Prestack Stochastic Inversion Research Articles

A New Stochastic Process of Prestack Inversion for Rock Property Estimation

In order to enrich the current prestack stochastic inversion theory, we propose a prestack stochastic inversion method based on adaptive particle swarm optimization combined with Markov chain Monte Carlo (MCMC). The MCMC could provide a stochastic optimization approach, and, with the APSO, have a better performance in global optimization methods. This method uses logging data to define a preprocessed model space. It also uses Bayesian statistics and Markov chains with a state transition matrix to update and evolve each generation population in the data domain, then adaptive particle swarm optimization is used to find the global optimal value in the finite model space. The method overcomes the problem of over-fitting deterministic inversion and improves the efficiency of stochastic inversion. Meanwhile, the fusion of multiple sources of information can reduce the non-uniqueness of solutions and improve the inversion accuracy. We derive the APSO algorithm in detail, give the specific workflow of prestack stochastic inversion, and verify the validity of the inversion theory through the inversion test of two-dimensional prestack data in real areas.

Prestack Stochastic Frequency-Dependent Velocity Inversion With Rock-Physics Constraints and Statistical Associated Hydrocarbon Attributes

Previous studies have demonstrated that P-wave velocity dispersion at seismic frequencies is often related to hydrocarbons, which results in frequency-dependent P-wave reflection coefficients. This effect is neglected in the conventional amplitude-versus-angle (AVA) inversion, or reduced in most AVA inversion involving seismic dispersion due to the linearization of either the forward modeling or the inversion objective function. As a consequence, there are times when nonnegligible error exists in the inverted dispersion-associated result, which is probably nonnegligible in some cases. In this letter, we adopt the propagator matrix forward modeling derived from the wave equation and the particle swarm optimization (PSO)-based inversion to solve the uncollapsed objective function to avoid any linearization operator at the cost of probably more computational complexity and inversion ill-posedness. To address the ill-posedness, in both the forward modeling and inversion, we introduce rock-physics constraints of frequency-independent S-wave velocity and limited variations of P-wave velocity with frequency. Furthermore, we statistically derive the average frequency-dependent P-wave velocity attribute, the P-wave velocity dispersion intensity attribute, and the characteristic frequency attribute corresponding to the maximum velocity dispersion gradient from multiple experimental inverted dispersive P-wave velocity results. These attributes can be directly applied to detect hydrocarbons. A synthetic data example and a real data example through a drilling well are used to demonstrate that PSO-based prestack stochastic inversion method with rock-physics constraints is effective, and that the statistical attributes derived from the multiple inverted dispersive P-wave velocities can be utilized to favorably indicate gas reservoirs.

Stochastic inversion of prestack seismic data using fractal-based initial models

In general, inversion algorithms rely on good starting models to produce realistic earth models. A new method, based on a fractional Gaussian distribution derived from the statistical parameters of available well logs to generate realistic initial models, uses fractal theory to generate these models. When such fractal-based initial models estimate P- and S-impedance profiles in a prestack stochastic inversion of seismic angle gathers, very fast simulated annealing — a global optimization method — finds the minimum of an objective function that minimizes data misfit and honors the statistics derived from well logs. The new stochastic inversion method addresses frequencies missing because of band limitation of the wavelet; it combines the low- and high-frequency variation from well logs with seismic data. This method has been implemented successfully using real prestack seismic data, and results have been compared with deterministic inversion. Models derived by a deterministic inversion are devoid of high-frequency variations in the well log; however, models derived by stochastic inversion reveal high-frequency variations that are consistent with seismic and well-log data.

Detection and Spatial Delineation of Thin-Sand Sedimentary Sequences With Joint Stochastic Inversion of Well Logs and 3D Prestack Seismic Amplitude Data

Summary We describe the successful application of a new prestack stochastic inversion algorithm to the spatial delineation of thin reservoir units otherwise poorly defined with deterministic inversion procedures. The inversion algorithm effectively combines the high vertical resolution of wireline logs with the relatively dense horizontal coverage of 3D prestack seismic amplitude data. Multiple partial-angle stacks of seismic amplitude data provide the degrees of freedom necessary to estimate spatial distributions of lithotype and compressional-wave (P-wave) and shear-wave (S-wave) velocities in a high-resolution stratigraphic/sedimentary grid. In turn, the estimated volumes of P- and S-wave velocity permit the statistical cosimulation of lithotype-dependent spatial distributions of porosity and permeability. The new stochastic inversion algorithm maximizes a Bayesian selection criterion to populate values of lithotype and P- and S-wave velocities in the 3D simulation grid between wells. Property values are accepted by the Bayesian selection criterion only when they increase the statistical correlation between the simulated and recorded seismic amplitudes of all partial-angle stacks. Furthermore, inversion results are conditioned by the predefined measures of spatial correlation (variograms) of the unknown properties, their statistical cross correlation, and the assumed global lithotype proportions. Using field data acquired in a fluvial-deltaic sedimentary-rock sequence, we show that deterministic prestack seismic-inversion techniques fail to delineate thin reservoir units (10-15 m) penetrated by wells because of insufficient vertical resolution and low contrast of elastic properties. By comparison, the new stochastic inversion yields spatial distributions of lithotype and elastic properties with a vertical resolution between 10-15 m that accurately describe spatial trends of clinoform sedimentary sequences and their associated reservoir units. Blind-well tests and cross validation of inversion results confirm the reliability of the estimated distributions of lithotype and P- and S-wave velocities. Inversion results provide new insight to the spatial and petrophysical character of existing flow units and enable the efficient planning of primary and secondary hydrocarbon recovery operations.