Jianguo Sun

The influence of sea water velocity variation on seismic traveltimes, ray paths, and amplitude

The main factors affecting seismic exploration is the propagation velocity of seismic waves in the medium. In the past, during marine seismic data processing, the propagation velocity of sea water was generally taken as a constant 1500 m/s. However, for deep water exploration, the sound velocity varies with the season, time, location, water depth, ocean currents, and etc.. It also results in a layered velocity distribution, so there is a difference of seismic traveltime, ray paths, and amplitude, which affect the migration imaging results if sea water propagation velocity is still taken as constant for the propagation wavefield. In this paper, we will start from an empirical equation of seismic wave velocity in seawater with changes of temperature, salinity, and depth, consider the variation of their values, build a seawater velocity model, and quantitatively analyze the impact of seawater velocity variation on seismic traveltime, ray paths, and amplitude in the seawater velocity model.

A finite difference scheme for solving the eikonal equation with varying grid spacing

Summary To improve the accuracy and stability of the finite difference solution to the eikonal equation along expanding wavefront, we present a finite difference scheme that uses varying grid spacing and that combines several formulas from the literature. Specifically, a grid densification is firstly performed in the grid squares directly surrounding the source. Then the grid spacing given by the process of the grid densification is successively enlarged according to whether the wavefront reaches the grid line counted from the source in ether 2- t h n x or direction, where is a positive integer. Numerical tests show that the strategy of varying grid spacing results in the traveltimes that have a higher accuracy order than those computed without using the local densification of the grid. For example, in a homogeneous medium with a velocity of 1000 m/s the traveltimes computed by using the varying grid spacing has an accuracy order of , while the traveltimes computed without using the varying grid spacing has an accuracy order of . z n

A fast algorithm for prestack Gaussian beam migration adopting the steepest descent approximation

In the past, prestack Gaussian beam migration adopted the steepest descent approximation to reduce the dimension of the integrals and speed up the computation. However, the simplified formula by the steepest descent approximation was still in the frequency domain, and it had to be evaluated at each frequency. To solve this problem, we present a fast algorithm by changing the order of the integrals. The innermost integral is regarded as a two-dimensional continuous function with respect to the real part and the imaginary part of the total traveltime. A lookup table corresponding to the value of the innermost integral is constructed at the sampling points. The value of the innermost integral at one imaging point can be obtained through interpolation in the constructed lookup table. The accuracy and efficiency of the fast algorithm are validated with the Marmousi dataset. The application to the Sigsbee2A dataset shows a good result.

Joint 3D traveltime calculation based on fast marching method and wavefront construction

Abstract3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method (FMM) is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method (WFC), which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models.

Wavefront construction using a two‐dimensional cubic convolution interpolation

Wavefront construction is a method used for fast seismic ray tracing. An essential process in the method is the interpolation of traveltimes from an irregular grid to a regular grid. Usually, this interpolation is realized by using bilinear interpolation. However, bilinear interpolation cannot give continuous derivatives across the grid element used for realizing interpolation. Therefore, it is not adequate for ray tracing in complex media with certain smoothness, because for computing rays traveltime derivatives should be continuous everywhere in the smoothed model. To have an interpolation scheme that meets the requirements for solving ray tracing system numerically, we introduce a two-dimensional cubic convolution interpolation. It is found that the twodimensional cubic convolution interpolation is efficient and accurate in comparison to bilinear interpolation. Also, it is found that the difference between the ray families respectively computed by the two-dimensional cubic convolution interpolation and by bilinear interpolation is large when the velocity change in the model used is strong. This leads to the conclusion that for obtaining correct ray trajectories in the complex velocity model, an interpolation formula with a smoothness order higher than that of bilinear interpolation formula is necessary.

A finite difference scheme for solving the eikonal equation including surface topography

Summary To imaging the subsurface structure directly from the earth’s surface with arbitrary relief, we present a finite difference (FD) scheme that uses nonuniform grid spacing in the region near the curved surface and that adapts the fast marching method (FMM) for treating the grid irregularity caused by the surface relief. Specifically, for adapting FMM we introduce new point types, namely the surface point, the point above the surface, the interface point, and the point under the interface. For adapting the upwind FD formula used in the original FMM, the grid spacing in the conventionally used rectangular grid is replaced by the vertical distance between the surface point and the grid point under consideration. Numerical results show that the scheme presented here can treat the irregular region problem caused by the curved earth’s surface with effectiveness and flexibility.

A Finite Difference Method For Modeling the DC Electrical Potential Field Including Surface Topography

Summary For modeling the direct current (DC) electrical potential field in the earth model with complex surface relief, we develop a finite difference (FD) method that avoids the direct numerical implementation of the surface boundary condition. The key point of the method is to determine the electrical potential at the points in the earth’s surface by using the fact that the DC equipotential lines or surfaces are perpendicular to the earth’s surface. In the practical implementation, the unit normal vector to the earth’s surface is firstly determined at a given surface point and then the normal is extended into the earth until it reaches a point that is a regular grid point located in the nearest vicinity of the surface, or that is located in a regular grid square. Next, the DC potential at the endpoint of the extended normal line is computed by bilinear interpolation or by direct assignment, according to whether the endpoint is located in a regular grid square or coincident with a regular grid point lying in the nearest vicinity of the surface. Finally, the potential value at the endpoint is assigned to the considered surface point. After this assignment step is finished, a linear equation system can be established by using the conventional FD stencils and by using the computed surface potential values. Numerical tests in 2D and 2.5D cases show that the method presented here is simple, flexible, efficient, and accurate enough for solving the modeling problem in DC electrical methods when the earth’s surface has a complex geometry.

Another AVO Cross-plotting For P-SV Wave

Based on the P-SV wave reflection coefficient given by Zheng (1992) and Ramos (2001), another cross-plotting for the converted wave AVO analysis is presented in this paper. The analysis of AVO cross-plotting for P-SV wave indicates that P-SV wave has negative AVO slope and its slope is dependent merely on the change of the ratio of compressionaland shear-wave velocity, so this relation can be used to extract . Furthermore, P-SV wave