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.

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.

A B S T R A C TConvolution of a minimum-phase wavelet with an all-pass wavelet provides a means of varying the phase of the minimum-phase wavelet without affecting its amplitude spectrum. This observation leads to a parametrization of a mixed-phase wavelet being obtained in terms of a minimum-phase wavelet and an all-pass operator. The WienerLevinson algorithm allows the minimum-phase wavelet to be estimated from the data. It is known that the fourth-order cumulant preserves the phase information of the wavelet, provided that the underlying reflectivity sequence is a non-Gaussian, independent and identically distributed process. This property is used to estimate the all-pass operator from the data that have been whitened by the deconvolution of the estimated minimum-phase wavelet. Wavelet estimation based on a cumulant-matching technique is dependent on the bandwidth-to-central-frequency ratio of the data. For the cumulants to be sensitive to the phase signatures, it is imperative that the ratio of bandwidth to central frequency is at least greater than one, and preferably close to two. Pre-whitening of the data with the estimated minimum-phase wavelet helps to increase the bandwidth, resulting in a more favourable bandwidth-to-central-frequency ratio. The proposed technique makes use of this property to estimate the all-pass wavelet from the prewhitened data. The paper also compares the results obtained from both prewhitened and non-whitened data. The results show that the use of prewhitened data leads to a significant improvement in the estimation of the mixed-phase wavelet when the data are severely band-limited. The proposed algorithm was further tested on real data, followed by a test involving the introduction of a 90 • -phase-rotated wavelet and then recovery of the wavelet. The test was successful.

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 Earth's 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 Earth's 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 Earth's 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 spectrum and the autocorrelation of the seismic traces, within a scale factor, in the time zone from where the wavelet is extracted (stationary assumption).

Seismic data are usually contaminated by both random and coherent noise, even when the data have been migrated reasonably well 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 post migration 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 to alleviate those problems.