Wide-angle Reflection Amplitude And Phase Characteristics Analysis Based On The Zoeppritz Equation

Seismic waves in the face of the interface will produce similar reflected wave, the reflected wave and the converted wave converter transmission and total reflection and refraction and other physical phenomena, we call this physical phenomenon is generalized seismic wave scattering at the interface surface. The content of this section is an important part of the seismic wave field theory is also widely used in seismic exploration and development of oil and gas, hydrates. In the study of seismic waves and the free surface of the elastic scattering interface consists of two aspects:one is the wave equation and boundary interface boundary conditions definite solution of the problem, on the other hand is the definite solution of the boundary value problem solving process. In short, we solve the boundary surface seismic wave scattering is to determine the boundary wave equation satisfy the definite solution of the problem and find solutions to the boundary value problem of definite solution function process. However, boundary value problem for determining solution is divided into the displacement position and displacement of these two forms of expression, so there are two different research methods. Research using bit shift function, which we call "bit shift method", a typical representative bit shift method is "Knott" equation. The use of displacement function study method called the "displacement method", a typical representative of the displacement process is "Zoeppritz" equation. Displacement method and the bit shift method consistent physical meaning, but the mathematical solution but there are slight differences.This paper deals with the longitudinal wave reflection plane longitudinal elastic wave harmonics who strikes boundary surface medium-wave reflection, transmission longitudinal waves, transverse waves when the transmission to shift bit amplitude equations. In this paper, the displacement of the wave function study, the first talk about some basic questions about Zoeppritz equation, including the solution of boundary value function of the displacement in the form of definite solution of the problem and solve the boundary value problem of definite solution. Derivation summarized in seismic exploration coordinates P wave and SV wave, respectively, from the four quadrants of the incident Zoeppritz equation. Solving Zoeppritz equation is first set to meet the plane wave function definite solution of the problem of wave equation, the wave function contains the incident, the same type of reflection, the same type of the transmitted wave and the reflected wave and the converted wave converted transmission wave five specific provisions of these waves rays the polarization direction of the volume element, then the wave function is substituted into equation interface, we also define the reflection coefficient and the transmission coefficient, and finally sorted out the solution is a function of the corresponding Zoeppritz equation. Then Zoeppritz numerical equations, numerical calculation allows us to more clearly more thorough understanding of the law of seismic wave scattering at the interface between different conditions. When the incident angle reaches the vicinity of the critical angle, the transmitted waves glide along the interface, and when than the critical angle, the transmitted wave at this time degenerate into uneven waves, wave number and the reflection coefficient of inhomogeneous waves are complex, wide-angle reflection this energy is received. Synthetic seismogram We found dramatic changes in the vicinity of the critical angle in amplitude and phase due to the presence of the critical angle so that the reflected wave phase axis distortion complex.