Wavefield Parameter Forward Modeling Based On The CRS Stack Technology

In recent years, professor Hubral has put forward a new imaging technology called Common Reflection Surface,which is only dependent on the near surface velocity and foreign to the macroscopic velocity model. It describes the kinematics reflected response of non-uniform medium curved interfaces by analysis formulas.It realizes seismic imaging by optimizing emergent angleα,the wavefront curvature radius of normal incidence point wave(NIP)and the wavefront curvature radius of normal direction wave(N).Its theoretical basis is geometrical seismology.It considers the local feature of reflector and the whole reflect of the first Fresnel zone, hence it utilizes all the information of multiple coverage reflect data effectively.Using the CRS stack technology,we can obtain a high quality ZO section and three wavefield parameter sections,by which the best velocity model can be deduced. CRS stack based on a complex top surface topography can process pre-stack data without static correction. Then data redatuming can be performed with the kinematic parameters produced by CRS stack. Real data processing indicates that the section of CRS stack based on a complex top surface topography is better that that of conventional stack in the aspect of S/N ratio and the continuity of reflection event.3D common reflection surface stack is an effective tool in processing stack on seismic data with low S/N ratio. 3D common reflection surface stack operator depends on eight kinematic wave-field parameters describing two theoretical wave-fronts. The theory about parameter modeling of 3D common reflection surface stack was discussed in detail and modeling process was designed and realized. The time-distance surface of common reflection surface stack was calculated based on the wave-field parameters derived by modeling. The comparison between the result of parameter modeling and the result of ray tracing proved the rightness of parameter modeling and actual process. Parameter modeling can give advice on 3D common reflection surface stack and inversion on velocity field using wave-field parameters of common reflection surface stack.The forward modeling of wave field attribute parameters in 3-D common reflection surface is more complex than that in 2-D. In the case of 3-D, the second order description of the wave front determines its direction and curvature. That is, the former is defined by polar angle and azimuthal angle of the propagation direction while the latter is described by the symmetric 2-by-2 matrix of curvature, which degrades into an angle and first order derivative in the case of 2-D respectively. Therefore, the wave field parameters of 2-D simulated zero-offset sections are added to eight in 3-D. Moreover, it is difficult to implement a description of the wave front and the transformation of three-dimensional system of coordinates. The parameters can be expressed into the matrix. Through the research of mathematical matrix and the theories of coordinates transformation as well as the establishment of suitable ray center coordinates and interface coordinates, we can solve the above problems efficiently and derive the travel formulas of 3-D common reflection surface and the matrix expressions of various parameters. Thus we can solve the forward problem of wave field attribute parameters efficiently and establish the foundation for the further 3-D CRS stack.