Algorithm for accurate velocity analysis of 1D acoustic reflection and transmission responses by projection constrained multi-physics inversion

Abstract

Velocity analysis is critical in seismic data interpretation. In sedimentary environment, 1D geometry is a reasonable assumption. Velocity analysis under such assumption has been done through the interpretation of either reflection or transmission responses. Recently, Marchenko method has also been applied to provide 1D velocity model from reflection data. However, none of the previous researchers attempted to invert the velocity model from combined physics from the reflection and transmission data with a projection constraint. The projection constraint is computed from the determinant of matrices of dot products of the velocity models. Although, the MATLAB code for the forward responses is given, the algorithm for performing the multi-physics inversion of 1D reflection and transmission data, with projection constraint, is presented. The concept is tested on two different velocity model examples with varying overburden thicknesses and layer thicknesses. Results are consistent even with up to 5% random noise. It is also worthy of note that while the near-surface velocity section remains less affected in the reflection response data, the deep-subsurface velocity values are equally resilient from the transmission response. This presents a much-desired complementary benefit for velocity analysis from a multi-physics interpretation.