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Study on selection and direct inversion method of brittleness index for shale reservoir

Qin Ziyu, Wen Xiaotao, Pan Shulin, Chen Jing-yi, Gou Qiyong

Acta Geophysica

2023

Vol. 71, no. 2

757--768

The brittleness index can be indirectly converted by elastic parameters which are obtain by pre-stack amplitude variation with offset inversion and extended to the whole work area. However, indirect conversion will bring cumulative errors. In order to improve the accuracy of obtaining the brittleness index, the exact Zoeppritz equation including different brittleness indices is derived. Before inversion, we analyzed the characteristics of the brittleness index under the changes of brittle minerals, porosity and organic matter content through rock physics model, and selected the brittleness index most suitable for the work area. Based on the Bayesian framework, we introduce the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method to invert theoretical and actual data. Theoretical data inversion results demonstrate this method can achieve good results in both PP- and PS-wave joint inversion as well as only PP-wave inversion. To further verify the effectiveness of the algorithm, the brittleness index of actual data is directly inverted by using the studied algorithm and process. The inversion results of the borehole-side trace are in good agreement with the brittleness index calculated by log data. Both theoretical and practical data prove the feasibility of our proposed method.

Nonstationary seismic inversion: joint estimation for acoustic impedance, attenuation factor and source wavelet

Hao Yaju, Wen Xiaotao, Zhang Hua, Zhu Yunfeng, Deng Chengxiang

Acta Geophysica

2021

Vol. 69, no. 2

459--481

Seismic signal can be expressed by nonstationary convolution model (NCM) which integrates acoustic impedance (AI), attenuation factor (AF) and source wavelet (SW) into a single formula. Although it provides attractive potential to invert AI, AF and SW, simultaneously, efective joint inversion algorithm has not been developed because of the extreme instability of this nonlinear inverse problem. In this paper, we propose an alternating optimization scheme to achieve this nonlinear joint inversion. Our algorithm repeatedly alternates among three subproblems corresponding to AI, AF and SW recovery until changes in inverted models become smaller than the user-defned tolerances. Also, when we optimize one parameter, other two parameters are fxed. NCM is an explicit linear formula for AI; therefore, AI recovery is accomplished by linear inver sion which is regularized by low-frequency model and isotropy total variation domain sparse constraints. However, NCM is a complicated nonlinear formula for AF. To facilitate the AF inversion, we propose a centroid frequency-based attenuation tomography method whose forward operator and observations are acquired from the time-varying wavelet amplitude spectra which is estimated according to Gabor domain factorization of NCM. SW is decoupled from NCM based on Toeplitz structure constraint, and we obtain an orthogonal wavelet transform domain sparse regularized SW inverse subproblem. Split Bregman technique is adopted to optimize AI and SW inverse subproblems. Numerical test and feld data application confrm that the proposed nonstationary seismic inversion algorithm can stably generate accurate estimates of AI, AF and SW, simultaneously.