Inversion of seismic reflection data from the Gialo Field, Sirte Basin

Abstract

This project is concerned with the development of software to invert seismic reflection data for acoustic impedance, with application to the YY-reservoir area in Gialo Field, Sirte Basin. The problem was that of inverting post-stack seismic reflection data from two seismic lines into impedance profiles. The main input to the inversion process is an initial guess, or initial earth model, of the impedance profile defined in terms of parameters. These parameters describe the impedance and the geometry of the number of layers that constitute the earth model. Additionally, an initial guess is needed for the seismic wavelet, defined in the frequency domain using nine parameters. The inversion is an optimisation problem subject to constraints. The optimisation problem is that of minimising the error energy function defined by the sum of squares of the residuals between the observed seismic trace and its prediction by the forward model for the given earth model parameters. To determine the solution we use the method of generalised linear inverses. The generalised inverse is possible only when the Hessian matrix, which describe the curvature of error energy surface, is positive definite. When the Hessian is not definite, it is necessary to modify it to obtain the nearest positive definite matrix. To modify the Hessian we used a method based on the Cholesky factorisation. Because the modified Hessian is positive definite, we need to find the generalised inverse only once. But we may need to restrict the step-length to obtain the minimum. Such a method is a step-length based method. A step-length based method was implemented using linear equality and inequality constraints into a computer program to invert the observed seismic data for impedance. The linear equality and inequality constraints were used so that solutions that are geologically feasible and numerically stable are obtained. The strategy for the real data inversion was to first estimate the seismic wavelet at the well, then optimise the wavelet parameters. Then use the optimum wavelet to invert for impedance and layer boundaries in the seismic traces. In the three real data examples studied, this inversion scheme proved that the delineation of the Chadra sands in Gialo Field is possible. Better results could be obtained by using initial earth models that properly parameterise the subsurface, and linear constraints that are based on well data. Defining the wavelet parameters in the time domain may prove to be more stable and could lead to better inversion results.