Spatial Mesh Refinement using Cubic Smoothing Spline Interpolation in Simulation of 2-D Elastic Wave Equation: Forward Modeling of Full-waveform Inversion
Amila Sudu Ambegedara *
Department of Mathematics, Faculty of Science, Unversity of Peradeniya, Sri Lanka.
U. G. I. G. K. Udagedara
Department of Mathematics, Faculty of Science, Unversity of Peradeniya, Sri Lanka.
Erik M. Bollt
Electrical and Computer Engineering and C3S2, The Clarkson Center for Complex Systems Science, Clarkson University, United States of America.
*Author to whom correspondence should be addressed.
Abstract
Full-waveform inversion (FWI) is a non-destructive health monitoring technique that can be used to identify and quantify the embedded anomalies. The forward modeling of the FWI consists of a simulation of elastic wave equation to generate synthetic data. Thus the accuracy of the FWI method highly depends on the simulation method used in the forward modeling. Simulation of a 3-D seismic survey with small-scale heterogeneities is impossible with the classic finite difference approach even on modern super computers. In this work, we adopted a mesh refinement approach for simulation of the wave equation in the presence of small-scale heterogeneities. This approach uses cubic smoothing spline interpolation for spatial mesh refinement step in solving the wave equation. The simulation results for the 2-D elastic wave equation are presented and compared with the classic finite difference approach.
Keywords: Full-waveform inversion, elastic wave propagation, heterogeneities, cubic smoothing spline interpolation