Ricardo Biloti

Restricted optimization: a clue to a fast and accurate implementation of the Common Reflection Surface Stack method

For a fixed, central ray in an isotropic elastic or acoustic media, traveltime moveouts of rays in its vicinity can be described in terms of a certain number of parameters that refer to the central ray only. The determination of these parameters out of multi-coverage data leads to very powerful algorithms that can be used for several imaging and inversion processes. Assuming two-dimensional propagation, the traveltime expressions depend on three parameters directly related to the geometry of the unknown model in the vicinity of the central ray. We present a new method to extract these parameters out of coherency analysis applied directly to the data. It uses (a) fast one-parameter searches on different sections extracted from the multi-coverage data to derive initial values of the sections parameters, and (b) the application of a recently introduced Spectral Projected Gradient (SPG) optimization algorithm for the final parameter estimation. Application of the method on a synthetic example shows an excellent performance of the algorithm both in accuracy and efficiency. The results obtained so far indicate that the algorithm may be a feasible option to solve the corresponding, harder, full three-dimensional problem, in which eight parameters, instead of three, are required.

MULTIPARAMETRIC TRAVELTIME INVERSION

In conventional seismic processing, the classical algorithm of Hubral and Krey is routinely applied to extract an initial macrovelocity model that consists of a stack of homogeneous layers bounded by curved interfaces. Input for the algorithm are identified primary reflections together with normal moveout (NMO) velocities, as derived from a previous velocity analysis conducted on common midpoint (CMP) data. This work presents a modified version of the Hubral and Krey algorithm that is designed to extend the original version in two ways, namely (a) it makes an advantageous use of previously obtained common-reflection-surface (CRS) attributes as its input and (b) it also allows for gradient layer velocities in depth. A new strategy to recover interfaces as optimized cubic splines is also proposed. Some synthetic examples are provided to illustrate and explain the implementation of the method.

Dip correction for coherence-based time migration velocity analysis

Migration velocity analysis (MVA) is a seismic processing step that aims to translate residual moveout in an image gather after migration with an erroneous velocity model into velocity updates. An analysis of the position of a reflection event in an image gather after migration with an incorrect velocity allows us to extend the original coherence-based MVA approach to dipping reflectors. The extended MVA technique includes the reflector dip which is treated as an additional search parameter that is to be detected together with the velocity updating factor. Both parameters are searched for simultaneously by the application of two-parameter search techniques. The search consists of determining trial curves as a function of the search parameters and stacking the migrated data along these curves. The highest coherence determines the best-fitting curve and thus the optimal parameter pair. A numerical example demonstrates that the additional search parameter improves the quality of the velocity updates, thus requiring less iterations in the MVA.

Automatic smoothing by optimal splines

We propose a method that is capable to filter out noise as well as suppress outliers of sampled real functions under fairly general conditions. From an a priori selection of the number of knots that define the adjusting spline, but not their location in that curve, the method automatically determines the adjusting cubic spline in a least-squares optimal sense. The method is fast and easily allows for selection of various possible number of knots, adding a desirable flexibility to the procedure. As an illustration, we apply the method to some typical situations found in geophysical problems.

A Frequency Criterion For Smoothing With Optimal Cubic Splines

When smoothing a function with high-frequency noise by means of optimal cubic splines, it is often not clear how to choose the number of nodes. The more nodes are used, the closer the smoothed function will follow the noisy one. In this work, we demonstrate that more nodes mean a better approximation of Fourier coefficients for higher frequencies. Thus, the number of nodes can be determined by specifying a frequency up to which all Fourier coefficients must be preserved. A comparison of the corresponding smoothing results with those obtained by filtering using a moving average of corresponding length and a lowpass with corresponding high-cut frequency show that optimal cubic splines yield better results as they preserve not only the desired low-frequency band but also important high-frequency characteristics.

Dip-correction for coherence-based migration velocity analysis

Migration velocity analysis (MVA) is a seismic processing step that aims at translating the velocity information that is contained in the residual moveout in an image gather after migration with an erroneous velocity model into velocity updates. In this paper, we extend the original coherence-based MVA approach to dipping reflectors. We devise a new MVA technique, where the reflector dip is treated as an additional search parameter that is to be detected together with the velocity updating factor. A numerical example demonstrates that the additional search parameter can indeed be helpful to improve the quality of the velocity updates.