Average‐derivative optimized 21‐point and improved 25‐point forward modelling and full waveform inversion in frequency domain

IF 1.8 3区地球科学 Q3 GEOCHEMISTRY & GEOPHYSICS

Geophysical Prospecting Pub Date : 2024-08-17 DOI:10.1111/1365-2478.13587

Yingming Qu, Zihan Xu, Jianggui Zhu, Longfu Xie, Jinli li

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引用次数: 0

Abstract

Seismic wave forward modelling is a crucial method for studying the propagation characteristics of seismic waves in subsurface media and is a key component of full waveform inversion. Compared to time‐domain forward modelling, frequency‐domain forward modelling offers advantages such as not being constrained by stability limits and reducing the dimension of the solution space. However, forward algorithms based on the rotation coordinate system in the frequency domain cannot adapt to situations with unequal spatial sampling intervals. To enhance the adaptability of the forward modelling algorithm in the frequency domain, we derived a 21‐point finite‐difference scheme based on the average derivative method and calculated the difference coefficients and dispersion conditions. Additionally, to address the significant computational cost in frequency domain forward modelling, we developed an improved 25‐point finite‐difference scheme. The improved 25‐point format is more accurate than the conventional 25‐point format. Building on this foundation, we applied the two derived differential schemes to full waveform inversion to synthesize the shot records of the inversion data. Additionally, we introduced a frequency compensation factor into the gradient processing, which effectively compensates for the deep layer while suppressing noise in the shallow gradient field. Finally, we demonstrated the effectiveness of our approach through a full waveform inversion application on the Marmousi model showcasing its capability in invertig fine subsurface structures.

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平均衍生优化的 21 点和改进的 25 点正向建模以及频域全波形反演

地震波前向建模是研究地震波在地下介质中传播特性的重要方法，也是全波形反演的关键组成部分。与时域前向建模相比，频域前向建模具有不受稳定性限制和减少求解空间维度等优点。然而，基于频域旋转坐标系的前向算法无法适应空间采样间隔不等的情况。为了提高前向建模算法在频域的适应性，我们基于平均导数法推导出了 21 点有限差分方案，并计算了差分系数和分散条件。此外，为了解决频域正演建模计算成本高的问题，我们开发了一种改进的 25 点有限差分方案。改进后的 25 点格式比传统的 25 点格式更加精确。在此基础上，我们将两种衍生的差分方案应用于全波形反演，以合成反演数据的拍摄记录。此外，我们还在梯度处理中引入了频率补偿因子，在抑制浅层梯度场噪声的同时，有效补偿了深层的噪声。最后，我们通过对 Marmousi 模型的全波形反演应用证明了我们方法的有效性，展示了其反演精细地下结构的能力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geophysical Prospecting 地学-地球化学与地球物理

CiteScore

4.90

自引率

11.50%

发文量

118

审稿时长

4.5 months

期刊介绍： Geophysical Prospecting publishes the best in primary research on the science of geophysics as it applies to the exploration, evaluation and extraction of earth resources. Drawing heavily on contributions from researchers in the oil and mineral exploration industries, the journal has a very practical slant. Although the journal provides a valuable forum for communication among workers in these fields, it is also ideally suited to researchers in academic geophysics.