Multicomponent, Multi-Azimuth Pre-Stack Seismic Waveform Inversion for Azimuthally Anisotropic Media Using A Parallel and Computationally Efficient non-Dominated Sorting Genetic Algorithm

li, tao ; mallick, subhashis;

Consideration of azimuthal anisotropy, at least to an orthorhombic symmetry is important in exploring the naturally fractured and unconventional hydrocarbon reservoirs. Full waveform inversion of multicomponent seismic data can, in principle, provide more robust estimates of subsurface elastic parameters and density than the inversion of single component (P wave) seismic data. In addition, azimuthally dependent anisotropy can only be resolved by carefully studying the multi component seismic displacement data acquired and processed along different azimuths. Such an analysis needs an inversion algorithm capable of simultaneously optimizing multiple objectives, one for each data component along each azimuth. These multicomponent and multi-azimuthal seismic inversions are non-linear with non-unique solutions; it is therefore appropriate to treat the objectives as a vector and simultaneously optimize each of its components such that the optimal set of solutions could be obtained. The fast non-dominated sorting genetic algorithm (NSGA II) is a robust stochastic global search method capable of handling multiple objectives, but its computational expense increases with increasing number of objectives and the number of model parameters to be inverted for. In addition, an accurate extraction of subsurface azimuthal anisotropy requires multi component seismic data acquired at a fines patial resolution along many source-to-receiver azimuths. Because routine acquisition of such data is prohibitively expensive, they are typically available along two or at most three azimuthal orientations at a spatial resolution where such an inversion could be applied. This paper proposes a novel multi-objective methodology using a parallelized version of NSGA II for waveform inversion of multicomponent seismic displacement data along two azimuths. By scaling the objectives prior to ranking, redefining the crowding distance as functions of the scaled objective and the model spaces, and varying the crossover and mutation parameters over generations, the proposed methodology is also an improvement of the original NSGA II in over all computational efficiency, preservation of population diversity, and rapid sampling of the model space. By first inverting the near-offset pre-stack data for the background isotropic properties and obtaining constraints on the vertical velocities, followed by an inversion of the long-offset data, it is demonstrated that the proposed method can reliably estimate density and azimuthally anisotropic subsurface properties up to the complexity of an orthorhombic symmetry on noisy synthetic data computed from a model based on a real well log under an assumption of 1-D subsurface layers where the ambiguities between lateral heterogeneity and anisotropy could be ignored. In addition, a practical way to approximately compute the uncertainty values in the derived parameters using the method is also demonstrated.