Inferring the Oriented Elastic Tensor from Surface Wave Observations: Preliminary Application Across the Western United States

Radial and azimuthal anisotropy in seismic wave speeds have long been observed using surface waves and are believed to be controlled by deformation within the Earth’s crust and uppermost mantle. Although radial and azimuthal anisotropy reﬂect important aspects of anisotropic media, few studies have tried to interpret them jointly. We describe a method of inversion that interprets simultaneous observations of radial and azimuthal anisotropy under the assumption of a hexagonally symmetric elastic tensor with a tilted symmetry axis deﬁned by dip and strike angles. We show that observations of radial anisotropy and the 2 ψ component of azimuthal anisotropy for Rayleigh waves obtained using USArray data in the western United States can be ﬁt well under this assumption. Our inferences occur within the framework of a Bayesian Monte Carlo inversion, which yields a posterior distribution that reﬂects both variances of and covariances between all model variables, and divide into theoretical and observational results. Principal theoretical results include the following: (1) There are two distinct groups of models (Group 1, Group 2) in the posterior distribution in which the strike angle of anisotropy in the crust (deﬁned by the intersection of the foliation plane with Earth’s surface) is approximately orthogonal between the two sets. (2) The Rayleigh wave fast axis directions are orthogonal to the strike angle in the geologically preferred group of models in which anisotropy is strongly non-elliptical. (3) The estimated dip angle may be interpreted in two ways: as a measure of the actual dip of the foliation of anisotropic material within the crust, or as a proxy for another non-geometric variable, most likely a measure of the deviation from hexagonal symmetry of the medium. The principal observational results include the following: (1) Inherent S -wave anisotropy ( γ ) is fairly homogeneous vertically across the crust, on average, and spatially across the western United States. (2) Averaging over the region of study and in depth, γ in the crust is approximately 4.1 ± 2 per cent. γ in the crust is approximately the same in the two groups of models. (3) Dip angles in the two groups of models show similar spatial variability and display geological coherence. (4) Tilting the symmetry axis of an anisotropic medium produces apparent radial and apparent azimuthal anisotropies that are both smaller in amplitude than the inherent anisotropy of the medium, which means that most previous studies have probably underestimated the strength of anisotropy. results are summarized as posterior distributions of smoothly depth-varying inherent (unrotated) moduli (A or V PH , C or V PV , N V SH , L or V SV and F or η ) as well as dip and strike angles. The standard deviation of the posterior distribution deﬁnes the uncertainties in these quantities. Anisotropy can be summarized with the Thomsen parameters, inherent S -wave anisotropy ( γ ) and inherent P -wave anisotropy ( ε ), and either η or δ (which is the third Thomsen crust is by the better than the mantle γ (inherent S -wave anisotropy) is determined more tightly than ε (inherent P -wave anisotropy), we focus interpretation on γ in the crust as well as the tilt angles. Major results the