Multicomponent seismic data registration by nonlinear optimization

Abstract

Mapping PS-wave data to the PP-wave time domain is a critical step before joint PP- and PS-wave data interpretation and inversion. Registration techniques are often constrained by having access to a known [Formula: see text] ratio. When an accurate [Formula: see text] ratio is not provided, one can solve the problem of seismic data registration by minimizing the difference between the PP-wave and the warped PS-wave data with a smoothing constraint applied on the warping function. To avoid undesirable foldings or rapid changes in the warped PS-wave image, we require a warping function that is monotonic and smooth. We invert the [Formula: see text] ratio directly from PP- and PS-wave data instead of estimating it from the warping function. Seismic data registration is posed as a constrained nonlinear optimization problem. Furthermore, we represent the [Formula: see text] ratio by spline functions and adopt a parameterization that guarantees monotonic warping functions. Our parameterization in terms of splines significantly reduces the number of unknowns of our problem, and the convergence to a smooth monotonic solution is guaranteed.