Spurious low velocity zones in joint inversions of surface ... · Seismic wave conversions and...

Geophys J Int (2019) 219 1032ndash1042 doi 101093gjiggz345Advance Access publication 2019 July 26GJI Seismology

Spurious low velocity zones in joint inversions of surface waves andreceiver functions

Chao Gao Erin Cunningham and Vedran LekicDepartment of Geology University of Maryland College Park MD USA E-mail cgao1terpmailumdedu

Accepted 2019 July 25 Received 2019 July 18 in original form 2019 June 19

S U M M A R YLow-velocity layers within the crust can indicate the presence of melt and lithologic differ-ences with implications for crustal composition and formation Seismic wave conversionsand reverberations across the base of the crust or intracrustal discontinuities analysed usingthe receiver function method can be used to constrain crustal layering This is commonlyaccomplished by inverting receiver functions jointly with surface wave dispersion Recentlythe proliferation of model-space search approaches has made this technique a workhorse ofcrustal seismology We show that reverberations from shallow layers such as sedimentarybasins produce spurious low-velocity zones when inverted for crustal structure with surfacewave data of insufficiently high frequency Therefore reports of such layers in the literaturebased on inversions using receiver function data should be re-evaluated We demonstrate thata simple resonance-removal filter can suppress these effects and yield reliable estimates ofcrustal structure and advocate for its use in receiver-function based inversions

Key words Crustal structure Inverse theory Surface waves and free oscillations

1 I N T RO D U C T I O N

Constraints on the layering and seismic velocities of Earthrsquos conti-nental crust provide key insights on its composition and formation(eg Christensen amp Mooney 1995 Rudnick amp Fountain 1995)However accurate quantification of crustal velocity structures fromseismological observations is challenging with primary constraintsoften coming from active-source experiments (for a recent reviewsee Mooney 2015) Recently passive source seismic investigationsof continental crust structure have benefited from the installation ofmassive seismic arrays (eg USArray Transportable Array Supe-rior Province Rifting Earthscope Experiment [Zhang et al 2016])and the development in improved imaging techniques (Shapiro et al2005 Kumar amp Bostock 2008 Langston amp Liang 2008 Rychert ampHarmon 2016)

Consequently efforts at combining different seismic observablesto improve the constraints on crustal models have grown Amongthose joint inversions of surface wave dispersion (SWD) and re-ceiver functions (RFs Ozalaybey et al 1997 Julia et al 2000Tkalcic et al 2006 Bodin et al 2012 Shen et al 2013 Chai et al2015) have gained in popularity due to their complementary con-straints absolute seismic velocities from SWD and sharp impedancecontrasts from RFs The resulting crustal models revealed featuresin greater detail and with smaller uncertainties including sharpdiscontinuities in the lithospheric mantle (Bodin et al 2016 Caloet al 2016) and crustal low velocity zones in various tectonic set-tings (Ward et al 2014 Li et al 2017 Li et al 2018)

While the complementarity of SWD and RF sensitivity helpsreduce the non-uniqueness of the seismic inverse problem (egOzalaybey et al 1997) differences in their inherent resolving powercan introduce inconsistencies between the two data types (eg Chaiet al 2015) The consequences of these inconsistencies on the inver-sion results have not been adequately quantified especially acrossdiverse geological settings Additional complications arise in re-gions where the low-velocity sedimentary layers overlay crystallinecontinental crust the strong impedance contrast at the bottom ofthe sediment layer can produce high amplitude long duration rever-berations in the RFs that could bias estimates of crustal thickness(Yeck et al 2013 Yu et al 2015)

In this study we assess the potential for artifacts in joint seis-mic inversions for crustal structure using a novel implementation oftransdimensional Bayesian (TB) inversion of SWD and RFs mea-sured across 49 stations of the EarthScope Transportable ArrayWe focus on the Trans-Hudson Orogen and Superior Craton partof which is overlain by the Williston Basin We compare our re-sults with analyses using synthetic data and discuss approaches formitigating these effects

2 DATA A N D M E T H O D

21 Ps receiver functions from transportable array

We focus on the east side of the Williston Basin where the thicknessof the sedimentary layer varies from 0 to 5 km (see Fig 1a) from

1032 Ccopy The Author(s) 2019 Published by Oxford University Press on behalf of The Royal Astronomical Society

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Spurious low velocity zones 1033

Figure 1 (a) Sediment thickness (Marshak et al 2017) across the study area (magenta box in inset) Transportable Array (TA) stations (triangles) Redtriangles show the stations where sediment correction is not needed green triangles show the stations where the sediment correction are applied in order toretrieve reliable posterior The green triangles with black contour are the stations where spurious low velocity zones are resolved when sediment correction isnot applied to RFs for the joint inversion (b) Ps RFs and (c) Love wave phase velocities at the TA stations shown in (a) sorted by longitude from west to eastThree stations are highlighted in (b) as they will be discussed in detail in the paper

east to west (eg Nelson et al 1993 Marshak et al 2017) andutilize data from EarthScope Transportable Array

At each station we compute P-to-s receiver functions using300 s three-component waveforms around the P arrival time fromMw gt 55 events at 30ndash90 epicentral distance which are trans-formed into the PndashSV system using the free-surface transform ma-trix (Kennett 1991) Optimal free-surface velocities are obtainedby minimizing the SV energy on the P component at the time ofthe P arrival and are listed in Table S1 It has been shown thatRFs in PndashSVndashSH system yield superior constraints on subsurfacestructure compared to ZndashR receiver functions (Reading et al 2003)We follow the Abt et al (2010) procedure and cull the data set toinclude data with a minimum Z-to-R cross correlation of 03 and amaximum 25 s discrepancy between the automatically determinedarrival time and prediction for ak135 We window the P and SVwaveforms prior to deconvolution and apply a fourth order Butter-worth bandpass filter to waveforms of 003ndash1 Hz We then use the

iterative time domain deconvolution with Gaussian half-amplitudehalf-width of sim05 s to calculate the receiver functions (Ligorria ampAmmon 1999)

These data selection criteria yield between 76 and 338 RFs at eachstation which we divide into 2ndash6 equal-sized bins based on theirray parameters to explicitly account for ray-parameter dependenceof RF waveforms In each RF bin we apply bootstrap sampling tocompute the average Ps RF and estimate its uncertainty Figs S1ndashS3show the individual Ps RFs as well as binned-average Ps RFs forthe three stations on which we focus our discussion in this paperIn these figures individual RFs are coloured according to their ray-parameter bin to illustrate that the binning by ray parameter allowsus to account for potential amplitude variations within the RF Dueto the limited deployment time (18ndash24 months) of the TransportableArray RF analyses using TA data generally suffer from incompletebackazimuthal coverage In this study we plot the RFs with respectto backazimuth to make sure they do not exhibit strong signs of

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Figure 2 Noise characterization of receiver functions Top left-hand panel data covariance matrix estimated from 338 Ps receiver functions calculated atstation MDND-TA Top right-hand panel a Toeplitz-type data covariance matrix constructed from the average covariance as a function of lag-time determinedfrom the data covariance matrix in the top left Bottom left-hand panel data covariance from Toeplitz type data covariance matrix versus type 3 parametrizationproposed by Kolb amp Lekic (2014) as a function of lag time Bottom right-hand panel covariance matrix corresponding to best-fitting type 3 parametrization tothe average covariance as a function of lag-time

azimuthal anisotropy (Figs S1ndashS3) Since we already binned thereceiver functions based on their ray-parameter the limited numberof events available for the Transportable Array does not enable us tofurther divide the data set by backazimuth to account for anisotropywhile maintaining robustness of the RF estimates

The average Ps RFs for each station are arranged by longitudeand shown in Fig 1(b) Strong reverberations at the beginning ofthe Ps RFs are observed to the west suggesting a layer on topof the crust bounded by large impedance contrast such signal isnot seen to the east Both features are consistent with the trendof basement depth from Marshak et al (2017) To quantify uncer-tainty of binned RFs we could use RFs within bins as samplesfor estimating the data covariance matrix (CD) However the rel-atively small number of samples available for this computationreduces its reliability and yields singular and ill-conditioned CD

(eg Ledoit amp Wolf 2004) Instead we represent CD with threeparameters (Kolb amp Lekic 2014) obtained by minimizing the L1

norm to the average covariance versus lag time estimated acrossRFs (see Fig 2) At each station a data covariance matrix is esti-mated following the procedure illustrated in Fig 2 This is done tocapture potential variations in noise characteristics across differentlocations

22 Surface wave dispersion from transportable array

At the station coordinates we also extract Rayleigh and Love wavedispersion curves between 5 and 40 s period from the transdimen-sional hierarchical Bayesian (THB) phase velocity maps (Olugbojiet al 2017) based on ambient noise measurements of Ekstrom(2017) The THB approach used to create the phase velocity mapsyields ensembles of solutions enabling uncertainties to be quanti-fied Fig 1(c) shows the Love wave dispersion data projected ontothe TA stations in the study area the dispersion curves arrangedby station longitude reflect the trends of the sedimentary thicknessmap confirming that sediment thickness variations manifest clearlyin the SWD data However unlike the Ps RF data SWD data on theedge of the Williston basin do not bear the signature of the sedi-ment layer even at the shortest period measured (see B29AmdashD31Afrom Figs 1b and c) This difference will be further discussed in theresults section

23 TB joint inversion with a progressive inclusion scheme

Joint inversions of SWD and RFs are highly non-linear and non-unique (eg Ammon et al 1990) Though linearized inversions

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Figure 3 Vs depth distributions from transdimensional Bayesian inversion of surface wave dispersion and Ps RFs for stations C25A-TA (left-hand panel)C31A-TA (middle panel) C35A-TA (right-hand panel) The ensemble solutions are displayed as probability density functions at each depth with warmercolours corresponding to higher posterior probabilities and the solid red line denoting the 5 per cent trimmed mean of the posterior NB The low-velocitylayer between 8 and 17 km at C31A is likely an artefact (see discussion in Section 4)

have been performed in the past (Owens et al 1984 Kosarev et al1993) they are easily trapped by local minima making the finalmodel strongly dependent on the starting model Furthermore lin-earized inversions often seek a single model that minimizes themisfit function and approximate uncertainty of the model parame-ters in ways that may not adequately represent the full uncertaintyHere we opt for a Bayesian inversion using a model space samplingframework that embraces the non-linearity and non-uniqueness ofseismic inversion Seismic Bayesian joint inversions of SWD andRFs with fixed parametrizations (Shen et al 2013 Shen amp Ritz-woller 2016) have been used to retrieve an ensemble of lithosphericshear velocity structures compatible with the data enabling uncer-tainty quantification on a data set of continental scale To allow amore flexible parametrization that introduces less prior informationa transdimensional sampling method was proposed and applied tothe joint inversion of SWD and RFs (Piana Agostinetti amp Malin-verno 2010 Bodin et al 2012) Unlike most of the seismic inverseproblems transdimensional inversions treat the number of modelparameters as an unknown It has been shown that the posteriordistribution acquired through TB inversions is naturally parsimo-nious (Malinverno 2002) due to the Bayesian formulation of modelselection (Malinverno 2000 Sivia amp Skilling 2006) This propertyof TB inversions punishes more complicated models and thereforerestricts the inverse problem from overfitting the data Instead TBinversions produce an ensemble solution where the model complex-ity is primarily determined by the data itself

Implementations of TB inversions of SWD and RFs have pre-viously been described in the literature (eg Bodin et al 2012)We adopt a similar approach by applying a reversible jump Markovchain Monte Carlo (rj-McMC) algorithm but differ from Bodinet al (2012) in some respects (1) we explicitly use covariance ma-trices representing data uncertainty ensuring optimal informationextraction from the two data types (2) we do not impose fixed Vpndash

Vs and densityndashVs scaling relationships based on prior knowledgebecause inverting for VpVs and density along with Vs minimizespotential bias (Dettmer et al 2015 Kim et al 2016 Gao amp Lekic2018) We assign uniform distributions between 05 and 55 km sndash116ndash19 and 26ndash31 g cmndash3 for Vs VpVs and density respectivelyand (3) we implement a progressive inclusion scheme for the RFdata which is described below

A major challenge for probabilistic sampling approaches isachieving convergence quickly and efficiently exploring the modelspace especially when involving multimodal density functionssuch as those associated with RF inversion We use a progressive-inclusion scheme to optimize convergence We start by invertingSWD data for 5times105 iterations using the approach of Gao amp Lekic(2018) who found that convergence is approached in around 105

iterations regardless of starting model Using the latter 25times105

steps we construct an estimate of a velocity structure that we thenuse as a starting model for the joint inversion of SWD and RF dataThe joint inversion also proceeds in a progressive fashion initiallyincluding the first 3 s of the Ps RFs to compute the likelihood usingthe Mahalanobis distance (for 1times105 iterations) before proceedingto include the first 5 s for additional 1times105 iterations and finallyinverting the 15-s-long Ps RFs for additional 3times105 iterations tocomplete the inversion 1times104 samples are drawn from this finalchain to create the ensemble solution which can be used to computethe uncertainty on the Vp and Vs inferences During final segmentof the progressive inclusion we ensure the misfit remains low andstable along the iteration after the burn-in period Additionally weverify that the statistical properties of the models do not changebetween the first and second half of the ensemble Finally we alsoshow the comparison of the model prediction from the posteriorand the observation (right-hand panel of Figs S4ndashS6) to assess theconvergence of the rj-McMC

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Figure 4 Individual 1-D velocity models from the ensemble solution of C25A C31A and C35A joint inversion (Fig 3) sorted by their misfit in an ascendingorder

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Figure 5 Left-hand panel Vs depth distributions from TB inversion ofSWD and resonance-removed Ps RF data at station C31A-TA The ensemblesolutions and the 5 per cent trimmed mean of the posterior (red) are shownas in Fig 2 Right top-hand panel comparison of RFs before (blue) andafter (red) applying the resonance removal filter Right bottom-hand panelautocorrelation of original RF showing how t and r0 are measured

Figure 6 (a) 1-D synthetic Vs model with (red) and without (blue) a sed-imentary layer (b) Associated Rayleigh and Love phase velocities and (c)Ps RFs from the model with (red) and without (blue) a sedimentary layer

3 R E S U LT S

31 Joint Inversion of SWD and Ps RFs

We perform a TB joint inversion of SWD and Ps RFs at three TAstations within the study area selected as archetypes of different sce-narios controlled by the thickness of the sedimentary layer (Fig 3)The sedimentary layer thicknesses for C25A C31A and C35A areapproximately 4 1 and 0 km respectively (Marshak et al 2017)Though we invert for structure down to 100 km depth here we onlypresent the top 70 km in order to highlight the crustal structureTo aid in the identification of layering in the ensemble models we

Figure 7 Left-hand panel Vs depth distributions from TB inversion ofsynthetic SWD and Ps RF data SWD data are generated for model withouta sedimentary layer while the Ps RF data are generated for the model with asedimentary layer (black dashed lines) The ensemble solutions are displayedas probability density functions at each depth and the solid red line denotingthe 5 per cent trimmed mean of the posterior Right-hand panel Same as theleft-hand panel except that the resonance removal filter has been applied tothe Ps RF

compute and plot the probability of a Vs changemdashcalled a transitionprobabilitymdashat every 1 km depth (see Figs S4ndashS6)

The posterior distributions of Vs retrieved from the joint inversionare intriguing For station C35A we see a 36 km thick two-layercrustal structure According to the transition probability the mostabrupt Vs jump within the crust occurs around 20 km The averageshear velocity above 20 km is 362 km sndash1 while the average shearvelocity between 21 and 36 km is 386 km sndash1 No sedimentarylayer is resolved at this location The SWD and RF predicted bythe ensemble solution reasonably fit the observations (Figs S4ndashS6)confirming that the models are consistent with the data

Unlike C35A both C25A and C31A resolve a thin low velocitylayer at shallowest depths which we interpret as the sedimentarylayer The posterior distribution of Vs at C25A resolves two layerswithin the 29-km-thick sediment package (see Fig S7 for a zoomedin version) the top layer has an average Vs of 112 km sndash1 and a thick-ness of 08 km the bottom layer has an average shear velocity of247 km sndash1 and a thickness of 21 km No clear crustal layering isresolved for this station the Moho is resolved as a relatively gradualVs increase between the 35 and 50 km where the trimmed mean ofVs changes from 38 to 46 km sndash1 The Vs structure retrieved fromC31A station shows a one-layer 08-km-thick sedimentary layer(see Fig S7) Based on the estimate of trimmed mean the shear ve-locity changes drastically from 190 to 374 km sndash1 right below thesedimentary layer While the crust beneath C31A appears to be rel-atively fast in Vs in the upper crust Vs drops significantly at around8 km depth to 357 km sndash1 and an intracrustal LVZ appears to spanthe 8ndash17 km depth range To demonstrate that such LVZ feature isnot due to the choice of the summary statistics of the trimmed meanwe analyse the posterior distribution obtained by the Bayesian inver-sion which is shown in Fig S7 A multimodal velocity distributionbelow the C31A sediment layer is observed across the ensembledemonstrating the non-uniqueness of the inversion due to lack ofdata constraints The posterior distribution of C31A between thedepth of 5 and 15 km appears to be non-Gaussian with a switch

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1038 C Gao et al

Figure 8 Posterior distributions from joint inversion with SWD and original RFs (upper panel) and from joint inversion with SWD and sediment-correctedRFs (lower panel) for five selected stations

of skewness from positive to negative around 8 km In contrast theposterior at the same depth for C25A is more Gaussian-like with atighter variation suggesting a relatively well-constrained velocitystructure In Fig 4 we show the individual models from the ensem-ble solutionmdashrepresenting samples from the posteriormdashsorted bytheir fit to the data in an ascending order This arrangement makesit very clear not only that a significant portion of the posterior bearsa clear LVZ signature in the mid-crust of C31A but that LVZs aremore prominent on the left meaning that models with LVZ are pre-ferred by the data The Moho depth is inferred at 40 km For bothC25A and C31A the SWD and RF predicted by these structuresagree well with observations (Figs S4 and S5)

32 Joint Inversion of SWD and Ps RFs correcting forsediment layer

The significant impedance contrast between the sedimentary layerand the underlying crystalline crust can produce large amplitudereverberations that appear as a decaying oscillatory signal in RFsThese shallow layer reverberations can overprint signals from directconversions across the Moho and other intra- and subcrustal inter-faces making it difficult to resolve accurate crustal structure (Zeltamp Ellis 1999) Yu et al (2015) proposed an approach to effectivelyremove such near surface reverberation by applying a resonanceremoval filter To assess the significance of these reverberations to

joint SWD and RF inversion for crustal structure we use this filterto obtain resonance-removed RFs that we invert jointly with SWDdata using our TB approach

To construct the resonance removal filter the traveltime of theS reverberation in sediment t and the relative strength of theSs reverberation r0 are needed The effect of the reverberationremoval filter on the RFs can be dramatic Fig 5 shows a comparisonbetween the original mean RF and the mean resonance-removedRF for station C31A It can be seen that the potential sedimentreverberation right after the direct sediment conversion has beensignificantly reduced after applying the filter clarifying signals fromlater lag-times corresponding to greater depths

After computing the resonance removal filter for each station werepeat our joint TB inversion using the resonance-removed RFs butintroduce a fixed one-layered lsquosedimentrsquo at the top of the modelSince the traveltime of the S reverberation in sediment t is usedto construct the removal filter our fixed lsquosedimentrsquo layer needs tohave the correct combination of thickness and Vs to be consistentwith the t During the inversion we first propose a Vs value forthe lsquosedimentrsquo layer Vs0

and then calculate the thickness H usingthe equation

H = (t2)radic

V minus2s0

minus p2

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where p stands for the median ray parameter of the binned receiverfunction At each step of the rj-McMC chain we introduce a 1-in-5 chance of perturbing Vs0 in the range of 0ndashVs1 km sndash1 whereVs1 is the shear velocity value of the layer right beneath the fixedlsquosedimentrsquo layer This allows H to vary during the inversion whileremaining consistent with the resonance removal filter

The Vs posterior distribution of the inversion is show in Fig 5The retrieved sedimentary layer has a thickness of 1 km and anaverage Vs of 2 km sndash1 which is similar as the sedimentary layerresolved in the inversion with original RFs The most prominentdifference between the two inversion results is the crustal structureIn this inversion no crustal LVZ is resolved the trimmed mean of Vs

increases from 359 to 404 km sndash1 along the depth with one abruptVs jump around 18 km The Moho depth is inferred at 37 km

Apart from the inversion with station C31A we also performTBI with SWD and resonance-removed RFs for C25A where the rj-McMC struggles to converge Given the same number of iterationsthe retrieved ensemble for C25A (Fig S8) resolves multiple sharpVs drops within a small depth range Meanwhile the predicted RFsand Love wave dispersion at 5 6 s from the ensemble fits poor withthe observation suggesting the inversion is unable to convergeespecially for the shallow structure

4 D I S C U S S I O N

The TB inversion results from the three selected stations show in-triguing and contrasting effects of sediment on the retrieval of struc-ture The three selected seismic stations are located in the SuperiorCraton and Trans-Hudson Orogen (Whitmeyer amp Karlstrom 2007)Crustal LVZs are not expected in this region and active source seis-mological studies find no evidence for them (Nelson et al 1993)At C35A where no sediment layer is present the TB inversion re-solves a seismic structure where the Vs increases with depth In thatcase our implementation of rj-McMC with a progressive inclusionscheme enables a fast stable convergence The shear velocity struc-ture is well constrained in terms of both absolute value and sharpchanges such as crustal layering and Moho

At station C31A lying on 1 km of sediment we resolve the sedi-mentary layer in both inversions whether using the original RFs orthe resonance-removed RFs However the inversion using the orig-inal RFs also contains an unexpected LVZ in the mid-crust no LVZis present in the inversion of RFs where sedimentary reverberationshave been removed We interpret the LVZ retrieved as an artifactresulting from the non-uniqueness of inverting RFs containing largeamplitude oscillatory reverberations together with SWD measure-ments that lack constraints on the sedimentary layer either becauseit is too thin for the period range of SWD or because it is a localfeature not resolved in the construction of the phase velocity mapsAnother possibility is that although both RFs and SWD contain suf-ficient constraints at the topmost depth they introduce conflictinginformation leading to the spurious LVZ To rule out this possibilitywe conduct a TB joint inversion with the SWD starting from 15 to40 s and uncorrected RFs (Fig S9) In this way we further reducethe strength of SWD at shallow depths The retrieved ensemblestill resolves a crustal LVZ consistent with the interpretation thatthe presence of LVZ is not due to the conflicting constraints but isinstead due to lack of constrains on absolute Vs This implies thatcrustal velocity structure should be carefully examined when SWDmeasurements in short period are unavailable or when only RFs areused

We confirm the paucity of SWD constraint on the sediment atC31A by performing a TB inversion using only SWD The retrievedVs structure (Fig S10) does not resolve any low-velocity layer ontop of the crust strongly suggesting that the SWD data do not seea low-velocity layer Meanwhile the RF data show large amplitudeoscillations at early lag times (Fig 5) indicating the existence of alarge impedance contrast at shallow depths When only the Ps RFis used in the TB inversion (Fig S11) the retrieved Vs structure re-solves as spurious mid-crustal low-velocity layer as expected Westress that absolute velocities are not well constrained in the RFonly inversion due to lack of data sensitivity Once we apply theresonance removal filter the signals after the first peak are signifi-cantly reduced confirming that the signal comes from the sedimentreverberation rather than from abrupt intracrustal Vs drops There-fore in joint inversions of SWD and uncorrected RFs constraintson Vs in the shallowest few kilometres only come from the first fewseconds of the RFs which on their own only very weakly constrainVs (eg Bodin et al 2012) However since this part of the RFs isdominated by both the direct conversion and sedimentary multiplesthe joint inversion readily obtains structures with redundant sharpvelocity changes due to the lack to constraints on absolute Vs

To further investigate the origin of the intracrustal LVZs we carryout synthetic tests that reproduce them and illustrate why apply-ing resonance removal to the RFs helps prevent their appearanceFig 6(a) shows two simple velocity models constructed to allowdifferences in predicted SWD and RFs to be straightforwardly at-tributed to the presence of a sediment layer One model (red) has1 km of sediment (Vs = 15 km sndash1) on top of a two-layer crustwith a Moho depth of 41 km The Vs is 43 km sndash1 below the MohoThe second model is identical to the first except that it lacks a sed-iment layer Differences in predicted SWD due to the sediment arelimited to only the shortest periods (Fig 6b) given that typical mea-surement uncertainties in this period range are sim01 km sndash1 theywould be difficult to detect in realistic data However the differ-ences between RFs due to the sediment are much more prominentS wave reverberations within the sediment produce large amplitudeoscillations that overprint the direct Moho conversion

In order to recreate a scenario where SWD measurement is in-capable of constraining the sediment layer we perform joint TBinversion using calculated SWD data from the model without sed-iment together with the RFs from the model with sediment Theretrieved Vs structure (Fig 7left-hand panel) resolves a mid-crustalLVZ that does not exist in either synthetic model After applyinga reverberation removal filter to the RFs and repeating the inver-sion the LVZ no longer appears in the retrieved Vs structure (Fig 7right-hand panel)

One might argue that the spurious LVZ results from using SWDpredicted from a model without a sediment layer We agree thatgiven sufficiently accurate and precise SWD measurements the ap-pearance of the spurious LVZ could be mitigated as illustrated in asynthetic test in Fig S12 However the situation illustrated by oursynthetic test is common in practice mainly due to the way SWD ismeasured Unlike RFs which are single-station-based observablesSWD curves are extracted from phase velocity maps whose resolu-tion is imperfect due to data coverage and modelling assumptionsTherefore while RF data are sensitive to the subsurface structuredirectly beneath the seismic station surface wave dispersion curvesmight not be particularly when dealing with structures of limitedspatial extent andor data from less dense seismic deployments

Previously Chai et al (2015) suggested that this potential dis-crepancy in sensitivity between RFs and SWD should be addressed

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1040 C Gao et al

by spatially smoothing the RFs to make their resolution more com-parable to that of SWD maps Here we show that this degradationof RF data is not always needed By applying a resonance-removalfilter to our RFs we are able to reduce the non-uniqueness of theinverse problem Additionally by requiring the two-way traveltimeof S wave in the sediment (t) to fit the value estimated from theautocorrelation of the RFs we pose a stronger prior constraint onthe TB inversion to help better constrain the sediment structureHowever crustal Vs structures constrained from RFs only or RFstogether with long period SWD data should be interpreted withextreme caution due the possibility of crustal artifacts

The joint inversion with SWD and resonance-removed RFs forstation C25A does not converge in our tests As is suggested byYu et al (2015) the resonance removal filter may perform poorlywhen the sediment layer is too thick due to several reasons the rapiddecay of reverberations with time weak impedance contrast at thebottom of the sediment layer that is unable to generate significantreverberations or complexity within the sediment layer requiringmore accurate modelling of the reverberations At C25A we believethat the complex sediment structure is the main reason for thefailed convergence of the joint inversion During the inversion theresonance removal filter that is applied to all proposed RFs assumesa single-layer sediment which is unlikely On the contrary theinversion with SWD and original RFs resolved a more realisticshear velocity structure with no crustal artifacts Unlike stationC31A the SWD data used for station C25A show a strong lowvelocity signal at shallow depths Our inversion with only SWDfor C25A confirms this observation (Fig S13) the retrieved VS

structure resolves a clear low-velocity sediment layer We believethat the strong signal of the sediment layer in the SWD data as wellas the relatively low measurement error associated with them helpsbetter constrain the shallow part of the structure beneath C25Aeven without applying the resonance removal filter Therefore dueto better constraints from SWD and the unsuitability of a single-layer resonance removal filter we advise that inversions use SWDand the original RFs in locations where the thick sediment layersare expected In Fig 8 we show comparisons between the jointinversion of original RFs and of the sediment-corrected RFs forfive additional seismic stations within our study area Crustal LVZsare observed at all five stations and are effectively removed bythe sediment-correction We want to point out that although it isclear that the sediment removal filter is suitable for the thin single-layer sediment setting sediment thickness should not be used asthe sole criterion to determine whether or not to apply a sedimentcorrection Both the layering and the frequency range of availableSWD data should also be considered Because information aboutsediment layering and basin complexity is typically limited it isseldom useful to rely on a measure of sedimentary basin complexityfor guidance on whether or not to apply the sediment removal filterCunningham and Lekic (in revision at GJI) proposed approachesfor evaluating the effectiveness of the sediment removal filter bycomparing the change of RF waveform as well as the fit of the RFautocorrelation to a decaying sinusoid In Fig 1(a) we highlightedthe seismic stations where the sediment removal filter is needed toretrieve accurate velocity structures using green colour

We also want to point out that applying a sediment resonanceremoval filter does not prohibit the retrieval of a real crustal LVZ InFig S14 we show a synthetic test where a mid-crust LVZ is imposedin the true model By performing TB joint inversion of SWD andsediment-corrected Ps RFs the posterior is able to resolve the LVZwithout significantly losing constraints on other features of the truemodel such as the sediment layer and Moho

5 C O N C LU S I O N S

In this paper we investigated the reliability of crustal structure in-ferences using an implementation of TB method capable of simul-taneously inverting surface wave dispersion and receiver functionsWe documented that shallow sedimentary layers can produce spu-rious intracrustal LVZs in joint seismic inversions and proposedan approach for removing these artifacts We found that in loca-tions where surface wave data and RFs show consistent signal ofthe shallowest layersmdashno sediment is expected by both data typesor the sedimentary layer is sufficiently thick to be seen by bothdata typesmdashTB joint inversions are able to retrieve realistic crustalstructures Finally we showed that applying a sediment resonanceremoval filter to our RFs can effectively remove the sediment rever-beration enabling recovery of a more realistic crustal model withoutLVZs

Seismological studies have identified crustal LVZs in variousgeological settings (Kind et al 1996 Beck amp Zandt 2002 Zorinet al 2002 Li et al 2003) While most such LVZs are reportedin active orogens some studies have suggested their presence incratonic regions (Chen et al 2015) Our results indicate that theinferences of LVZs from joint inversions should be scrutinized insedimented regions Furthermore they provide guidance on bestpractices for avoiding spurious intracrustal LVZs and performingreliable joint inversion of SWD and RFs under different shallow-layer scenarios

A C K N OW L E D G E M E N T S

The authors thank Lara S Wagner for extensive suggestions thathave improved this manuscript We also thank the editor LapoBoschi and two anonymous reviewers for their constructive re-views We acknowledge support from NSF grants EAR 1352214and EAR 1361325 as well as the Packard Fellowship for Scienceand Technology to VL

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Ammon CJ Randall GE amp Zandt G 1990 On the nonuniquenessof receiver function inversions J geophys Res Solid Earth 95(B10)15303ndash15318

Beck SL amp Zandt G 2002 The nature of orogenic crust in the centralAndes J geophys Res Solid Earth 107(B10)

Bodin T Leiva J Romanowicz B Maupin V amp Yuan H 2016 Imag-ing anisotropic layering with Bayesian inversion of multiple data typesGeophys J Int 206(1) 605ndash629

Bodin T Sambridge M Tkalcic H Arroucau P Gallagher K amp Rawl-inson N 2012 Transdimensional inversion of receiver functions andsurface wave dispersion J geophys Res Solid Earth 117(B2)

Calo M Bodin T amp Romanowicz B 2016 Layered structure in the uppermantle across North America from joint inversion of long and short periodseismic data Earth planet Sci Lett 449 164ndash175

Chai C Ammon CJ Maceira M amp Herrmann RB 2015 Invertinginterpolated receiver functions with surface wave dispersion and gravityapplication to the western US and adjacent Canada and Mexico GeophysRes Lett 42(11) 4359ndash4366

Chen Y Gu YJ Dokht RM amp Sacchi MD 2015 Crustal imprintsof Precambrian orogenesis in western Laurentia J geophys Res SolidEarth 120(10) 6993ndash7012

Christensen NI amp Mooney WD 1995 Seismic velocity structure andcomposition of the continental crust a global view J geophys ResSolid Earth 100(B6) 9761ndash9788

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ber 2019


Dettmer J Dosso SE Bodin T Stipcevic J amp Cummins PR 2015Direct-seismogram inversion for receiver-side structure with uncertainsourcendashtime functions Geophys J Int 203(2) 1373ndash1387

Ekstrom G 2017 Short-period surface-wave phase velocities across theconterminous United States Phys Earth planet Inter 270 168ndash175

Gao C amp Lekic V 2018 Consequences of parametrization choices in sur-face wave inversion insights from transdimensional Bayesian methodsGeophys J Int 215(2) 1037ndash1063

Julia J Ammon CJ Herrmann RB amp Correig AM 2000 Joint in-version of receiver function and surface wave dispersion observationsGeophys J Int 143(1) 99ndash112

Kennett BLN 1991 The removal of free surface interactions from three-component seismograms Geophys J Int 104(1) 153ndash163

Kim S Dettmer J Rhie J amp Tkalcic H 2016 Highly efficient Bayesianjoint inversion for receiver-based data and its application to lithosphericstructure beneath the southern Korean Peninsula Geophys J Int 206(1)328ndash344

Kind R Ni J Zhao W Wu J Yuan X Zhao L amp Hearn T 1996Evidence from earthquake data for a partially molten crustal layer insouthern Tibet Science 274(5293) 1692ndash1694

Kolb JM amp Lekic V 2014 Receiver function deconvolution using trans-dimensional hierarchical Bayesian inference Geophys J Int 197(3)1719ndash1735

Kosarev GL Petersen NV Vinnik LP amp Roecker SW 1993 Receiverfunctions for the Tien Shan analog broadband network contrasts in theevolution of structures across the Talasso-Fergana fault J geophys ResSolid Earth 98(B3) 4437ndash4448

Kumar MR amp Bostock MG 2008 Extraction of absolute P velocity fromreceiver functions Geophys J Int 175(2) 515ndash519

Langston CA amp Liang C 2008 Gradiometry for polarized seismic wavesJ geophys Res Solid Earth 113(B8)

Ledoit O amp Wolf M 2004 A well-conditioned estimator for large-dimensional covariance matrices J Multivariate Anal 88(2) 365ndash411

Ligorria JP amp Ammon CJ 1999 Iterative deconvolution and receiver-function estimation Bull seism Soc Am 89(5) 1395ndash1400

Li J Song X Zhu L amp Deng Y 2017 Joint inversion of surfacewave dispersions and receiver functions with P velocity constraintsapplication to Southeastern Tibet J geophys Res Solid Earth 1227291ndash7310

Li M Zhang S Bodin T Lin X amp Wu T 2018 Transdimensionalinversion of scattered body waves for 1D S-wave velocity structuremdashapplication to the Tengchong volcanic area Southwestern China J AsianEarth Sci 159 60ndash68

Li X et al 2003 Receiver function study of the Hellenic subductionzone imaging crustal thickness variations and the oceanic Moho of thedescending African lithosphere Geophys J Int 155(2) 733ndash748

Malinverno A 2000 A Bayesian criterion for simplicity in inverse problemparametrization Geophys J Int 140(2) 267ndash285

Malinverno A 2002 Parsimonious Bayesian Markov chain Monte Carloinversion in a nonlinear geophysical problem Geophys J Int 151(3)675ndash688

Marshak S Domrois S Abert C Larson T Pavlis G Hamburger Mamp Chen C 2017 The basement revealed tectonic insight from a digi-tal elevation model of the Great Unconformity USA cratonic platformGeology 45(5) 391ndash394

Mooney WD(2015) Crust and lithospheric structuremdashglobal crustal struc-ture in Treatise of Geophysics 2nd edn Vol 1 pp 339ndash390 Elsevier

Nelson KD Baird DJ Walters JJ Hauck M Brown LD Oliver JEamp Sloss LL 1993 Trans-Hudson orogen and Williston basin in Montanaand North Dakota new COCORP deep-profiling results Geology 21(5)447ndash450

Olugboji TM Lekic V amp McDonough W 2017 A statistical assessmentof seismic models of the US continental crust using Bayesian inversion ofambient noise surface wave dispersion data Tectonics 36(7) 1232ndash1253

Owens TJ Zandt G amp Taylor SR 1984 Seismic evidence for an an-cient rift beneath the Cumberland Plateau Tennessee a detailed analysisof broadband teleseismic P waveforms J geophys Res Solid Earth89(B9) 7783ndash7795

Piana Agostinetti N amp Malinverno A 2010 Receiver function inversionby trans-dimensional Monte Carlo sampling Geophys J Int 181(2)858ndash872

Reading A Kennett B amp Sambridge M 2003 Improved inversion forseismic structure using transformed S-wavevector receiver functions re-moving the effect of the free surface Geophys Res Lett 30(19)

Rudnick RL amp Fountain DM 1995 Nature and composition of thecontinental crust a lower crustal perspective Rev Geophys 33(3) 267ndash309

Rychert CA amp Harmon N 2016 Stacked P-to-S and S-to-P receiverfunctions determination of crustal thickness Vp and Vs the H-V stackingmethod Geophys Res Lett 43(4) 1487ndash1494

Shapiro NM Campillo M Stehly L amp Ritzwoller MH 2005 High-resolution surface-wave tomography from ambient seismic noise Science307(5715) 1615ndash1618

Shen W amp Ritzwoller MH 2016 Crustal and uppermost mantle structurebeneath the United States J geophys Res Solid Earth 121(6) 4306ndash4342

Shen W Ritzwoller MH amp Schulte-Pelkum V 2013 A 3-D model of thecrust and uppermost mantle beneath the Central and Western US by jointinversion of receiver functions and surface wave dispersion J geophysRes Solid Earth 118(1) 262ndash276

Sivia D amp Skilling J 2006 Data Analysis A Bayesian Tutorial OUPOxford

Tkalcic H Pasyanos ME Rodgers AJ Gok R Walter WR amp Al-Amri A 2006 A multistep approach for joint modeling of surfacewave dispersion and teleseismic receiver functions implications for litho-spheric structure of the Arabian Peninsula J geophys Res Solid Earth111(B11)

Ward KM Zandt G Beck SL Christensen DH amp McFarlin H 2014Seismic imaging of the magmatic underpinnings beneath the Altiplano-Puna volcanic complex from the joint inversion of surface wave dispersionand receiver functions Earth planet Sci Lett 404 43ndash53

Whitmeyer SJ amp Karlstrom KE 2007 Tectonic model for the Proterozoicgrowth of North America Geosphere 3 (4) 220ndash259

Yeck WL Sheehan AF amp Schulte-Pelkum V 2013 Sequential H-κ stacking to obtain accurate crustal thicknesses beneath sedimentarybasins Bull seism Soc Am 103(3) 2142ndash2150

Yu Y Song J Liu KH amp Gao SS 2015 Determining crustal structurebeneath seismic stations overlying a low-velocity sedimentary layer usingreceiver functions J geophys Res Solid Earth 120(5) 3208ndash3218

Zelt BC amp Ellis RM 1999 Receiver-function studies in the Trans-Hudson orogen Saskatchewan Can J Earth Sci 36(4) 585ndash603

Zhang H Lee S Wolin E Bollmann TA Revenaugh J Wiens DA ampStein S 2016 Distinct crustal structure of the North American Midcon-tinent Rift from P wave receiver functions J geophys Res Solid Earth121(11) 8136ndash8153

Zorin YA Mordvinova VV Turutanov EK Belichenko BG Arte-myev AA Kosarev GL amp Gao SS 2002 Low seismic velocity layersin the Earthrsquos crust beneath Eastern Siberia (Russia) and Central Mon-golia receiver function data and their possible geological implicationTectonophysics 359(3ndash4) 307ndash327

Ozalaybey S Savage MK Sheehan AF Louie JN amp Brune JN 1997Shear-wave velocity structure in the northern Basin and Range provincefrom the combined analysis of receiver functions and surface waves Bullseism Soc Am 87(1) 183ndash199

S U P P O RT I N G I N F O R M AT I O N

Supplementary data are available at GJI online

Figure S1 Individual receiver functions at station C25A sortedby the backazimuth (left panel top right panel for zoomed-in viewbetween 300 and 321) Bottom right-hand panel shows the averageRF at different bins based on their ray parameters Individual RFsare coloured based on their bin number in the left- and top right-handpanel using the same colour scheme as bottom right-hand panel

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Figure S2 Same as Fig S1 but for C31AFigure S3 Same as FigS3 but for C35AFigure S4 Left panel Vs depth distributions retrieved using trans-dimensional Bayesian inversion of SWD and Ps RF data from sta-tion C25A-TA (right red) The ensemble solutions are displayedas probability density functions at each depth with warmer colourscorresponding to higher posterior probabilities and the solid redline denoting the 5 per cent trimmed mean of the posterior Middlepanel transition probability of the Vs ensemble calculated at ev-ery kilometre Note that the transition probability only takes intoaccount the occurrences of the velocity change not the changeof value associated with them Therefore large amplitude veloc-ity changes that have a low probability show up as simply lowprobability ones in the transition probability plots Conversely highprobability but low amplitude velocity changes show up as highprobabilities of transition Right panel from top to bottom-handRayleigh wave dispersion Love wave dispersion and original Psreceiver function data fit Data are denoted in red while values pre-dicted by the ensemble solution are plotted as probability densityfunctions The inversion scheme is described in the detailed methoddescription section in the supporting informationFigure S5 Same as Fig S4 but for station C31A-TAFigure S6 Same as Fig S4 but for station C35A-TAFigure S7 Left panel Vs depth distributions at the top 15 km re-trieved using transdimensional Bayesian inversion of surface wavedispersion and Ps receiver function data The ensemble solutionsare displayed as probability density functions at each depth withwarmer colours corresponding to higher posterior probabilities andthe solid red line denoting the 5 per cent trimmed mean of the pos-terior Right-hand panel transition probability of the Vs ensemblecalculated at every 100 mFigure S8 Same as Fig S4 except that the resonance removal filterhas been applied to Ps receiver function for C25A-TAFigure S9 Same as Fig S5 but SWD in the 15ndash40 s range is usedhere instead of the 5ndash40 s period range used elsewhereFigure S10 Left-hand panel Vs depth distributions retrieved usingtransdimensional Bayesian inversion of surface wave dispersiondata from station C31A-TA The ensemble solutions are displayedas probability density functions at each depth with warmer colourscorresponding to higher posterior probabilities and the solid red

line denoting the 5 per cent trimmed mean of the posterior Right-hand panel Rayleigh (top) and Love (bottom) wave dispersion datafit Data are denoted in red colour while values predicted by theensemble solution are plotted as probability density functionsFigure S11 Left panel Vs depth distributions retrieved using trans-dimensional Bayesian inversion of Ps RF data from station C31A-TA (right red) The ensemble solutions are displayed as probabilitydensity functions at each depth with warmer colours correspond-ing to higher posterior probabilities and the solid red line denotingthe 5 per cent trimmed mean of the posterior Right-hand paneloriginal Ps receiver function data fit Data are denoted in red whilevalues predicted by the ensemble solution are plotted as probabilitydensity functionsFigure S12 Left panel Vs depth distributions retrieved using trans-dimensional Bayesian inversion of synthetic surface wave disper-sion and Ps receiver function data The ensemble solutions are dis-played as probability density functions at each depth with warmercolours corresponding to higher posterior probabilities and the solidred line denoting the 5 per cent trimmed mean of the posterior Thetarget model (black dashed lines) is used to generate synthetic dataRight-hand panel transition probability of the V ensemble calcu-lated at every kilometreFigure S13 Same as Fig S10 but for C25A-TAFigure S14 Posterior of transdimensional Bayesian inversion ofsurface wave dispersion and sediment-corrected receiver functionsfor synthetic model (shown in black dashed line) The ensemble so-lutions are displayed as probability density functions at each depthwith warmer colours corresponding to higher posterior probabili-ties and the solid red line denoting the 5 per cent trimmed meanof the posterior Right-hand panel From top to bottom Rayleighwave dispersion Love wave dispersion and original Ps receiverfunction data fit Data are denoted in red while values predicted bythe ensemble solution are plotted as probability density functionsTable S1 Assumed free-surface velocities for stations C25A C31Aand C35A

Please note Oxford University Press is not responsible for the con-tent or functionality of any supporting materials supplied by theauthors Any queries (other than missing material) should be di-rected to the corresponding author for the paper

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Figure 1 (a) Sediment thickness (Marshak et al 2017) across the study area (magenta box in inset) Transportable Array (TA) stations (triangles) Redtriangles show the stations where sediment correction is not needed green triangles show the stations where the sediment correction are applied in order toretrieve reliable posterior The green triangles with black contour are the stations where spurious low velocity zones are resolved when sediment correction isnot applied to RFs for the joint inversion (b) Ps RFs and (c) Love wave phase velocities at the TA stations shown in (a) sorted by longitude from west to eastThree stations are highlighted in (b) as they will be discussed in detail in the paper

east to west (eg Nelson et al 1993 Marshak et al 2017) andutilize data from EarthScope Transportable Array

At each station we compute P-to-s receiver functions using300 s three-component waveforms around the P arrival time fromMw gt 55 events at 30ndash90 epicentral distance which are trans-formed into the PndashSV system using the free-surface transform ma-trix (Kennett 1991) Optimal free-surface velocities are obtainedby minimizing the SV energy on the P component at the time ofthe P arrival and are listed in Table S1 It has been shown thatRFs in PndashSVndashSH system yield superior constraints on subsurfacestructure compared to ZndashR receiver functions (Reading et al 2003)We follow the Abt et al (2010) procedure and cull the data set toinclude data with a minimum Z-to-R cross correlation of 03 and amaximum 25 s discrepancy between the automatically determinedarrival time and prediction for ak135 We window the P and SVwaveforms prior to deconvolution and apply a fourth order Butter-worth bandpass filter to waveforms of 003ndash1 Hz We then use the

iterative time domain deconvolution with Gaussian half-amplitudehalf-width of sim05 s to calculate the receiver functions (Ligorria ampAmmon 1999)

These data selection criteria yield between 76 and 338 RFs at eachstation which we divide into 2ndash6 equal-sized bins based on theirray parameters to explicitly account for ray-parameter dependenceof RF waveforms In each RF bin we apply bootstrap sampling tocompute the average Ps RF and estimate its uncertainty Figs S1ndashS3show the individual Ps RFs as well as binned-average Ps RFs forthe three stations on which we focus our discussion in this paperIn these figures individual RFs are coloured according to their ray-parameter bin to illustrate that the binning by ray parameter allowsus to account for potential amplitude variations within the RF Dueto the limited deployment time (18ndash24 months) of the TransportableArray RF analyses using TA data generally suffer from incompletebackazimuthal coverage In this study we plot the RFs with respectto backazimuth to make sure they do not exhibit strong signs of

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Spurious low velocity zones in joint inversions of surface ... · Seismic wave conversions and...

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Transcript of Spurious low velocity zones in joint inversions of surface ... · Seismic wave conversions and...