Extraction of Dispersion and Attenuation Curves for Rayleigh Waves using Matrix-Pencil Method

Abstract

Phase velocities of surface waves can be used to estimate near-surface S-wave velocity (\(V_s\)), while attenuation coefficients of surface waves are used to characterize quality factor (\(Q_s\)). Studies show that simultaneous inversion with higher modes and the fundamental mode can increase model resolution and investigation depth. However, the existence of higher modes in surface waves introduces errors in estimated surface-wave attenuation coefficients, reducing the accuracy of estimated \(Q_s\). To address this issue, we propose a novel technique to generate both dispersion and attenuation curves using the matrix-pencil (MP) method. We first introduce the MP method and the procedure for extracting dispersion and attenuation curves and inverting \(V_s\) and \(Q_s\). We present two synthetic cases and one real-world case demonstrating the effectiveness of the proposed method in generating distinguished dispersion curves for the fundamental mode as well as higher modes. Essentially, the MP method successfully separates and constructs an attenuation-coefficient image for each mode. Even with a relatively small number of receivers, the approach nevertheless produces remarkably accurate images. The enhanced measurements provide a cleaner, higher-resolution dispersion and attenuation images which will aid further inversion of S-wave velocities and quality factors.