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-by-element 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.
Highlights
The increasing demand for high-resolution imaging of deep lithospheric structures requires the utilization of teleseismic datasets for waveform inversion
The element-byelement parallel spectral-element method (EBE-SEM) is specially designed for teleseismic wave modeling (i.e., Eq 9 is for teleseismic total wave field propagation if the proper teleseismic incident boundary condition is added and Eq 16 is for absorbing the scatted wave field), EBE-SEM can be directly used for wave field simulation of an earthquake that occurred in the interior of the model if a source term is added to Eq (9)
In the 2-D case, the element-by-element scheme is combined with the Chebyshev orthogonal polynomialbased SEM
Summary
The increasing demand for high-resolution imaging of deep lithospheric structures requires the utilization of teleseismic datasets for waveform inversion. S. Liu et al.: Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling full-wave field simulations are required to perform an adjoint tomography inversion (Tape et al, 2007, 2009). In addition to the large computational demand (CPU time) associated with the 3-D hybrid methods, satisfying the memory requirements for storing the boundary wave fields to construct teleseismic incident boundary conditions is another important issue that should be carefully considered. Tong et al (2015) adapted the Clayton and Engquist-type (CE-type) boundary condition (Clayton and Engquist, 1977) to interface the 1-D background analytical solution with a numerical solver on the boundary of a reduced model This treatment can both assign the teleseismic incident condition for the computational domain and absorb the scattered wave field from the interior of the heterogeneous model. The high efficiency of the EBE-SEM for teleseismic wave modeling and misfit gradient construction is demonstrated by using three numerical examples
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