Resolution improvement of velocity spectra using weighted semblance method

Velocity analysis is one of the most important steps of seismic reflection data processing which estimates the appropriate velocity for stacking and normal moveout correction. Taner & Koehler (1969) introduced the conventional semblance method for velocity analysis which is a normalized coherency measure. Semblance-based velocity analysis generates a velocity spectra for a common midpoint gather. Various parameters such as offset، signal to noise ratio، window length and etc. influence the resolution of semblance velocity spectra. For velocity analysis of a single reflector، if we consider the true velocity، then the hyperbolic reflection event aligns to the horizontal event in an analysis window and computed value of semblance is equal to one. If the operator selects an incorrect velocity، the hyperbolic event does not align to the horizontal event and the semblance value is reduced. If the selected velocity is close to the true value، then the computed semblance has a value close to one. Therefore، the resolution of the velocity spectra is reduced. Various methods have been introduced to improve the resolution of the semblance velocity spectra. Biondi and Kostov (1989) used the eigenstructure method to increase the resolution of velocity spectra. Sachi (1998) obtained the high resolution velocity spectra using the bootstrap algorithm. Roshandel et al (1387) improved the resolution of velocity spectra by multiplying the ratio of the two first eigen values of analysis window and the semblance value. In this study، we used the weighted semblance value introduced by Luo and Hale (2012) to obtain the high resolution velocity spectra. In this method، the weight functions are added to the semblance equation. The weight functions make the semblance value more sensitive to velocity and increase the resolution of the velocity spectra. Therefore، the weight functions must be calculated in a way that it is sensitive to the temporal change in normal moveout correction for every velocity at every offset. To illustrate the efficiency of the weighting function on the resolution of semblance spectra، weighted semblance and conventional semblance implemented on both synthetic and real CMP gathers. In the first synthetic example، we generated a CMP gather for a 37-layered earth model with linearly increased velocity. We computed its velocity spectra by both conventional and weighted semblance methods. Then، we added random noise to the synthetic CMP gather and re-calculated the velocity spectra. In these two synthetic examples، we have observed that the weighted semblance had a better resolution than conventional form. In the next step، we added multiple to CMP gather with near velocity to the primary event. Comparing the velocity spectra obtained from two mentioned methods showed that the conventional semblance cannot completely distinguish between the primary and multiple velocities. But they were easily separated from each other in velocity spectra of weighted semblance. Finally، both methods were applied to real data relating to the South West of Iran. The obtained result showed that extension of peak in the velocity spectra in the weighted semblance decreased. Thus، we can say the weighted semblance method has a better resolution than that of conventional methods.