Recovering the Reflectivity Matrix and Angle-dependent Plane-wave Reflection Coefficients from Imaging of Multiples

A joint migration approach employing the complete wavefield (containing primary and multiple reflections) requires properly imaged multiples of all orders. By solving a Fredholm integral equation of the first kind, we compute the reflected impulse response (i.e., reflectivity) matrix at every image level and extract the angle dependent plane wave reflection coefficients. We tested this imaging technique employing a simple 1D layered model with multiple reflections included. We obtained the correct Amplitude Versus Angle (AVA) response of the estimated plane wave reflection coefficient. By simultaneously imaging primaries and multiples, we also achieved an overall better image.