Abstract: Method for determining best and worst cases for values of model parameters such as porosity and shale volume fraction generated by non-unique matrix inversion of physical data such as seismic reflection amplitudes. The matrix is diagonalized, and then orthonormal basis vectors associated with insignificant diagonal elements are used to generate upper and lower bounds on the solution. Best and worst case solutions are determined as linear combinations of the null basis vectors, where the expansion coefficients are determined by making a best fit to the upper and lower bounds.

Abstract: Method for obtaining rock parameters such as porosity and vshale directly from inversion of seismic data corresponding to a single trace location. This method is distinguished from existing methods that obtain elastic properties from inversion of seismic data, then relate the elastic parameters to rock lithology parameters such as porosity or vshale because it is accomplished in one step, can incorporate anisotropy and does not require multiple trace locations for stability. The data are separated into partial stacks, and a wavelet is specified for each stack. A set of linearized equations are constructed relating seismic reflectivity to changes in elastic parameters, and another set of linearized equations is constructed relating the changes in elastic parameters to the lithologic parameters. The linearized reflectivity equations are combined with the linearized rock physics equations, convolved with the specified wavelets, and equated to the seismic data.

Abstract: Method for obtaining rock parameters such as porosity and vshale directly from inversion of seismic data corresponding to a single trace location. This method is distinguished from existing methods that obtain elastic properties from inversion of seismic data, then relate the elastic parameters to rock lithology parameters such as porosity or vshale because it is accomplished in one step, can incorporate anisotropy and does not require multiple trace locations for stability. The data are separated into partial stacks, and a wavelet is specified for each stack. A set of linearized equations are constructed relating seismic reflectivity to changes in elastic parameters, and another set of linearized equations is constructed relating the changes in elastic parameters to the lithologic parameters. The linearized reflectivity equations are combined with the linearized rock physics equations, convolved with the specified wavelets, and equated to the seismic data.

Abstract: Method for predicting lithology and porosity of subsurface rocks from seismic reflection data. The seismic data is inverted to yield elastic properties of the rocks such as the compressional and shear impedances. A rock physics model is built to relate porosity, the shale volume fraction, the fluid content of the rock and the elastic properties of the rock. The model is run backward in a second inversion process to solve for porosity and lithologic properties such as the shale volume fraction.

Abstract: A method for controlled-amplitude prestack time migration of seismic data traces. According to the inventive method, common-offset gathers of the prestack seismic data traces are 3-D Fourier transformed from the space-time domain to a preselected alternate data domain, such as the frequency-wavenumber domain, the wavenumber-time domain, or the slant-stack domain. A migration operator that substantially preserves the seismic amplitudes of the original data traces is computed in the {right arrow over (p)}−z domain. This migration operator is applied to the transformed data traces in the alternate data domain, an imaging condition is applied, and the resulting migrated data traces are then transformed back to the space domain.