Non-linear inversion of seismic data for the determination of reflector geometry and velocity structure
A nonlinear method is used to compute first seismic arrivals and reflection travel times for velocity models with complex reflector geometry. The method uses a combination of refraction and reflection travel-times for simultaneous determination of velocity and interface depth of the model. The elastic waves assumed to be transmitted or reflected at interfaces at which the raypaths satisfy Snell’s law. The travel times of critically refracted waves and derivative matrix are computed by applying a revised ray bending method, supplemented by an approximate computation of the first Fresnel zone at each point of the ray. Travel-times and raypaths of reflected waves are computed by applying a fast finite-difference scheme based on a solution to the eikonal equation and following the travel-time gradient backward from the receiver to the source, respectively. A damped least squares inversion scheme is used to reconstruct the velocity model above the reflector and the geometry of the interface by minimizing the difference between observed and calculated (direct, refracted and reflected) travel-times. In order to reduce inversion artifacts both damping and smoothing regularization factors are applied. The applicability of the proposed method is tested using synthetic data. This simultaneous inversion scheme is appropriate for static seismic corrections, as well as determination of lateral velocity variations and reflector’s geometry.