横向非均匀介质多道瑞雷波频散曲线正演

Forward modeling of multichannel Rayleigh wave dispersion curve in laterally inhomogeneous media

作为近地表横波速度结构成像的主要手段之一,面波多道分析法的正问题研究对现场观测系统设计及后续反演计算具有重要意义.目前面波频散曲线的正演主要分为两类:一是对水平层状介质中面波的本征值问题进行求解,该类方法计算效率高但较难考虑地下介质在横向上的不均匀性;二是基于波动方程的全波场模拟,该类方法在理论上可考虑任意复杂的地质模型但计算成本相对较高.本文基于振幅归一化加权的聚束分析,提出了一种适用于横向非均匀介质模型的多道瑞雷波频散曲线正演方法.首先,基于聚束分析的计算公式推导得到了经振幅归一化加权后输出功率谱中相速度与局部相速度之间的关系,然后通过黄金分割极值搜索算法计算得到了多道瑞雷波数据的理论频散曲线.数值分析结果表明,该算法能够快速地实现横向非均匀介质中多道瑞雷波频散曲线的正演计算,所求取的频散曲线与采用二维弹性波时间域有限差分模拟分析得到的结果误差较小,这在一定程度上说明了该计算方法的可靠性,从而可为面波多道分析法中的观测系统快速优化设计以及横向非均匀介质中频散曲线的反演解释提供理论支撑.

Multichannel analysis of surface wave(MASW)method has been one of the effective tools for retrieving near-surface shear-wave velocity.As with other geophysical methods,its forward problem is of great importance to the design of the field survey and the solution of the inversion.Currently,the forward algorithms of surface wave dispersion curve are generally classified into two categories:solution of surface wave eigenproblems in a horizontally layered model,which is time-efficient but difficult to consider lateral variations;and wave equation-based full wavefield simulation,which can theoretically deal with any complicated geological model but requires high computational costs.In this paper,we present a forward algorithm of multichannel Rayleigh wave dispersion curves in laterally inhomogeneous media based on amplitude-normalized beamforming.By analyzing the formula of beamforming,the relationship between the local phase velocity and the phase velocity in the power spectrum estimated by the amplitude-normalized beamforming is derived,and then the theoretical dispersion curve of multichannel Rayleigh wave data is calculated by utilizing the Golden Section search method.Numerical results show that the proposed algorithm can quickly and efficiently calculate the theoretical dispersion curve of multichannel Rayleigh waves in laterally inhomogeneous media.The difference between dispersion curves calculated by the proposed algorithm and produced by the 2D elastic wave finite-difference time-domain algorithm is small,which indicates the reliability of the proposed algorithm.The proposed forward algorithm can provide a theoretical foundation for the inversion of dispersion curves in laterally inhomogeneous media and an efficient tool for the optimization design of the MASW acquisition system.