influence of observed mantle anisotropy on isotropic...

Influence of observed mantle anisotropy on isotropictomographic models

S. M. Lloyd and S. van der LeeDepartment of Earth and Planetary Sciences, Northwestern University, 1850 Campus Drive, Evanston, Illinois60208-2150, USA ([email protected])

[1] There is a potential for isotropic tomographic models to be biased by ignored anisotropy; anisotropycould be mapped as artificial isotropic velocity perturbations. We investigate the distribution and strengthof this potential bias for three tomographic S velocity models based on regional S and Rayleigh waveforms.We use observed SKS delay times and fast-axis orientations to compute equivalent S velocity perturbationsfor each wave path used for the tomographic models. These synthetic perturbations are then combined intoa three-dimensional isotropic model which reflects the potential bias in the actual tomographic model. Wequantify anisotropic bias and find that it indeed exists in the isotropic tomographic models investigatedhere. This bias gets weaker with increasing depth of the anisotropic material, and compared to the isotropicvelocity anomalies typically interpreted by tomographers, the bias from anisotropy is small.

Components: 3559 words, 3 figures.

Keywords: anisotropy; tomography; surface waves.

Index Terms: 7270 Seismology: Tomography (6982, 8180); 7255 Seismology: Surface waves and free oscillations; 7208

Seismology: Mantle (1212, 1213, 8124).

Received 21 February 2008; Revised 16 May 2008; Accepted 20 May 2008; Published 9 July 2008.

Lloyd, S. M., and S. van der Lee (2008), Influence of observed mantle anisotropy on isotropic tomographic models,

Geochem. Geophys. Geosyst., 9, Q07007, doi:10.1029/2008GC001997.

1. Introduction

[2] Inversion of traveltimes or waveforms of seis-mic waves for three-dimensional seismic velocitymodels is a common procedure in seismology,finding widespread application. The resultingtomographic models provide insights into theEarth’s interior structure and constrain the temper-ature, composition, and associated dynamics of themantle. Interpreting the seismic velocities requiresa thorough understanding of the complex uncer-tainties and errors. One such error could come fromignoring azimuthal anisotropy. Although observa-tions of split SKS phases, for example, provide

evidence for anisotropy, many tomographic modelshave been obtained under the assumption that theseismic velocity structure of the Earth is isotropic.This anisotropy might thus have biased the isotropicvelocity models. Sobolev et al. [1999] investigatedthis bias in isotropic P velocity models inferred fromteleseismic P wave traveltimes. They found thatanisotropy-induced artifacts appear for a varietyof anisotropic structures. We investigate this bias inisotropic S velocity models inferred from regionalS and surface waveforms.

[3] Sobolev et al. [1999] illustrate that quantifyinganisotropic bias is not straightforward. This isbecause the location and intensity of the anisotropic

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effects depend on how azimuthally uniform thewave path coverage is in an anisotropic region. Ifseismic waves traverse an anisotropic body pre-dominately parallel to the fast velocity axis, seis-mic velocity at the location will be overestimatedin the tomographic model. Conversely, if the wavestravel predominantly in the slow-velocity direction,velocities there will be underestimated. Only if ananisotropic region is perfectly uniformly sampledby the seismic waves used for the tomographicinversion can its mean velocity be well estimated.In reality, study regions are imperfectly sampled.Thus, the strength of anisotropic bias at a givenlocation in a tomographic model is expected to notonly depend on the strength of the observedanisotropy at that location but also on the wavepath coverage. To estimate the bias, it is necessaryto separate the data into an isotropic and ananisotropic component. In this study we investigateand quantify the potential anisotropic bias in iso-tropic S velocity models due to ignoring azimuthalanisotropy [e.g., Marone and Romanowicz, 2007;Montagner and Griot, 2000]. To this end weconvert the delay times and orientations of observedshear wave splitting into equivalent S velocityperturbations for each wave path. We invert theseperturbations to image potential bias and subtractthem from observed data before the inversion for ananisotropy corrected isotropic model. We do sofor three 3-D tomographic S velocity models:NA04 for North America [van der Lee andFrederiksen, 2005], EAV03 for the Mediterraneanregion [Marone et al., 2004], and SA99 forSouth America [van der Lee et al., 2001] toquantify the possible bias caused by ignoringazimuthal anisotropy.

2. Method

2.1. Inversion

[4] The Partitioned Waveform Inversion (PWI)[Nolet, 1990; van der Lee and Nolet, 1997] is atwo-step method, which was used to obtain thethree tomographic models under investigation.First, a nonlinear waveform inversion is performedfor each wave path separately, to determine uncor-related path averaged linear constraints on thevelocity structure between respective source andreceiver pairs. In a second step, these constraintsare combined in an inversion to infer a 3-D Svelocity model. This system of linear equationsinverted in this second step is

Gm ¼ dobs; ð1Þ

where m is the unknown model vector, represent-ing either SA99, EAV03, or NA04, depending onwhich data was used in the first step of the PWI todetermine the data vector dobs. Ideally the wave-forms fitted in the first step constrain purelyisotropic signal, such that the resulting linearequations are free from anisotropic effects. Inreality this is not likely the case, and equation (1)may be written as

G miso þmbiasð Þ ¼ diso þ daniso: ð2Þ

where

miso þmbias ¼ m ð3Þ

and

diso þ daniso ¼ dobs: ð4Þ

We estimate a likely anisotropic contribution to thedata vector daniso from delay times and orientationsof the fast velocity axes of split shear waves. Wethen consider the following two equations for theanisotropic bias mbias and an anisotropy-correctedisotropic model miso:

Gmbias ¼ daniso ð5Þ

Gmiso ¼ dobs � daniso: ð6Þ

2.2. Anisotropy Data Vector

[5] The inversion described above requires theanisotropy data vector daniso. It is derived fromthe observed azimuthal anisotropy in three steps:(1) interpolation of observed anisotropy over aregular grid (see auxiliary material Text S11),(2) conversion to equivalent orientation-dependentS velocity perturbations that produce the observedsplitting delay times and orientations, and (3) aver-aging of the orientation-dependent equivalent Svelocity perturbations along each wave path. Theresult of these three steps is a path averaged 1-Dvelocity model containing the anisotropic effects foreach wave path. It is described by uncorrelatedparameters, which, together with the constraints forthe other wave paths, form daniso.

[6] In constructing our anisotropy data vector welimit ourselves to the assumptions made in thestudies that provide the input data (observed

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anisotropy). Thus we consider only orthorhombicanisotropy (which is the configuration of, e.g.,olivine, wadsleyite and ringwoodite [Mainprice etal., 2000]) with a horizontal symmetry axis asassumed in many SKS studies [Savage, 1999].Similarly we do not consider variations in azimuthof anisotropy with depth as the observations typi-cally constrain such variations insufficiently. Thedepth and the thickness of the anisotropic regioncannot be well constrained from analysis of splitshear waves. It is possible that all the inferredanisotropy is in the lithosphere [e.g., Silver,1996], in the sublithospheric mantle [e.g., Vinniket al., 1992], or distributed over lithosphere andasthenosphere [e.g., Fouch et al., 2000; Marone etal., 2007]. We explore scenarios for the distributionof anisotropy using natural boundaries of the Earth.Because independent constraints on crustal thick-ness were used in the isotropic tomographic inver-sions, crustal structure is effectively separated frommantle structure. Therefore we ignore crustalanisotropy and pick the Moho (CRUST2.0 [Bassinet al., 2000]) as the upper boundary for possibleanisotropy occurrence. However, since SKS split-ting is affected by crustal anisotropy our projectionof all SKS splitting into the mantle tends tooverestimate anisotropy in the mantle slightly.The lithosphere-asthenosphere boundary definesan intermediate depth boundary, for which weuse the thermal model TC1 [Artemieva, 2006].TC1 requires xenolith data to determine the geo-therm in tectonically active regions; since these arenot always available, for example in the Mediter-ranean, it is heterogeneously resolved. Nonethelessit is a better approximation than a constant depthboundary. The diffusion-dislocation creep transi-tion marks the deepest level to which anisotropymight easily reach [e.g., Karato and Wu, 1993]. Weposition this transition at 200 km below the bottomof the lithosphere, but nowhere deeper than 300 km[Podolefsky et al., 2004; Mainprice et al., 2005].We define two end-member cases with all theanisotropy either in the mantle lithosphere orentirely below the lithosphere. In addition wedefine an intermediate case, with the anisotropybeing equally strong in both regions. In regionswhere the lithosphere is thin (e.g., the westernmargin of North America) its thickness is too smallto physically accommodate all of the observedanisotropy. In order to reproduce the observedSKS delay times, the lithospheric velocity in thefast direction would have to be up to dV = 900 m/sgreater than in the slow direction. If all olivinecrystals were aligned, this difference would be atmost 500 m/s [e.g., Abramson et al., 1997; Brugger,

1965]. Since olivine only accounts for about half ofthe composition of the lithosphere we limit themaximum possible velocity difference to 250 m/sand assume the remainder of the observed anisotro-py originates below the lithosphere. However, thislimit appears to have a negligible effect on ourresults and conclusions.

[7] The accumulated SKS delay time caused by theanisotropic velocity difference dV within one azi-muthally anisotropic layer of thickness dz is

dt ¼ dzVS0 � 1

2dV

� dzVS0 þ 1

2dV

: ð7Þ

After reordering and dropping dV2 terms (since inthe case of weak anisotropy VS0

2�dV2) we obtain

dt ¼ dzdVV 2S0� 1

2dV 2

� dzdVV 2S0

; ð8Þ

which is the same expression as given byMontagner and Griot [2000]. The total SKS delaytime for multiple layers with identical fast axisdirection is

dt ¼Xn

i¼1

dzidVi

V 2S0i

: ð9Þ

Our hypothesized anisotropy distributions use amaximum of two layers (n = 2) with differentstrengths (wi) of the anisotropy. Substituting dVi =d �Vwi and assuming two layers we find anexpression for the velocity difference between thefast and the slow axes:

d�V ¼dtV 2

S01V 2S02

dz1w1V2S02

þ dz2w2V2S01

: ð10Þ

For each hypothesized anisotropy distribution wecalculate d�V at each point in the grid and calculatethe azimuth dependant horizontal velocities as seenby surface waves according to Montagner andGriot [2000]. We then use our sensitivity matrix Gto compute the effect of these velocities on our datafor each wave path. The effects of anisotropycombined for all wave paths (in our data set) aregrouped in a data vector daniso. This proceduretakes into account that Rayleigh wave sensitivitydiminishes with depth and that higher frequencyRayleigh waves sample shallower than lowerfrequency Rayleigh waves. We do not accountfor the evidence that SKS splitting may be morestrongly affected by upper layer anisotropy then by


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lower layer anisotropy [e.g., Rumker and Silver,1998; Saltzer et al., 2000], in part because we donot have details on the variation of frequencycontent of the individual SKS measurements fromthe more than 80 studies we used from theanisotropy database in step 1.

[8] Using the same parameterization and regulari-zation as in the original models, this data vectormay now be inverted for mbias, or can be used toremove the contribution from anisotropy from ourobserved data dobs. The corrected data is theninverted for an anisotropy-corrected model miso.

3. Results

[9] Figure 1 shows the anisotropic bias mbias forNA04 for all three anisotropy distributions and theisotropic velocity perturbations in NA04. Figures 2and 3 showmbias for EAV03 and SA99 only for theshallowest anisotropic case because this causes thestrongest bias and thus represents a worst-case end-member. For these end-member scenarios, auxiliarymaterial Figures S1–S4 compare the originalmodels with the respective anisotropy correctedmodels miso.

3.1. NA04

[10] Figure 1 shows that anisotropic bias could bepresent in model NA04 because the inversion ofthe equivalent S velocity perturbations yields non-zero values in mbias (henceforth we refer to thesepseudovelocity perturbations as dVbias). PositivedVbias indicates regions where the velocity ispossibly overestimated in NA04 because of ignor-ing anisotropy, while negative values indicateregions where the velocity may be underestimated.Anisotropic bias is observed for all hypothesizedanisotropy distributions, but they differ in themagnitude of the bias introduced. The strongestbias occurs in the 90 km slice of Figure 1a, whichwas obtained assuming all the anisotropy isconcentrated in the lithosphere. When the aniso-tropy is evenly distributed over the lithosphere andasthenosphere (Figure 1b), or if it is completely inthe asthenosphere (Figure 1c), the associatedanisotropic bias is much less. The distribution ofpositive and negative regions is the same for alldepths throughout the different hypothesizedanisotropy distributions. The largest positive (blue)bias is located beneath Northern California/southernOregon. Here, dVbias reaches values of up to

Figure 1. (a) Resulting anisotropic bias, mbias, for the case where the anisotropic material is assumed to be entirelyin the lithosphere. In regions with positive dVbias velocities in NA04 could be overestimated; in regions with negativedVbias they could be underestimated. (b) Same as Figure 1a, but for the anisotropy evenly distributed in thelithosphere and asthenosphere. (c) Same as Figure 1a, but for all the anisotropy in the asthenosphere. (d) The muchstronger isotropic velocity perturbations (compared to mbias) in NA04 [van der Lee et al., 2001].



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140 m/s. The largest negative bias (red) is beneaththe western Gulf of Mexico and southern Mexico.The dVbias of this anomaly is around �120 m/s andconnects to the less negative dVbias that pervadesthe Atlantic Ocean. Several patches within theUnited States show weaker bias (jVbiasj 100 m/s).Positive bias is imaged beneath Wyoming andColorado, as well as the east coast of the US.Canada also contains both positive and negativedVbias, but the amplitudes are relatively smallcompared to the ones observed in the US becausethe sparse SKS constraints on anisotropy there yieldsmooth anisotropic heterogeneity. Compared to theisotropic velocity perturbations dVS in NA04(Figure 1d), even the strongest anisotropic biasvisible for the worst-case scenario (all the aniso-tropy in the lithosphere) the anisotropic bias issmall.

[11] Because the effect of anisotropy is small, thevalidity of NA04 is not altered by our results.However, since several tectonic regions discussedby van der Lee and Frederiksen [2005] correlatewith the distribution of anisotropy (i.e., similargeographic extent of isotropic and anisotropic-biasfeatures) it is worth mentioning the effect ofanisotropy in these regions. For example, theyimage higher S velocities in the Atlantic uppermantle compared to the Pacific upper mantle, high

upper mantle S velocities beneath the Aleutian arc,and the absence of high velocities in the uppermantle beneath Wyoming. In all three cases, takingthe possible anisotropic bias into account wouldincrease the effects leading to these observations.Conversely, accounting for anisotropy might havea weakening effect on the North American cratonbeing disconnected from Greenland’s lithosphere.

3.2. EAV03

[12] Shallow anisotropy in the Mediterraneanregion produces dVbias at comparable strength asfor North American model NA04 (Figure 2, left).Positive bias (dVbias � 100 m/s) is found in thewesternmost Mediterranean region, the northernCarpathians and in eastern Turkey. Regions witha negative dVbias are beneath the British islands,most of the eastern Mediterranean Sea (from theIonian Sea eastward) and most of Northern Africa.For the part of the Atlantic included in EAV03,dVbias is mostly positive. This is likely due to thedirection of the wave paths traversing this regionand the fast S velocity direction both being pre-dominantly east–west.

[13] Features discussed by Marone et al. [2004]that are stronger after anisotropic correction arelow velocities beneath northern Algeria at 100–200 km depth and high velocities beneath 300 km,

Figure 2. Same as Figure 1 but for the Mediterranean. We only show mbias for the case where all the anisotropy isin the lithosphere.



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high velocities beneath the bay of Biscay, Italy,Adriatic Sea, Peloponnese and southern Greece,and low velocities beneath the Pannonian andMoesian basins. Features that become weaker arehigh velocities in the western Mediterranean andbetween 25�W and the European coast, low veloc-ities at the Mid-Atlantic Ridge, Azores, and beneaththe western part of the Iberian peninsula. However,as with NA04, we note that the bias is much weakerthan the lateral variations in isotropic velocities(Figure 2, right).

3.3. SA99

[14] SA99 differs from NA04 and EAV03 in thatdVbias is weaker and reaches peak values of ±80 m/s(Figure 3, left). This weakness is most likely aresult of the sparse constraints on anisotropy forthis continent. We identify two regions with highdVbias: the northwestern margin of south Americaand an east–west corridor in central South America.These two regions border a region of negative bias

in the eastern Amazon Basin. The observed varia-tions in dVbias are negligible compared to theisotropic velocity variations and maps of SA99(Figure 3, right). We therefore conclude that SA99is not significantly biased by known anisotropy.

4. Summary and Discussion

[15] For the three tomographic models investigatedin this study anisotropic bias does not seem tointroduce major artifacts. Anisotropic bias appearsto be strongest if the observed anisotropy origi-nates entirely in the lithosphere, in particular whenthe lithosphere is thin (e.g., western North America).If the anisotropy originates below the lithosphere, itwould yield smaller anisotropic bias. Correctingthe isotropic tomographic models for the estimatedanisotropic bias yields small corrections at most.This is encouraging in that ignoring azimuthalanisotropy in Rayleigh and S wave tomographicinversions with decent wave path coverage does

Figure 3. Same as Figure 2 but for South America.



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not appear to introduce significant artifacts.Maroneet al. [2007] reach similar conclusions for NorthAmerica. In addition, they find that radial anisotropypredominantly originates below the lithosphere. Ifazimuthal and radial anisotropy share this relativelydeep origin, the actual anisotropic bias in isotropicmodel NA04 would be less than that of thehypothesized worst-case end-member in this study.In eastern North America anisotropy seems to bedistributed over the lithosphere and asthenosphere[Fouch et al., 2000; Marone et al., 2007], likewiseyielding less bias than assumed in Figure 1a.Therefore we conclude that isotropic modelNA04 is not significantly biased by ignored azi-muthal anisotropy. Mediterranean model EAV03and South-American model SA99 appear similarlyrobust with respect to ignoring azimuthal anisotropy.

Acknowledgments

[16] This study began as an undergraduate research project at

the Federal Institute of Technology in Switzerland. We thank

Federica Marone and Christian Schmid for their help during

the initial stages of this study. This work was partially

supported by National Science Foundation grant EAR

0538267.

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