A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.
A novel computational method to evaluate the Sommerfeld integral (SI) efficiently and accurately is presented. The method rewrites the SI into two parts, applying discrete complex image method (DCIM) to evaluate the infinite integral while using double exponential quadrature rules (DE rules) for the computation of the finite part. Estimation of signal parameters via rotational invariance techniques (ESPRIT) is used to improve the accuracy and efficiency of extracting DCIM compared to the generalized pencil of function (GPOF). Due to the symmetry of the horizontal layered media, the Green function, representing the seismic fields due to a point source, can be written in the form of Sommerfeld integral in cylindrical coordinate system and be calculated by the proposed method. The performance of the method is then compared to the DE rules with weighted average partition extrapolation (WA), which shows a good agreement, with computational time reduced by about 40%.
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