×

zbMATH — the first resource for mathematics

Fast geostatistical seismic inversion coupling machine learning and Fourier decomposition. (English) Zbl 1425.86013
Summary: Geostatistical seismic inversion uses stochastic sequential simulation and co-simulation as techniques to generate and perturb subsurface elastic models. These steps are computational demanding and, depending on the size of the inversion grid, time consuming. This paper introduces a technique to achieve considerable reductions in the consumption of computational resources of geostatistical seismic inversion without compromising the quality of the inverse elastic models. We achieve these improvements by reducing one of the dimensions of the data domain to a periodic function approximated by a Fourier series of \(n\) terms. Then, instead of simulating over the entire original data volume, in the original data domain, we simulate independently each term of the series over the area of interest. If the number of terms in the series is considerably smaller than the size of the collapsed data domain, then the computational overhead of the inversion procedure decreases. Symbolic regression is used to obtain automatically the approximation to the periodic function that captures the behavior of the property in the reduced dimension. The advantages related to the use of symbolic regression over alternative machine learning algorithms are discussed. We use the method to simulate acoustic impedance in a geostatistical seismic inversion of a synthetic dataset representing a hydrocarbon reservoir, where the true acoustic impedance model is available. Results demonstrate a considerable speedup over traditional methods while achieving similar performance in terms of the misfit between real and synthetic seismic and a good representation of the true impedance model. The frequency content of the resulting inverted data is discussed and compared with the one inferred from traditional methods, demonstrating an expected reduction of the high-frequency component.
MSC:
86A15 Seismology (including tsunami modeling), earthquakes
86A32 Geostatistics
Software:
fda (R); GPTIPS; GSLIB
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Azevedo, L., Nunes, R., Soares, A., Mundin, E.C., Neto, G.S.: Integration of well data into geostatistical seismic amplitude variation with angle inversion for facies estimation. Geophysics. 80(6), M113-M128 (2015)
[2] Azevedo, L., Soares, A.: Geostatistical Methods for Reservoir Geophysics. Springer (2017)
[3] Azevedo, L., Nunes, R., Soares, A., Neto, G.S., Martins, T.S.: Geostatistical seismic amplitude-versus-angle inversion. Geophys. Prospect. 66(S1), 116-131 (2018)
[4] Bosch, M., Mukerji, T., Gonzalez, E.F.: Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: A review. Geophysics. 75(5), 75A165-75A176 (2010)
[5] Buland, A., Omre, H.: Bayesian linearized AVO inversion. Geophysics. 68(1), 185-198 (2003)
[6] Deutsch, V.C, Journel, A.: GSLIB. Geostatistical Software Library and User Guide. 2nd edn. Oxford University Press, (1992)
[7] Dimitrakopoulos, R., Luo, X.: Generalized Sequential Gaussian Simulation on Group Size ν and Screen-Effect Approximations for Large Field Simulations. Math. Geol. 36(5), 567-591 (2004) · Zbl 1267.86008
[8] Doyen, P.: Seismic Reservoir Characterization: An Earth Modeling Perspective. EAGE, (2007)
[9] Ferreirinha, T., Nunes, R., Azevedo, L., Soares, A., Pratas, F., Tomás, P., Roma, N.: Acceleration of stochastic seismic inversion in OpenCL-based heterogeneous platforms. Comput. Geosci. 78, 26-36 (2015)
[10] de Figueiredo, L.P., Bordignon, F., Grana, D., Roisenberg, M., Rodrigues, B.B.: Impact of seismic-inversion parameters on reservoir pore volume and connectivity. SEG Technical Program Expanded Abstracts (2018)
[11] de Figueiredo, L., Grana, D., Roisenberg, M., Rodrigues, B.: Multimodal McMC meethod for non-linear petrophysical seismic inversion. Geophysics, Just-accepted Articles (2019).
[12] González, E.F., Mukerji, T., Mavko, G.: Seismic inversion combining rock physics and multiple-point geostatistics. Geophysics. 73(1), R11-R21 (2008)
[13] Grana, D., Della Rossa, E.: Probabilistic petrophysical properties estimation integrating statistical rock physics with seismic inversion. Geophysics. 75(3), O21-O37 (2010)
[14] Grana, D., Mukerji, T., Dvokin, J., Mavko, G.: Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method. Geophysics. 77(4), M53-M72 (2012)
[15] Grana, D., Fjeldstad, T., Omre, H.: Bayesian Gaussian mixture linear inversion for geophysical inverse problems. Math. Geosci. 49, 1-37 (2017) · Zbl 1387.86050
[16] Grujic, O., da Silva, C., Caers, J.: “Functional Approach to Data Mining, Forecasting, and Uncertainty Quantification in Unconventional Reservoirs,” in SPE Annual Technical Conference and Exhibition (2015)
[17] Koza, J.R.: Genetic Programming: On the programming of computers by means of natural selection. MIT Press, Cambridge (1992) · Zbl 0850.68161
[18] Le Ravalec-Dupin, M., Noetinger, B.: Optimization with the gradual deformation method. Math. Geol. 34(2), 125-142 (2002) · Zbl 1031.86011
[19] Liu, M., Grana, D.: Stochastic nonlinear inversion of seismic data for the estimation of petroelastic properties using the ensemble smoother and data reparameterization. Geophysics. 83(3), 1 MJ-1Z13 (208)
[20] Mariethoz, G.: A general parallelization strategy for random path based geostatistical simulation methods. Comput. Geosci. 36(7), 953-958 (2010)
[21] Menafoglio, A., Grujic, O., Caers, J.: Universal Kriging of functional data: Trace-variography vs cross-variography? Application to gas forecasting in unconventional shales. Spat. Stat. 15, 39-55 (2016)
[22] Menafoglio, A., Secchi, P., Dalla Rosa, M.: A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space. Electronic Journal of Statistics. 7, 2209-2240 (2013) · Zbl 1293.62120
[23] Nerini, D., Monestiez, P., Manté, C.: Cokriging for spatial functional data. J. Multivar. Anal. 101(2), 409-418 (2010) · Zbl 1180.91215
[24] Nunes, R., Almeida, J.A.: Parallelization of Sequential Gaussian, Indicator and Direct Simulation Algorithms. Comput. Geosci. 36(8), 1042-1052 (2010)
[25] Ramsay, J.O., Silverman, B.W.: Functional data analysis. Springer (2006) · Zbl 1079.62006
[26] Reyes, A., Giraldo, R., Mateu, J.: Residual Kriging for Functional Spatial Prediction of Salinity Curves. Communications in Statistics - Theory and Methods. 44(4), 798-809 (2015) · Zbl 1325.86016
[27] Russell, B.: Introduction to seismic inversion methods. SEG (1998).
[28] Searson, D.P.: GPTIPS 2: an open-source software platform for symbolic data mining. in Handbook of Genetic Programming Applications. Springer, New York (2015)
[29] Soares, A.: Direct Sequential Simulation and Cosimulation. Math. Geol. 33(8), 911-926 (2001) · Zbl 1010.86017
[30] Soares, A., Diet, J., Guerreiro, L.: Stochastic Inversion with a Global Perturbation Method, in EAGE Petroleum Geostatistics, Cascais (2007)
[31] Soares, A., Nunes, R., Azevedo, L.: Integration of Uncertain Data in Geostatistical Modeling. Math. Geosci. 49(2), 253-273 (2017) · Zbl 1365.86024
[32] Sambridge, M.: Geophysical inversion with a neighborhood algorithm-I. Searching a parameter space. Geophys. J. Int. 138(2), 479-494 (1999)
[33] Sen, M.K., Stoffa, P.L.: Nonlinear one dimensional seismic waveform inversion using simulated annealing. Geophysics. 56(10), 1624-1638 (1991)
[34] Sen, M., Stoffa, P.: Global optimization methods in geophysical inversion: Elsevier Science Publ. Co., Inc. (1995) · Zbl 0871.90107
[35] Srinivasan, B.V., Duraiswami, R., Murtugudde, R.: Efficient kriging for real-time spatio-temporal interpolation. in 20th Conference on Probablility and Statistics in Atmospheric Sciences (2010).
[36] Tarantola, A.: Inverse Problem Theory. Elsevier (1987) · Zbl 0875.65001
[37] Vardy, M.E.: Deriving shallow-water sediment properties using post-stack acoustic impedance inversion. Near Surface Geophysics. 13(2), 143-154 (2015)
[38] Vargas, H., Caetano, H., Filipe, M.: Parallelization of Sequential Simulation Procedures. in EAGE Conference on Petroleum Geostatistics, Cascais, Portugal (2007)
[39] Yang, X., Zhu, P.: Stochastic seismic inversion based on an improved local gradual deformation method. Comput. Geosci. 109, 75-86 (2017)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.