Mantle flow under the western United States from shear wave splitting
Introduction
Parts of the upper mantle are seismically anisotropic and particularly shear wave splitting from SKS waves has often been used to infer deformation and flow at depth [1], [2]. Especially in continental regions such studies may be used to constrain the degree of lithosphere-mantle coupling [3], [4], an issue that is still debated. We wish to contribute to this discussion and test if a geodynamic model of mantle flow and inferred lattice preferred orientation (LPO) of olivine can explain the observed anisotropy. We focus on splitting observations in the westernmost United States (Fig. 1), for several reasons: the data coverage there is better than in geologically more simple regions such as oceanic plates and can be expected to improve significantly through the EarthScope program. For a continental region, the setting is relatively simple as the region is tectonically young and underlain by slow velocity anomalies, indicating a thin lithosphere [e.g. [5]]. Lastly, previous interpretations of the data have invoked a variation of the polarization orientation of the fastest shear wave (fast azimuth) with depth from parallel to the San Andreas Fault in the shallow mantle [6], [7], [8] to close to E–W deeper [6], [9], [10]. The splitting signal along the San Andreas has recently also been compared with the tectonic setting in New Zealand using a model that includes lateral viscosity contrasts in the lithosphere across the plate boundary [4].
Of particular interest here is the model by Silver and Holt [13] (hereafter: SH02), who used surface strain-rates from geodesy and SKS splitting to infer an EW oriented return flow underneath North America (in a hotspot reference frame), whereas the surface motion of the plate is NESW (in both hotspot and no-net-rotation reference frames). In the kinematic description chosen by SH02, a complete decoupling of the lithosphere from the underlying asthenospheric flow is suggested. Here, we substantiate our earlier findings that an alternative model with a continuum mechanics treatment of plate motion and underlying mantle flow fits the data just as well for typical radial viscosity profiles, though with a low viscosity, asthenospheric channel [14]. We use a global circulation model similar to Becker et al. [15], with recent improvements due to inclusion of the Kaminski and Ribe [16] method of predicting LPO development and treatment of lateral variations in viscosity [17], [18], though we do not fully explore the latter at this point. To generate synthetic splitting that is as close as possible to the published seismological results, we improve on Hall et al.'s [19] and Fouch et al.'s [48] studies and compute full waveforms. We show that not only fast azimuths but also the amplitudes of delay times can be explained by mantle-based LPO anisotropy, allowing inferences on the accumulated finite strain. A large degree of waveform complexity is predicted, which casts doubt on simple interpretations of anisotropy as being due to one or two layers with hexagonal symmetry in the horizontal plane. Models that include density anomalies due to geodynamic subduction models [20], [21] lead to reduced misfits compared to those based on plate-motion driven flow only, or based on density inferred from global shear wave tomography. We find that the inferred density structure of the mantle appears to have the strongest effect on anisotropy predictions and flow, compared to other uncertainties such as lateral viscosity variations. It may thus be possible to use anisotropy for tests of models of the tectonophysical history of the region [cf. [22]].
Section snippets
Data
Fig. 1 shows available shear wave splitting data for the study region, and the subset selected for our study from [6], [9]. Moving east from the Pacific to the North American plate, fast propagation directions trend roughly NW–SE and turn in the plate boundary region to a more W–E orientation. Data from different studies agree overall on regional scales, but there are large variations in splitting at individual stations depending on event back-azimuth. Such variations require a departure from
Modeling anisotropy
We are mainly considering sub-lithospheric anisotropy, but recognize the potentially complicating nature of the crust and lithospheric mantle in the sense of carrying frozen-in anisotropy from past tectonics. There may also be brittle damage anisotropy with a more complicated relationship to large-scale viscous deformation than mantle LPO. As we will show, the match of mantle-based LPO predictions to observations is good, implying either coherence of mantle and lithospheric deformation, or a
Mantle flow
Global mantle flow in a spherical shell is estimated based on prescribing plate motions on the surface while the core–mantle boundary is mechanically free-slip [15]. The buoyancy driven component of flow, and lateral viscosity variations for some models, are inferred from seismic velocity anomalies as imaged and inferred from a range of tomography and subduction models, analyzed in detail in [34]. We have verified that the buoyancy forces in such models would lead to realistic plate velocities
LPO fabrics
There is field and laboratory evidence on how the crystallographic axes of olivine, an inherently anisotropic mineral, align with shear [e.g. [44], [45]], and mineral physics theories allow quantitative estimates of LPO development [46], [16]. Anisotropy has been modeled on regional and global scales [e.g. [47], [19], [48], [13], [49], [15], [50]], and such linked geodynamic and seismic models successfully reproduce part of the observed structure. Recent work has focused on evaluating some of
SKS splitting
It is well known that fast azimuths of shear wave splitting measurements depend on back-azimuth for single layers whose anisotropy is not purely hexagonal with axis oriented in the horizontal, and splitting measurements suffer from non-linear superposition effects if anisotropy varies spatially [63], [64], [65]. However, such important geometries are rarely taken into account for geodynamic interpretation. Hall et al. [19] and Fouch et al. [48] perhaps achieved the greatest seismological
Results
Fig. 2 compares modeled velocities at different layers with predicted fast seismic azimuth, as visualized by hexagonal axes, at depth. (We only show TI axes for reference, the full tensor is used for the seismological modeling below.) For this particular region and flow model at ξc = 1, the depth averaged mean anisotropy is 7.6% for tensor norms. Out of this, the hexagonal symmetry component makes up ∼ 79% [cf. [62], [18]], the largest remainder, ∼ 17% of the total, is orthorhombic. The strength of
Discussion
Fig. 5 shows model performance in terms of 〈Δα〉 and 〈Δδ〉 for all experiments performed (see Table 1), separated by saturation target strains ξc and assumptions on the depth extent of LPO anisotropy. For a “good” model, we will consider low Δα and Δδ as criteria, but discuss those separately. A wide range of models with different assumptions on density or viscosity structures are able to fit the data quite well. We show results where all the computed LPO upper mantle anisotropy is used above
Conclusions
Models such as ours indicate that regional seismic anisotropy in the western US is consistent with simplified mantle flow models, substantiating earlier conclusions based on global datasets. Splitting can be explained both in terms of amplitudes and fast azimuths using kinematically based methods for computing the development of LPO during mantle flow [16], where preferred geodynamic models exhibit a return current at depth driven by the Farallon anomaly. This is similar to what was suggested
Acknowledgments
This work was inspired by extensive discussions with P. Silver, for which we are grateful. We also thank R.D. van der Hilst, M. Savage, and an anonymous reviewer for their constructive and helpful comments, E. Kaminski for providing D-REX, H. Schmeling for comments, A. McNamara, J. van Hunen, and E. Tan for the help with Citcom, S. Zhong, L. Moresi, M. Gurnis and others involved in geoframework.org for sharing this code, W. Menke for providing his splitting routines, S. Chevrot for the help
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