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为了模拟富含小尺度非均质体的勘探区内地震波能量的变化,本文将天然地震中的辐射传输理论引入到地震勘探频段内,给出了基于Born散射系数的二维声波辐射传输方程,并介绍了蒙特卡洛数值模拟的思路。为了检验基于Born散射系数的声波辐射传输蒙特卡洛方法的正确性和实用性,将辐射传输蒙特卡洛模拟的结果与声波方程有限差分模拟的结果进行对比。结果表明,辐射传输蒙特卡洛模拟的结果与声波有限差分模拟的结果基本吻合。同时,相比于声波方程有限差分数值模拟,辐射传输蒙特卡洛模拟的计算成本远小于声波有限差分数值模拟。因此,对于复杂的非均质储层,辐射传输蒙特卡洛模拟是一种有效的地震散射波能量建模方法。而且,对于物理模型实验观测到的地震散射波的数据,我们采用基于辐射传输蒙特卡洛模拟的网格扫描方法来估算非均匀介质的统计参数-相关长度和扰动强度。计算结果与物理模型的真实值基本吻合,表明辐射传输蒙特卡洛模拟可以被用来估算非均质储层的统计参数。
In order to simulate the variation of seismic energy in the exploration area rich in small-scale heterogeneous bodies, this paper introduces the theory of radiation transmission in natural earthquakes into the seismic exploration frequency band, and presents a two-dimensional acoustic radiation transmission equation based on the Born scattering coefficient. The idea of Monte Carlo numerical simulation is introduced. In order to verify the correctness and practicability of Monte Carlo method based on Born scattering coefficient, the results of Monte Carlo simulation of radiative transfer were compared with the results of finite difference simulation of acoustic wave equation. The results show that the results of Monte Carlo simulation of radiation transmission are basically consistent with the results of finite difference simulation of acoustic wave. Meanwhile, compared with the finite difference numerical simulation of acoustic wave equation, the computational cost of Monte Carlo simulation of radiation transmission is far less than that of finite difference numerical simulation of acoustic wave. Therefore, for complex heterogeneous reservoirs, Monte Carlo simulation of radiative transfer is an effective energy modeling method for seismic scattering wave. Moreover, for the data of seismic scattering waves observed by physical model experiments, we use the grid scanning method based on Monte Carlo simulation of radiative transfer to estimate the statistical parameters of the inhomogeneous medium - the correlation length and the perturbation intensity. The calculated results are in good agreement with the real values of the physical model, indicating that the Monte Carlo simulation of radiative transfer can be used to estimate the statistical parameters of heterogeneous reservoirs.