FMG_INV, a Fast Multi-Gaussian Inversion Method Integrating Well-Log and Seismic Data.

High-resolution prestack inversion combining the well-logging and seismic data is a significant geophysical task, and can be achieved by two kinds of stochastic inversion approaches, the geostatistical inversion (GSI) and Bayesian linearized inversion (BLI). Nevertheless, the existing GSI is restricted by the heavy iteration calculation. Although BLI can avoid this issue, it suffers from the large core matrix inverse. A fast multi-Gaussian inversion (FMG_INV) is proposed herein to achieve the well-log and seismic combined inversion with higher efficiency than GSI and BLI. FMG_INV is derived from prestack BLI, which requires a large core matrix inverse. However, FMG_INV utilizes a simplification strategy and reduces the core matrix dimension of BLI. This improvement is presented under the assumption of statistical independence between well-logging and seismic data, which relieves the issue of large matrix inverse in BLI to a great extent. Moreover, the spatial and statistical correlation between different parameters in prestack stochastic inversion is presented by a multi-Gaussian distribution and may reduce inversion accuracy, and FMG_INV solves this problem by a novel decorrelation strategy. One-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) field tests and a synthetic data test are given herein to verify the effectiveness of FMG_INV. 1D and 2D tests of traditional BLI are also conducted for comparison. The results demonstrate that FMG_INV achieves the same satisfying inversion accuracy and resolution with BLI but much lower time consumption than BLI.