Articles | Volume 8, issue 5
Solid Earth, 8, 969–986, 2017
Solid Earth, 8, 969–986, 2017

Method article 28 Sep 2017

Method article | 28 Sep 2017

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

Shaolin Liu1, Dinghui Yang1, Xingpeng Dong1, Qiancheng Liu2, and Yongchang Zheng3 Shaolin Liu et al.
  • 1Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China
  • 2King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
  • 3Department of Liver Surgery, Peking Union Medical College Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, 100730, China

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.

Short summary
Teleseismic wave adjoint tomography is able to image the deep structure of the lithosphere. Here we proposed the element-by-element spectral-element method (EBE-SEM) for efficient teleseismic wave modeling. A detailed discussion of the teleseismic seismic incident boundary condition and PML absorbing boundary condition for the scattered waves are presented. Beside the high efficiency of EBE-SEM for the forward modeling of teleseismic waves, it is able to easily construct misfit kernels.