Method for calculating plane wave reflection coefficients in elastic multi-layered medium

Abstract

The invention discloses a method for calculating plane wave reflection coefficients in an elastic multi-layered medium. The method comprises the following steps: (1) if plane harmonic waves enter into a target layer series from a medium n+1, generating reflected longitudinal waves and reflected transverse waves in the n+1 medium, generating transmitted longitudinal waves and transmitted transverse waves in a medium 1, and writing each medium layer in a scalar potential form and a vector potential form; (2) determining relation among the displacement, stress and bit shift; (3) loading the scalar potential and vector potential of the step (1) into the step (2) to obtain a displacement and stress relation expression between the (n+1)th layer and the first layer; and (4) obtaining a displacement and stress transfer matrix containing elasticity coefficients of each layer according to the displacement and stress relation expression, which is obtained in the steps (3), between the (n+1)th layer and the first layer, solving, and obtaining reflection and transmission coefficients. According to the method, the influence of multiple waves and transformed waves of the elastic layer series as well as thickness and frequency on the reflection coefficient is considered fully, so that the method is applicable to thin-layer AVO (Amplitude Variation with Offset) analytical simulation and is high in calculation efficiency.

Description

technical field [0001] The invention relates to a calculation method of plane wave reflection coefficient in an elastic multi-layer medium, belonging to the technical field of thin-layer AVO simulation. Background technique [0002] Simulated thin-layer AVO is divided into two categories, (1) time-domain convolution model, for a certain angle, the reflection coefficient is calculated for the time-domain sampling points one by one, and the wavelet and reflection coefficient are used to convolve to form the angle Corresponding to seismic traces, although this method is fast in calculation, simple in formula and easy to implement, it is difficult to reflect the thin layer effect and the simulation accuracy is low. (2) Using the integral solution finite difference method of the elastic wave equation to simulate the thin-layer wave field can simulate the thin-layer effect, but the calculation efficiency is low, which is greatly affected by the modeling, and it is difficult to be ...

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Problems solved by technology

[0002] Simulated thin-layer AVO is divided into two categories, (1) time-domain convolution model, for a certain angle, the reflection coefficient is calculated for the time-domain sampling points one by one, and the wavelet and reflection coefficient are used to convolve to form the angle Corresponding to seismic traces, although this method is fast in calculation, simple in formula and easy to implement, it is difficult to reflect the thin layer effect and the simulation accuracy is low

(2) Using the integral solution finite difference method of the elastic wave equation to simulate the thin-layer wave field can simulate the thin-layer effect, but the calculation efficiency is low, and it is greatly affected by the modeling, and it is difficult to be practical in industrial production

[0003] The conventional Zoeppritz equation calculates the reflection coefficient based on a single interface and has no thickness variable. Although it can also calculate AVO characteristics, it cannot directly analyze the effect of thickness on each frequency component.

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