916 virtual source-receiver pairs, the to-tal number of all calculated individual interferogramsamounts to approximately 31,000,000. In this section wedraw conclusions on the obtained final interferograms,in particular with respect to the frequency content andthe noise source. Due to the large number of interfero-grams, emphasis is laid upon exemplary and summativeillustrations. Overall, the comparison between the threecomponents suggests the presence of both Rayleigh and


Figure 10. Interferograms of the vertical (a,d), radial (b,e), and transverse (c,f) components for virtual source L51 alongsegment 2. The trace spacing is equidistant. The right column (d-f) shows the application of the Hilbert transform. The broken

lines indicate linear move-outs for different velocities.


Figure 11. Common offset stacking applied to a subset of Hilbert-transformed interferograms (see text for details). The broken

lines indicate linear move-outs for different velocities. (a,b,c,): Vertical, radial, and transverse component data, respectively.

Love waves due to their different apparent velocities.Surface waves appear clearer on Z- and T-componentsthan on R-components. The derived waveforms have astrong amplitude and high S/N ratio. Nevertheless, thearrivals are not always characterized by one pronouncedpeak, but often by a sequence of two, three, or morepeaks of similar amplitude (e.g. Figures 5 - 8). This is aconsequence of the narrow frequency spectrum (Figure9). A closer inspection shows that the maxima at 2.3Hz and 2.8 Hz are differently pronounced on the verti-cal and horizontal components. Thus they are related toa slightly varying frequency response of the vertical andhorizontal component instruments. Overall, the narrowband prevents the extraction of dispersion properties(cf. section 4). Frequency-wave number analysis is ham-pered by the limited spatial sampling and could onlybe used to get rough and approximate phase velocities,which however can also be obtained from the interfer-ograms in the time domain. The individual peaks inthe interferograms can be correlated, but the true onsetof the arrivals is not always clear. Thus the envelopefunction (modulus of the analytical signal) is appliedin order to reduce the wavelet to a single peak. Theenvelope function is additionally raised to its 5th powerto enhance the strongest amplitude, which mostly corre-sponds to the surface wave arrival (Figure 10). This pro-cedure retains the kinematic properties of the observedwave, and the transformed wavelet now represents groupvelocities instead of phase velocities. The envelope cal-culation of the horizontal components may be flawed atshort offsets, where Love and Rayleigh waves are super-imposed. Also, non-stationary contributions will resultin inaccuracies, but overall the analyst can pick arrivals

much more consistently than prior to the envelope cal-culation. To obtain a more representative picture of theinvestigated area, we stack a sub-set of the final inter-ferograms into offset bins with a size of 100 m. Dueto local velocity variations, we have to expect to mixphases with different arrival times in each bin and thusvelocity information deduced from the stacks must beinterpreted with caution. The data subset is defined bythe stations L12-L31 and L42-L55, which feature inter-ferograms with the clearest appearance. Since the move-out and the spacing of the stations are too large withrespect to the wavelength, we stack the Hilbert trans-formed data. The results for all three components areshown in Figure 11. Arrivals on the T-component havea higher apparent velocity, and these arrivals can be ob-served over longer offsets. Z- and R-component arrivalsappear rather similar, with an overall lower S/N ratio ofthe R-components. This observation is also made by Linet al. (2008), although they analyzed data on a globalscale. The higher S/N ratio on the Z-component in com-parison to the R-component may be related to the sub-surface structure (e.g. Boore and Toksoez (1969)). Over-all, the common offset stacks strengthen the assumptionthat both Rayleigh and Love waves are observed. Over-all we obtain a substantial set of useful interferograms,both on inline and cross-line virtual source receiverpairs, which indicate a wide distribution of stationarysource points. The examples shown so far feature a pro-nounced difference of the causal and acausal parts. Thisis observed throughout the area, where on average theacausal part dominates. Note that the westernmost sta-tions (L01 - L11) exhibit a lower S/N ratio. For virtualsources located west of the state road, receivers at and


east of the mesa (L32 - L41) show only little coherentenergy, and observed surface waves often arrive with un-reasonably high velocities. The latter observation couldbe explained by the existence of a dominant noise sourcelocated in-between virtual sources and receivers. Alto-gether, there is strong evidence for a dominant noisesource in the eastern part of the deployment, and weconclude that traffic from the state road 235 excites themajority of the observed surface waves. The observedvariability of the quality of the interferograms with re-spect to the used time frame (section 3.4) might alsobe explained by irregular traffic activity. With respectto the geometry of the deployment, the north-south ori-ented road provides a large number of stationary sourcepoints. Lak et al. (2011) analyze the frequency responseof roads to traffic. They take into account the construc-tion of the road, the type of the vehicle, and the soilstructure. They focused on the near-field effect (2 to 64m) and concluded that the resulting spectrum mainlydepends on the eigenfrequencies of the vehicles whichrange from 2 to 15 Hz. Since the offsets in our study aremuch larger, we expect to observe only the lower end ofthis spectrum.

4 INVERSION

The inversion of surface waves for depth-dependentshear wave velocities is a standard procedure for globalsurface wave data. The frequency-time analysis method(FTAN; Dziewonski et al. (1969)) makes use of the dis-persion characteristics of surface waves and is commonlyapplied to Rayleigh waves (Bensen et al. (2007), andreferences therein), and also to Love waves (Lin et al.,2008). FTAN provides dispersion curves for group ve-locities for a single source receiver combination. Thesurface wave velocity - frequency relation is invertedfor an average shear wave velocity - depth relation be-tween the source and receiver. We also applied FTAN tothe interferograms, but due to the limited bandwidth inconjunction with the lateral geologic variability we didnot derive meaningful dispersion curves. On the otherhand, we derive a substantial number of useful interfer-ograms on both inline and cross-line virtual source re-ceiver combinations. The envelope calculation facilitatesconsistent manual picking of surface wave arrival times.Consequently, these arrival times can be inverted forlaterally varying group velocities by a tomographic ap-proach similar to the simultaneous iterative reconstruc-tion technique (SIRT; e.g. van der Sluis and van derHorst (1987)). Modifications of the SIRT method forlateral velocity modelling are given by Iwasaki (2002),Song et al. (2004), and Behm et al. (2007). We parame-terize the surface velocities at grid points with a lateralspacing of 250 m. Surface wave paths are approximatedby straight rays between the virtual source and the re-ceiver. We are aware that these simplifications may in-troduce artefacts in the obtained models, but we con-

sider them to be of equal or minor effect in comparisonto the accuracy of travel time picking. If the surface ve-locity at a grid point is expressed as the slowness s, thetravel time t for a specific ray is calculated from:

t =

N∑i=1

li ·M∑j=1

λj · sj (6)

The ray is split into N segments of equal length li,where N is the ratio of the total ray length (offset) to thegrid point spacing (250 m). The corresponding slownessfor each segment is represented by the second summa-tion term in equation (6), and it is interpolated from theslownesses sj at the neighbouring grid points. λj is a fac-tor which decreases with the distance between the raysegment midpoint and the j-th grid point. The numberM of contributing grid points is defined by a maximumdistance of 375 m. The λj are calculated from a distance-dependent Gaussian function to guarantee smooth be-haviour for the velocity interpolation, and they are nor-malized such that their sum is 1. For all observed traveltimes tobs, a set of linear equations is established andsolved for the unknown slownesses sj at the grid points.Travel time residuals to an initial model are calculated,and singular value decomposition (SVD) is used for theinversion. The trade-off between the RMS error of thetravel time residuals and the variance of the derived ve-locity map is controlled by a cut-off value for the eigen-values and additional smoothing of the obtained slow-ness improvements. At this stage we focus on the large-scale structure of the region which is more sensitive tosystematic mispicks (e.g., following a wrong phase) thanto slightly inaccurate travel time readings. Correlation-based travel time picking improves the accuracy of in-dividual picks, but nonetheless a visual control is nec-essary to check for systematic mispicks. We thereforechose to pick travel times manually. Travel times areonly picked if the phases can be clearly correlated over atleast two adjacent stations. Additional quality criteriaare the S/N ratio and a realistic apparent velocity (1000- 3000 m/s). Those envelope travel times (Figure 12) areinverted for group velocities, where vertical-componentdata provide Rayleigh wave velocities and transverse-component data provide Love wave velocities. We choseconstant velocity initial models, and calculate the veloc-ities from the slope of the regression lines in Figure 12.Picks are limited to traces with offsets between 0.3 and5 km. The inversion statistics are summarized in Table1.

The lower number of T-component travel times re-flects the uncertainty of picking the horizontal compo-nent, which we attribute to the imperfect separation ofLove and Rayleigh waves. This is also the reason why wedon’t include the R-component data in the inversion forRayleigh wave velocities. Phase velocities are associatedwith the interferograms prior to the Hilbert transform.As outlined before, the true onset of the phases (the


Figure 12. Picked surface wave travel times vs. offset for Hilbert-transformed interferograms of the Z- and the T-components.The slopes of the regression lines correspond to 1880 m/s and 2250 m/s, respectively. The zero-offset times are in the order of

+0.05 s and are attributed to the entire post-processing steps including the Hilbert transform. They are subtracted from thetravel times prior to the inversion.

Type no. of traveltime picks

initial velocity[m/s]

Travel time resid-ual RMS prior to

inversion [s]

Travel time resid-ual RMS after in-

version [s]

avg. / std.dev / min / maxof the velocities after inver-

sion [m/s]

Z-comp. 634 1880 0.272 0.117 1757 / 325 / 1104 / 2373

T-comp. 247 2250 0.154 0.109 2179 / 256 / 1545 / 2618

Table 1. Table 2: Statistics and results for the inversion of envelope travel times.

absolute travel time) is difficult to determine at mostoccasions, but the phases can be clearly correlated overadjacent traces. Thus the travel time difference betweentwo adjacent traces can be estimated with comparablyhigh accuracy, and equation (6) is reformulated to ex-press travel time differences. In this case, the initialmodel is of great importance due to the relative na-ture of the input data, and we chose the result from thegroup velocity inversions as initial models. Due to theeffective absence of dispersion as a consequence of thelimited bandwidth, we do not expect a large systematicdisparity between group and phase velocities. Instead,we anticipate more localized velocity information anda larger coverage by the additional use of phase traveltime differences. The RMS error of travel time residualsdoes not significantly change after the inversion, and incase of the Z-component it even slightly increases (Table2). On the other hand, this error is considerably smallerthan the RMS error of the absolute travel times (Ta-ble 1), and the results change only locally (Figure 13).This implies that the limited bandwidth of the dataeffectively results in identical group- and phase veloci-ties. The additional use of phase travel time differencesprovides improved coverage and confirms the large-scale

structure of the group velocity model, but local changesto the velocity model may be regarded as possible inver-sion artefacts. In whole, all four inversions correlate withsurface geology. The carbonates west of the Hogsbackthrust are represented by higher velocities than the clayand silt stones in the east. We estimate the depth sensi-tivity by the vertical eigenfunction of the surface waves(e.g., Stein and Wysession (2003)). The amplitude A ofa Love wave as a function of depth z is proportional to

A ∼ e−kx·r·z (7)

where kx is the horizontal wave number and r isgiven by

r =

√1− c2

β2(8)

c is the phase velocity of the surface wave and is theshear-wave velocity of the bottom layer. Based on ourresults and previous investigation of the area, we assumea frequency of 2.5 Hz, an average Love wave velocity (c)of 2100 m/s, and a bottom layer shear-wave velocity (β)of 3000 m/s, and evaluate equation (7). A(z) decays to


Type no. of travel

time picks

Travel time resid-

ual RMS prior toinversion [s]

Travel time resid-

ual RMS after in-version [s]

avg. / std.dev / min / max

of the velocities after inver-sion [m/s]

Z-comp. 643 0.046 0.052 1809 / 369 / 1122 / 2624

T-comp. 465 0.027 0.026 2107 / 261 / 1636 / 2619

Table 2. Table 1: Statistics and results for the inversion of travel time differences.

Figure 13. Results from travel time inversion. Z- and T-component travel times are related to Rayleigh and Love wave velocities,

respectively. Envelope travel times represent the Hilbert transformed interferograms and group velocities, while the travel time

differences from the original interferograms reflect phase velocities. See text for details. Note the different colour scaling for Z-and T-components. Varying coverage results from picking different virtual source receiver combinations.

a third of its maximum value at a depth of 206 meters,which is approximately a quarter of the wavelength andwe use this value as a rough estimate of the depth sensi-tivity of the surface waves. This estimation is in agree-ment with layer depth calculation based on Rayleighand Love wave velocities (e.g. Shearer (1999)). Both es-timations depend on several assumptions, in particularon the poorly known bottom layer shear wave veloci-ties, but we conclude that the observed surface wavesrepresent average velocities from the upper 100 to 300

meters. We finally calculate the ratio of the Love andRayleigh wave velocities (Figure 14). Due to the overallindifference of group and phase velocities, we chose thelatter one because of their larger coverage. The averageratio is 1.18, and the variations correlate again with sur-face geology with the region east of the thrust havinghigher values.


Figure 14. Ratio of Love and Rayleigh wave velocities.

5 CONCLUSIONS

We successfully applied interferometry to passive seis-mology data from a local deployment in an industrialsetting. Well-established methods from the global seis-mology community were adapted to the needs for localstudies. Traffic noise from a state highway was the mainsource of the extracted surface waves. The orientationof the road with respect to the deployment results in ahigh number of stationary points, thus enabling a largecoverage. Stacking of five days of data is sufficient toretrieve surface waves up to 5 kilometres of distance.Longer observation periods do not necessarily lead tobetter results. The S/N ratio of the interferograms isproportional to the length of the windows which areused to calculate the correlations, and we find a lengthof 120 seconds sufficient for our purposes. The perfor-mance of different interferometry algorithms depends onthe pre-processing. Cross-coherence is regarded as themost flexible method with respect to the input data, andprovides robust results in this study. Both the verticaland horizontal components are of similar quality, andcan be used to discriminate between Love and Rayleighwaves. The limited band width prevents the calcula-tion of depth-dependent shear wave velocities, but thehigh number of usable interferograms allow for inversionfor laterally varying Love and Rayleigh wave velocities.These velocities correlate well with surface geology andrepresent the few upper hundred meters of the subsur-face. An important lesson is the relatively low amount ofneeded input data in areas with traffic noise. If and howthe depth-sensitivity of locally excited surface wavescan be increased poses an important research question.From a practical point of view, the spectral characterof the noise source ultimately determines the ability toobtain dispersion curves and therefore depth dependentstructure. Ideally, a noise source spanning a sufficientlywide frequency range (perhaps from 0.5 to 10 Hz) will

provide sufficient frequency coverage to obtain robustgeologic models for more sophisticated imaging appli-cations. In a frequency limited scenario (such as ours),the models may still be useful for calculation of near-surface shear wave statics from surface wave velocitiesand large scale geologic characterization.

ACKNOWLEDGMENTS

ExxonMobil provided funding of this study. We thankMike Mooney (CSM), Berk Byriol (University of Ari-zona), Kyle Lewallen and Jelena Tomic (ExxonMobil)for discussion and administrative support. IRIS datamanagement centre was used to access waveform data.Kees Wapenaar and two anonymous reviewers helped toimprove the manuscript by their detailed and thought-ful comments. Data analysis was done with the softwarepackage Seismon (Mertl and Hausmann, 2009), to whichinterferometry processing tools have been added.

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