- 标题
- 摘要
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- 实验方案
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Second-order Scalar Wave Field Modeling with First-order Perfectly Matched Layer
摘要： 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.
关键词： seismic waves,second-order wave equation,boundary conditions,conventional-grid,absorption
更新于2025-09-10 09:29:36
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A method of solving the coefficient inverse problems of wave tomography
摘要： In this paper, the problem of nonlinear wave tomography is formulated as a coefficient inverse problem for a hyperbolic equation in the time domain. Efficient methods for solving the inverse problems of wave tomography for the case of transparent boundary conditions are presented. The algorithms are designed for supercomputers. We prove the Fréchet differentiability theorem for the residual functional and derive an exact expression for the Fréchet derivative in the case of a transparent boundary in the direct and conjugate problems. The expression for the Fréchet derivative of the residual functional remains valid if the experimental data are provided for only a part of the boundary. The effectiveness of the proposed method is illustrated by the numerical solution of a model problem of low-frequency wave tomography. The model problem is tailored to apply to the differential diagnosis of breast cancer.
关键词： Coefficient inverse problems,Wave tomography,Wave equation,Fréchet derivative,Supercomputer,Transparent boundary conditions
更新于2025-09-09 09:28:46
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Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schr?dinger and linearized stochastic Korteweg–de Vries equations
摘要： We establish weak convergence rates for noise discretizations of a wide class of stochastic evolution equations with non-regularizing semigroups and additive or multiplicative noise. This class covers the nonlinear stochastic wave, HJMM, stochastic Schr¨odinger and linearized stochastic Korteweg–de Vries equation. For several important equations, including the stochastic wave equation, previous methods give only suboptimal rates, whereas our rates are essentially sharp.
关键词： stochastic evolution equations,multiplicative noise,additive noise,linearized stochastic Korteweg–de Vries equation,stochastic Schr¨odinger,non-regularizing semigroups,weak convergence rates,HJMM,stochastic wave equation
更新于2025-09-04 15:30:14