Cubic B-spline based elastic and viscoelastic wave propagation method

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-08-30 DOI:10.1016/j.cam.2024.116236

Yaomeng Li , Feng Wang , Qiao Li , Chao Fu , Xu Guo

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引用次数: 0

Abstract

The requirement for high computational efficiency in inversion imaging poses challenges to further enhancing the accuracy of imaging large elastic and viscoelastic models. Considering that forward modeling serves as a prerequisite for inversion imaging, it is essential to introduce a wave propagation simulation method that can enhance simulation accuracy without significantly compromising computational speed. In our paper, cubic B-spline is introduced into the forward modeling of the wave equation. The B-spline collocation method offers a linear complexity for computation and exhibits fourth-order convergence in terms of computational errors. We also find that it can perfectly adapt to the boundary conditions of the perfectly matched layer in the forward modeling solution of the wave simulation. Several typical numerical examples, including 2-D acoustic wave equation, 2-D elastic wave propagation, and 2-D viscoelastic propagation in homogeneous media, are provided to validate its convergence, accuracy, and computational efficiency.

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基于立方 B 样条的弹性和粘弹性波传播方法

反演成像对计算效率的要求很高，这对进一步提高大型弹性和粘弹性模型的成像精度提出了挑战。考虑到前向建模是反演成像的先决条件，有必要引入一种既能提高模拟精度，又不会明显影响计算速度的波传播模拟方法。本文在波方程的正演建模中引入了三次 B 样条。B 样条配准法的计算复杂度为线性，在计算误差方面表现出四阶收敛性。我们还发现，在波浪模拟的前向建模求解中，它能完美地适应完全匹配层的边界条件。我们提供了几个典型的数值示例，包括二维声波方程、二维弹性波传播和二维粘弹性波在均匀介质中的传播，以验证其收敛性、准确性和计算效率。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.