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The development of an efficient algorithm for teleseismic wave field\udmodeling is valuable for calculating the gradients of the misfit function\ud(termed <q>misfit gradients</q>) or Fréchet derivatives when the teleseismic\udwaveform is used for adjoint tomography. Here, we introduce an\udelement-by-element parallel spectral-element method (EBE-SEM) for the\udefficient modeling of teleseismic wave field propagation in a reduced geology\udmodel. Under the plane-wave assumption, the frequency–wavenumber (FK)\udtechnique is implemented to compute the boundary wave field used to construct\udthe boundary condition of the teleseismic wave incidence. To reduce the\udmemory required for the storage of the boundary wave field for the incidence\udboundary condition, a strategy is introduced to efficiently store the\udboundary wave field on the model boundary. The perfectly matched layers\udabsorbing boundary condition (PML ABC) is formulated using the EBE-SEM to\udabsorb the scattered wave field from the model interior. The misfit gradient\udcan easily be constructed in each time step during the calculation of the\udadjoint wave field. Three synthetic examples demonstrate the validity of the\udEBE-SEM for use in teleseismic wave field modeling and the misfit gradient\udcalculation

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