Increasing deployment of dense arrays has facilitated detailed structure imaging for tectonic investigation, hazard assessment and resource exploration. Strong velocity heterogeneity and topographic changes have to be considered during passive source imaging. However, it is quite challenging for ray-based methods, such as Kirchhoff migration or the widely used teleseismic receiver function, to handle these problems. In this study, we propose a 3-D passive source reverse time migration strategy based on the spectral element method. It is realized by decomposing the time reversal full elastic wavefield into amplitude-preserved vector P and S wavefields by solving the corresponding weak-form solutions, followed by a dot-product imaging condition to get images for the subsurface structures. It enables us to use regional 3-D migration velocity models and take topographic variations into account, helping us to locate reflectors at more accurate positions than traditional 1-D model-based methods, like teleseismic receiver functions. Two synthetic tests are used to demonstrate the advantages of the proposed method to handle topographic variations and complex velocity heterogeneities. Furthermore, applications to the Laramie array data using both teleseismic P and S waves enable us to identify several south-dipping structures beneath the Laramie basin in southeast Wyoming, which are interpreted as the Cheyenne Belt suture zone and agree with, and improve upon previous geological interpretations.

The spectral-element method (SEM) for simulating wave propagation is widely used with adjoint methods for full-waveform inversion. Typically, SEM is used to compute forward and adjoint wavefields, which is then applied to evaluate the Fréchet derivatives for updating the seismic structural model. The Hessian is rarely computed as the high computational and storage costs, although it can improve the accuracy of the model update and model convergence. Instead the approximate Hessian is determined, which is obtained with less computational effort. We present a method for simultaneously constructing Fréchet and Hessian kernels on the fly, which we call Multi-solver spectral-element and adjoint methods (Multi-SEM). Rather than storing all the wavefields, Multi-SEM is computed on the fly and requires only about a 2-fold computational cost when compared to the computation of Fréchet kernels. Numerical examples demonstrate the functionality of the method and the computer codes are provided with this contribution.

Adjoint tomography (i.e., full-waveform inversion) has been recently applied to ambient seismic noise and teleseismic P waves separately to unveil fine-scale lithospheric structures beyond the resolving ability of traditional ray-based traveltime tomography. In this study, we propose a joint inversion scheme that alternates between frequency-dependent traveltime inversions of ambient noise surface waves and waveform inversions of teleseismic P waves to take advantage of their complementary sensitivities to the Earth’s structure. We apply our method to ambient noise empirical Green’s functions from 60 virtual sources, direct P and scattered waves from 11 teleseismic events recorded by a dense linear array (～ 7 km station spacing) and other regional stations (～ 40 km average station spacing) in central California. To evaluate the performance of the method, we compare tomographic results from ambient noise adjoint tomography, full-waveform inversion of teleseismic P waves, and the joint inversion of the two data sets. Both applications to practical field data sets and synthetic checkerboard tests demonstrate the advantage of the joint inversion over individual inversions as it combines the complementary sensitivities of the two independent data sets towards a more unified model. The 3D model from our joint inversion not only shows major features of velocity anomalies and discontinuities in agreement with previous studies. but also reveals small-scale heterogeneities which provide new constraints on the geometry of the Isabella Anomaly and mantle dynamic processes in central California. The proposed joint inversion scheme can be applied to other regions with similar array deployments for high-resolution lithospheric imaging.