Research On The Method Of Time-distance Relation Under Wide-angle Reflection Normal Moveout With High Precision

There are some shielded layers of high velocity among the underground medium in some area with complex geological structures. Due to the large velocity contrast between shielded layer of high velocity and its neighbor layers, and there exists large impedance at the same time, thus it makes the seismic rays hard to penetrate the high velocity layers and continue to travel down for getting more deep reflection information. In order to solve this exploration problem, many geophysicists have done a lot of research on seismic records and found that there are some reflection records prevalent in the long-offset place, these reflection records have large offset, generally appear outside the direct wave records, and their amplitude energy are also very strong, can hardly affected by the interference wave. In addition, the lower frequency than general reflections help them to travel further and deeper. After research and demonstration by scholars, this special seismic reflection actually is a wide-angle reflection information. Because of the three characteristics the wide-angle reflection seismic wave have, they can penetrate the shielded layers of high velocity among the underground medium, getting reflection information and achieving accurately imaging of deepstructure.In seismic data processing, the conventional normal moveout method will make the reflection events seriously lack of correction and waveform distortion for large offset distance of wide-angle reflection. The basic reason is the travel time errors IV between formulas which are applying for computing travel time and the real travel time of seismic rays are varied with offset, the larger offset is, the bigger travel time errors are. Therefore, there is one of the basic methods to solve the problem of wide-angle reflection normal moveout is to find a better time-distance relationexpression with higher precision under wide-angle reflection to describe travel time more accurately. In this paper, firstly is a summary of related research that scholars had done, followed by numerical calculation and error results analyzing based on different velocity models using the high order Taylor series formulas and their optimization form. Then, starting from the parameter time-distance equation of horizontal multilayer media, calculating all-order derivatives of travel time t on offset x around the shot-point through the parameter equation, and getting a six order polynomial equation around the shot-point. After that, by means of analyzing the behavior of relational equations and mathematical derivation, finally have the estimation formula of wide-angle reflection normal moveout correction under long-offset conditions. In addition, discussing the applicable range of the six order polynomial and the estimation formula in theory. Repeating the numerical calculation to verify the accuracy and robustness of the new formulas. Finally, applying all of formulas above to forward modeling of normal moveout and compare the correction precision and application range of each formula.Numerical calculation results and forward modeling results both concluded that conventional hyperbolic time-distance equation is no longer applicable to large offset normal moveout under wide-angle condition; the travel time errors of 4th order and 6th order Taylor expansion formula increase rapidly when the offset/depth ratio is more than 2, optimized 4th order and optimized 6th order Taylor formula have better calculation convergence and correction effects; the separated-offset time-distance formula which introduced by this paper is superior to those formulas above in the filed of overall accuracy within the whole offset range and also can acquire better normal moveout effects at different offset, especially at the large offset of wide-angle reflection.So the separated-offset time-distance formula is an effective method with high precision in wide-angle reflection normal moveout correction.