Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling

Abstract

Abstract. The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed "misfit gradients") or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-byelement parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

“…To accurately reconstruct the source wavefield, the wavefields at the boundary nodes need to be replaced by the corresponding stored correct wavefield values at each time step of the backward extrapolation of the source wavefield. In general, this reconstruction method shares similar ideas with the method proposed by Liu SL et al () in teleseismic wavefield modeling using the hybrid method. The storage cost is comparable to that of the method proposed by Liu SL et al () using the FD method.…”

“…Although this method can be applied to dissipative media, it still requires a huge amount of memory to save the wavefields between the adjacent restart time instants. Recently, Liu SL et al () proposed a memory‐efficient storage method at the interface of teleseismic wavefield modeling with a hybrid method that significantly reduces the storage demand.…”

On the Numerical Evaluation of Invertible Preconditioners Based on High-Order Discretizations of the Laplace Operator for Linear Systems

“…As an important research field in geophysics, seismic tomography is also an inverse problem from the view point of computing mathematics [22]. Its primary task is to take use of the seismic observation data at the surface to compute subsurface physical parameters, which is critical to explore the deep structure of the Earth [24].…”

“…Furthermore, the band structure of the corresponding finite difference based preconditioners are analyzed and we quantitatively derive the dependency between the bandwidth of preconditioners and the order of finite difference discretization to the Laplace operator. Due to the simplicity of the finite difference stencils when compared with finite element or other numerical schemes [24], the constructed high-order preconditioners have small bandwidth and the computing cost of the corresponding preconditioning processes can be saved. Then, the numerical experiments of both one-dimensional and two-dimensional inverse problems are performed to investigate our analysis and the obtained results illustrate the superiority of the proposed preconditioners when compared with classical methods in improving computing efficiency.…”

Passive Adjoint Tomography of the Crustal and Upper Mantle Beneath Eastern Tibet With a W2‐Norm Misfit Function

“…Waveform tomography has been developed in recent years to obtain high‐resolution seismic images of the Earth's interior by minimizing the misfit between predicted and observed waveform data (e.g., Fichtner et al, ; Lailly, ; Liu et al, ; Liu & Tromp, ; Tape et al, ). Adjoint tomography calculates sensitive kernels by convolving the forward wavefield and adjoint wavefield (Fichtner et al, 2006a, 2006b; Liu & Tromp, ; Tromp et al, ), which can be calculated efficiently by the spectral element method (Fichtner et al, ; Komatitsch & Tromp, 2002a, 2002b; Liu et al, ; Tape et al, ). Most of these studies employ the L2 norm of the misfit between synthetic and observed data in their inversions (e.g., Tape et al, ; Zhu et al, ; Chen et al, ; Fichtner & Villaseñor, ).…”