The Study And Application Of Stochastic Inversion

By means of seismic inversion, we can convert the seismic information to lithology and physical property distribution information, finally attaining some parameters which can reflect the fluid change characteristics of reservoir, such as porosity, permeability and saturation. Seismic inversion is itself based on some inaccurate data, which will inevitably lead to the uncertainty results. Meanwhile, most post-stack inversion and prestack inversion usually get a deterministic result, eventually causing some accuracy problems.There mainly exists two problems in the deterministic inversion, namely, scaling problem and low frequency problem. It's hard for seismic inversion impedance to constraint the modeling with the smoothing problem, what's worse, lacking in the high vertical resolution, it's difficult to identify thin layer, while just depending on the interpolation and extrapolation of well information to acquire low frequency trend will lead to “visual continuity”, and the oneness of low frequency model will also affect the inversing precision.To these problems, this paper proposes stochastic inversion, it can properly solve some problems that deterministic inversion has confronted, some advantages include: it can attain higher resolution to satisfy the modeling requirement; it can accurately simulate the losing low and high seismic frequency information, what's more, it can also get multiple inversion results matching well and seismic information, not just a optimization solution.The paper contains two main part: Constrained sparse spike inversion(CSSI) and Stochastic inversion, and the stochastic inversion is based on CSSI. Firstly, the paper analyses some inversion parameters in the CSSI, such as seismic S/N, seismic mismatch factor p and impedance mismatch factor q, then through the actual data, we continue a test based on quantitative control method. In the third chapter, because inversion impedance is difficult to distinguish sand from mudstone and gamma curves can properly recognize lithology information, we propose using mobile smoothing method to distract low and high frequencyof sonic and gamma curves information, depending on the relationship of two kind of curves' high frequency information to fit out the new sonic curve, then through actual data, we confirm the feasibility of this method in the region where the gamma curves highly match lithology information. In the stochastic inversion part, according to the fitting problem of variogram, the fourth chapter for the first time put forward the particle swam optimization(PSO) to the variogram fitting and registering, compared with traditional least square method,PSO algorithm owns a higher resolution in the fitting and registering process and it's much easier to master. Chapter 5 is mainly about kriging interpolation, first it briefly expounds two types of kriging algorithm: Simple kriging(SK) and Ordinary kriging(OK), then this chapter mainly analyze the origin of kriging matrix with ill-posed through three aspects: grid size delta x, matrix dimension N and the kind of covariance model. We conclude that robust kriging matrix requires larger grid size, low matrix dimension and reasonable covariance model such as spherical or exponential ones. Chapter six is the most important part which is based on the former ones, we first analyze some limitations and problems of deterministic inversion, such as error estimate caused by smoothing, scale problem in modeling, etc. then we introduce two kinds of stochastic algorithms, namely, Sequential Gaussian simulation(SGS) and simulated annealing(SA), meanwhile, we respectively adopt kriging interpolation and SGS method to simulate the wells' porosity data. Research has shown that kriging interpolation just acquire a smoothing optimal solution, despite the existence of variance, it can't afford to analyze the uncertainty of inversion result. Meanwhile, stochastic simulation can acquire a few of equal probability simulation results, although the variances are larger or smaller than the kriging ones, it's properly consistent with the whole impedance trend and can also analyze the uncertainty according to geological background. Finally, the paper comparatively analyses the difference between deterministic inversion and stochastic inversion, in conclusion, the stochastic inversion results not only retain the deterministic inversion trend, but it also match the nonuniqueness of geophysical inversion problem.