Somanath Misra

Global optimization with model-space preconditioning: Application to AVO inversion

Linearized-inversion methods often have the disadvantage of dependence on the initial model. When the initial model is far from the global minimum, optimization is likely to converge to a local minimum. Optimization problems involving nonlinear relationships between data and model are likely to have more than one local minimum. Such problems are solved effectively by using global-optimization methods, which are exhaustive search techniques and hence are computationally expensive. As model dimensionality increases, the search space becomes large, making the algorithm very slow in convergence. We propose a new approach to the global-optimization scheme that incorporates a priori knowledge in the algorithm by preconditioning the model space using edge-preserving smoothing operators. Such nonlinear operators acting on the model space favorably precondition or bias the model space for blocky solutions. This approach not only speeds convergence but also retrieves blocky solutions. We apply the algorithm to estimate the layer parameters from the amplitude-variation-with-offset data. The results indicate that global optimization with model-space-preconditioning operators provides faster convergence and yields a more accurate blocky-model solution that is consistent with a priori information.

Coherence and curvature attributes on preconditioned seismic data

Seismic data are usually contaminated with both random and coherent noise, even when the data have been properly migrated and are multiple-free. Seismic attributes are particularly effective at extracting subtle features from relatively noise-free data. Certain types of noise can be addressed by the interpreter through careful structure-oriented filtering or postmigration footprint suppression. However, if the data are contaminated by multiples or are poorly focused and imaged due to inaccurate velocities, the data need to go back to the processing team.

Phase stability via nonlinear optimization A case study

Accurate wavelet estimation is crucial in the deconvolution of seismic data. As per the convolution model, the recorded seismic trace is the result of convolution of the Earths unknown reflectivity series with the propagating seismic source wavelet along with the additive noise. The deconvolution of the source wavelet from the recorded seismic traces provides useful estimates of the Earths unknown reflectivity and comes in handy as an aid to geological interpretation. This deconvolution process usually involves estimation of a wavelet, before it is removed by digital filtering. Because the Earths reflectivity and seismic noise are both unknown, the wavelet estimation process is not easy. Statistical methods estimate the wavelet using the statistical properties of the seismic data and are based on certain mathematical assumptions. The most commonly used method assumes that the wavelet is minimum phase and that the amplitude spectrum and the autocorrelation of the wavelet are the same as the amplitude sp...