An Algorithm to Calculate the Seismic Reflectivity and Transmissivity from General Anisotropic Structures

Abstract:

While seismic anisotropy is known to exist within the Earth’s crust and even deeper, isotropic or simple anisotropy assumptions for seismic imaging is an over simplification resulting in artifacts in the seismic image, wrong target positioning and hence interpretation. To partly overcome issues with anisotropic medium, approximations to the full solutions for wave propagation and reflectivity for specific material symmetries are used. Here, we have developed an algorithm to extend these capabilities to the general case of reflectivity from the interface between two anisotropic slabs of arbitrary symmetry and orientation. To achieve this, the algorithm solves full elastic wave equation for polarization, amplitude and slowness of all six wave modes generated by an incident plane-wave from welded interface. In the first step, the plane-wave slownesses and polarizations of all three orthogonal wave modes are calculated for a given incidence angle. Later, the algorithm determines the reflection and transmission angles of all possible scattered modes followed by their respective velocities and polarization vectors. With this information, the algorithm solves a system of equations incorporating the imposed boundary conditions to arrive at the scattered wave amplitudes. By comparing this reflectivity algorithm against leading approximate solution in a much simpler anisotropic environment, we understood that unlike other simplified linear solution, this algorithm is stable in almost all propagation direction and like its predecessor is not limited to near vertical range. There is no need to emphasis that the algorithm capability to quickly solve plane-wave properties in low symmetric anisotropic medium with arbitrary orientation opens new doors to better understand elasticity.