Abstract
Abstract. The forward modeling of a scalar wave equation plays an important role in the numerical geophysical computations. The finite-difference algorithm in the form of a second-order wave equation is one of the commonly used forward numerical algorithms. This algorithm is simple and is easy to implement based on the conventional grid. In order to ensure the accuracy of the calculation, absorption layers should be introduced around the computational area to suppress the wave reflection caused by the artificial boundary. For boundary absorption conditions, a perfectly matched layer is one of the most effective algorithms. However, the traditional perfectly matched layer algorithm is calculated using a staggered grid based on the first-order wave equation, which is difficult to directly integrate into a conventional-grid finite-difference algorithm based on the second-order wave equation. Although a perfectly matched layer algorithm based on the second-order equation can be derived, the formula is rather complex and intermediate variables need to be introduced, which makes it hard to implement. In this paper, we present a simple and efficient algorithm to match the variables at the boundaries between the computational area and the absorbing boundary area. This new boundary-matched method can integrate the traditional staggered-grid perfectly matched layer algorithm and the conventional-grid finite-difference algorithm without formula transformations, and it can ensure the accuracy of finite-difference forward modeling in the computational area. In order to verify the validity of our method, we used several models to carry out numerical simulation experiments. The comparison between the simulation results of our new boundary-matched algorithm and other boundary absorption algorithms shows that our proposed method suppresses the reflection of the artificial boundaries better and has a higher computational efficiency.
Highlights
Modeling of a seismic wave field is accomplished by simulating the pattern of the seismic waves as they propagate through various geologic media and computing the simulated measurements at observation points on the Earth’s surface or underground, given that the underground medium’s structure and the relevant physical parameters are known
We propose a new boundary-matched algorithm that can bridge the gap between an staggered grid (SG)-based perfectly matched layer (PML) algorithm and a conventional grid (CG)-based numerical simulation of a seismic wave field with neither introduction of intermediary variables nor reformulation of the PML equations
We propose a new boundary-matched algorithm that effectively combines the CG scheme in the computational area and the SG scheme in the PML boundary conditions, while preserving the high computational efficiency of the CG scheme and the good absorption effect of PML boundary conditions
Summary
Modeling of a seismic wave field is accomplished by simulating the pattern of the seismic waves as they propagate through various geologic media and computing the simulated measurements at observation points on the Earth’s surface or underground, given that the underground medium’s structure and the relevant physical parameters are known. In order to preserve the original efficiency of the PML boundary processing method as well as the accuracy and efficiency of the CG scheme, it is worth trying to integrate the classic first-order PML algorithm into the CG finite-difference scheme in a second-order system and make it easy to implement. We propose a new boundary-matched algorithm that uses a CG finite-difference scheme within a limited computational area and an SG finitedifference scheme in a PML area. The proposed algorithm was evaluated by comparing its absorption efficiency and computational cost with those of the classic SG PML method, the second-order PML method (CG scheme both in computational area and PML area) introduced by Pasalic and McGarry (2010), and the hybrid ABC method The numerical experimental results indicated that our algorithm provides an excellent absorption effect and was easier to implement
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