Stochastic parameter estimation of heterogeneity from crosswell seismic data based on the Monte Carlo radiative transfer theory

Coda waves are usually regarded as noise in the conventional seismic exploration fields. Our work is to use the energy of coda waves to estimate the stochastic parameters of random media, which is necessary to characterize the subsurface reservoir and assess the oil or gas total volume in the heterogeneous reservoir. In this paper, we briefly present the Monte Carlo radiative transfer (MCRT) theory in acoustic media, which is often used to model the envelopes of seismic energy in approximated random media in seismology. Then, we estimate the fluctuation strength and correlation length in 2D acoustic heterogeneous media based on the MCRT simulation from the synthetic crosswell seismic data. Our results show that sufficient energy information at a range of offsets can alleviate the nonunicity of the inversion result. In order to properly balance the energy effect of direct waves and coda waves in the inversion process, we modify the objective function to compare the logarithm values of the RT envelopes and of the envelopes computed with the finite difference method. Revision of this objective function makes the inversion result more accurate and more stable. Even when there is strong noise in the envelopes of seismic data, the modified equation tends to estimate the correct values. Moreover, the estimated results of the correlation length and fluctuation strength are influenced by the type of random model used in the MCRT simulation. It is better to choose the type of random media matching the investigated medium, when we apply the MCRT simulation to estimate the stochastic parameters of the investigated medium.