A constrained parametric inversion for velocity analysis based on CFP technology

A method of velocity analysis based on the common focusing point (CFP) method is presented. The two important aspects of the method are the use of the CFP domain and the use of a new parameterization—a vertical velocity gradient to describe the lateral velocity variation within a layer. The layer velocity is defined with only two parameters: an average velocity (v0) and a vertical velocity gradient (β). Layer velocity parameterization using v0 and β assumes that the lithology of the layer is constant and that the overburden and fluid pressure increase linearly with depth. This type of parameterization is suitable for areas with gross changes in lithology (clastic-carbonate-salt) and for rock in hydrostatic equilibrium. A layer based model is required for these areas. The salt dome data example presented belongs to this type of area, so the layer-based model with the defined parameterization produced a very good subsurface velocity model. The method is based on the principle of equal traveltime between the focusing operator and the corresponding focus point response. The velocity estimation problem is formulated as a constrained parametric inversion process. The method of perturbation is applied where linear assumptions are made; the velocity inversion, however, is a nonlinear problem, and the model parameter updates are computed iteratively using Newton's method. The velocity model is built by layers in a top-down approach, which makes the problem quasi-linear.