黏声波动方程变机制数有限差分正演

实际地下介质普遍具有黏弹性，一般采用品质因子Q表征介质黏弹性程度。在勘探地震频带范围内，通常认为Q不随频率变化，这种常Q特征可以用广义标准线性固体模型进行较好地刻画，因此广义标准线性固体模型成为了黏弹性地震波正演模拟的首选。但是目前这类黏弹介质地震波正演方法往往使用固定的松弛机制数，存在模拟精度与计算效率不能较好统一的缺陷。本文基于广义标准线性体模型，提出了一种黏声波动方程变松弛机制数有限差分地震波场正演方法，即在模型不同区域使用不同松弛机制数、不同模拟精度的求解方式，以达到计算效率与模拟精度的统一。将本文模拟结果与解析解对比，分析模拟精度与机制数、Q值和传播距离的关系，确定不同机制数的适用范围；进一步对比变松弛机制数模拟结果与固定松弛机制数模拟结果的精度和计算效率，结果表明前者适用范围广，模拟精度高，并可有效提高计算效率。

Finite-difference numerical modeling with variable mechanisms for viscoacoustic wave equation

Subsurface media are generally not elastic but viscoelastic, and the viscoelasticity is normally depicted by a dimensionless quantity, i.e., quality factor Q.Within the frequency band of seismic exploration, Q is widely considered frequency-independent, which can be properly characterized by the generalized standard linear solid (GSLS) mo-del.Thus, the GSLS model has become the mainstream while viscoelastic seismic wave modeling.However, when GSLS model has been chosen, the current modeling schemes commonly adopt a fixed number of relaxation mechanisms, which leads to a shortcoming, not being able to integrate the computational efficiency and precision.In this paper, we propose a finite difference viscoelastic seismic-wave modeling scheme with variable mechanisms based on GSLS model.More precisely, we use different number of mechanisms to approximate the Q in different areas of earth model, thereby integrating both computational efficiency and precision.We compare our results with the analytical solution, and analyze the relation between the precision and the number of mechanisms, and Q and the tra-veling distance to determine the appropriate applicable range of different mechanisms.We also compare the precision and efficiency of variable mechanisms with those of a fixed number of mechanisms, and analyze the applicability of the proposed method.The results indicate some merits of the proposed scheme:wider applicability, higher computational precision, and more efficient simulation.