3C–3D VSP vector wavefield separation with constrained inversion

Abstract

Summary Vector wavefield separation of multicomponent offset VSP data based on an optimized localized parametric inversion was introduced in this paper. We developed and employed a constrained optimization search algorithm (COSA) in this inversion to determine the optimum incident angles and velocities. We firstly approximately evaluate the range of both the velocities and the incident angles of P and SV wave, which can respectively refer to the acoustic longing data and the geometry. Then the results were applied to the COSA. Synthetic and field data examples show that application of the COSA makes the inversion method more stable and fast to decompose multicomponent offset VSP wavefield. Introduction 1Vertical Seismic Profiles (VSP) has been applied to many fields of oil industry, such as imaging the vicinity of the well, analyzing anisotropic velocity, forecasting formation pressure and so on (Chen, 2007; Cao, 2008). 3C VSP wavefield separation is one of the most fundamental and important steps in the processing of 3D VSP. The reason is that wavefield separation prior to migration (reflection imaging) has historically been performed and the separated wavefields can be used in deterministic deconvolution (down-going P wavefield), true amplitude AVO analysis, event identification and time picking for tomography (Leaney, 2002). The method described in this paper is related to the method of Esmersoy (1998, 1990) and Leaney (1989, 1990). The distinction is that we develop a constrained optimization search algorithm to determine the range of optimum values for velocities and incident angles. The speed of convergence is obviously increased, and the wavefield decomposed is crisper. Modeling the VSP data as the superposition of a small number of plane waves (up- and down-going P, up- and down-going SV) well approximates to field seismic data. Additionally, this method can estimate the arrival angle and medium velocity at receiver locations more reliably (Esmersoy, 1990). The problem of inversion is usually ambiguity. Thus if we can acquire some prior information (such as the range of velocities; angles; the ratio of P and SV velocity; stratigraphic information; even Snell’s Law for isotropic formation), and add them in the inversion algorithm, the multiplicity of solution will be greatly diminished.