Normal move-out correction in anisotropic and laterally heterogeneous media using simultaneous velocity variation with offset

Abstract

In this paper, we present a new method of normal move-out (NMO) correction that works on a trace by trace basis technique rather than the current conventional sample by sample semblance analysis. The method corrects the pre-stack seismic data due to the NMO effect in both anisotropic and laterally heterogeneous mediums and simultaneously provides a full NMO velocity field that covers every single offset/azimuth in a common depth point (CDP). Also, we introduce a new computational method to recover the anisotropy effect from the extracted NMO velocity field. The presented method gives every single primary seismic reflector in a CDP, three different corrections; Positive correction (where the NMO velocity increases), Negative correction (where NMO velocity decreases) and zero correction (where NMO velocity doesn't change). The first two corrections (positive and negative) work only in case of anisotropy or laterally heterogeneous mediums while the last correction is applicable in case of the seismic reflector is isotropic. The method starts by picking the NMO velocity for each seismic reflector using the conventional semblance plot, then we use these picked NMO velocities as an initial input to our method and since every seismic reflector has three different possibilities, getting all the possible combinations is crucial. To get these combinations, we simply use the combination with repetition mathematical method. To control the degree of the increasing and the decreasing of the NMO velocity correction, we use two parameters called the Anisotropy range parameter(Ar) and its increment. The Ar parameter is used to modify the picked NMO velocity of the primary seismic reflector N times (by adding and subtracting a correction value) based on the number of combinations. The total number of times where initial NMO velocities are modified is based on both the Ar parameter and the number of the seismic reflectors. After all the picked NMO velocities are modified then, we use each of the modified NMO velocity traces (after the interpolation between the modified NMO velocities) to correct the corresponding seismic trace due to the NMO effect then, measure the similarity/semblance between the pilot trace (e.g. Zero offset trace but it dynamically changes) and that seismic trace under the NMO correction. This corresponding seismic trace is corrected due to the NMO effect N times and at each time we measure the semblance value. The modified NMO velocity trace that gives the highest semblance measure is selected. The process is repeated for all the other seismic traces in a CDP. We tested the method on different real and synthetic examples; Isotropic, anisotropic and laterally heterogeneous mediums synthetic examples are presented. Furthermore, we tested the method on a pre-stack CDP real example using Alaska dataset. The results show an excellent flattening to the seismic reflectors and provides a reasonably accurate normal move-out velocity field that covers every offset in a CDP.