Fresnel Volume Tomography With First Arrivals And Its Application To The Static Corrections In Mountains

The velocity of the earth’s surface is vital important to the process of the seismicdata, while it is difficult to acquire the velocity of the surface in complex mountains.Tomography with first arrivals is usually used to inverse the velocity field of thesurface, but it is based on geometry ray theory which considers only the infinitelynarrow media the center ray passes through and that is different from the realpropagation process of waves. Also, the reverse matrix built on the traditionaltomography is usually ill conditioned for the less of the ray density. In this paper, weapply the fresnel volume tomography to inverse the velocity model and calculate thestatic corrections.This paper introduces the calculation of the fresnel volume based on itsdefinition and gives the approximate calculation method of the fresnel volume andcompares the calculated fresnel by the theory and the approximate method. Bycomparison, it is found that both the shape and size of the fresnel calculated throughthe two methods are similar, and the medium used for inversion are almost the same.Through fitting weight coefficients calculated by the theory using different functions,we also gave the approximate method to calculate the weight coefficients of differentnodes within the fresnel volume. Through comparing the fresnel with weightcoefficients calculated by the theory and the approximate method, it can be seen thatthe difference of the medium with coefficients used for inversion between the twomethods is very small and predicted that the inversion results should be equivalent.For the reason that tomography with the approximate fresnel volume does not need tocalculate the receivers’wave front travel times of all the model nodes, it saves a lot ofcomputing time and improves the efficiency. The model tests also verify that thevelocity models inversed from tomography with theory definition calculated fresnelvolume and tomography with the approximately calculated fresnel volume weresimilar while the calculating time reduced a lot. So the approximate fresnel volume tomography is more applicable for real seismic data inversion. At last, we used thevelocity felid inversed from the fresnel volume tomography and the travel timeresiduals to calculate the long wavelength static corrections and the short wavelengthstatic corrections of the shots and receivers and then applied the corrections tomountains and found that it can solve the problem in mountains well, also shows thepractical applicability for the three-dimensional real seismic data.Based on these studies, we wrote programs using the C++programminglanguage and implemented the theory fresnel volume tomography and staticcorrection and the approximate fresnel volume tomography and static correction, andthen used MATLAB programming language to image all kinds of pictures of relevantdata. The program includes the model setting, forward and inversion, the calculationof static correction, the input and output interface, and so on. The output of velocityusing other processing system’s format provides the possibility to combined seismicdata processing with other systems. Through inversions of different three-dimensionreal seismic data, the program achieved good application effect in solving the staticsproblem in complex mountains.