A fast algorithm for seismic velocity analysis based on AB semblance

Building velocity model is one of the most significant topics in seismic data processing and interpretation. In seismic data processing, executing the stages of normal moveout (NMO) correction, proper stacking, depth and time migration, and so on require an appropriate velocity model. There are several methods for building a velocity model from seismic data. Most of these methods are based on criteria which describe the consistency between the velocity model and the seismic data, but they differ in the way these criteria are defined, calculated and utilized for estimating the velocity model. The most conventional method for velocity analysis is based on moveout of reflection events, which uses the coherency measure for building a velocity model. Semblance is the commonly used coherency measure. Although it is effective in most practical situations, this measure faces problems in the presence of strong variations of amplitude along seismic events or polarity reversals. An algorithm, called AB semblance, has been introduced for solving this problem. This method, like other methods of semblance, also requires amplitudes of events to be summed along hyperbolic trajectories in the time gates, which can be very time-consuming for processing large data sets. In this paper, fast hyperbolic Radon transform in log-polar coordinates is employed to speed-up the calculations of semblance-based velocity analysis. 

Methodology and Approaches:

 Recently, an algorithm with complexity O(N2 logN), where N denotes the number of data samples, has been introduced for evaluation of the hyperbolic Radon transform. It is based on rewriting the Radon operator in log-polar coordinates, with which the main computational parts reduce to computing convolutions. This allows to use the Fourier domain for fast calculation of it. In order to apply fast Fourier transforms (FFTs), samples in log-polar coordinates must be chosen on an equally spaced grid. Since data is sampled in the time-offset domain, a resampling is required for switching between coordinates. In this paper, we use this algorithm in the computation of AB semblance, for summing along hyperbolic trajectories in each time gate. In this method, the time gate width will be one sample. The final result thus requires convolution with an appropriate Gaussian window.

Results and Conclusions

Velocity analysis based on direct computations could be time-consuming in the presence of a large data set. In this paper, a fast algorithm with complexity O(N2 logN) is used for velocity analysis based on AB semblance. Field and synthetic data examples have been used in order to examine the proposed method. The results from the tests show large speed-ups of the method compared to other similar velocity analysis methods.