Numerical computation of the sensitivity kernel for monitoring weak changes with multiply scattered acoustic waves

Abstract

Monitoring of weak localized changes within a medium using coda waves, we can either use the decorrelation and/or the phase shift of the coda waves. The formulation for both the decorrelation and the phase shift of the coda waves due to weak changes contain a common sensitivity kernel that is needed to image the weak localized changes. We provide a novel approach to compute the sensitivity kernel which uses finite difference modelling of the wavefields from the source and the receiver with an a priori scattering model. These wavefields give the intensities needed to compute the sensitivity kernels. This approach unlike methods that computes the sensitivity kernel with analytical approximations of the scattered intensity computes the numerical solution of the scattered intensity with a prior scattering model. The numerical solution of the sensitivity kernel allows us to use an arbitrary earth model that includes a free surface without simplifying the property of the scattering model.We demonstrate the computation of the numerical sensitivity kernel within statistically heterogeneous models and models with irregular topography. The statistically heterogeneous models we explore include a simple model for vertically fractured and horizontally layered shale reservoirs. We compare the impact of either the horizontal or the vertical source-receiver configuration on the characteristics of the sensitivity kernel. All computations of the numerical kernel we present in this study use 2-D heterogeneous scattering models, however, the kernel computation is easily extended to 3-D scattering models.