Abstract:Nonlinear inversion based on Metropolis sampling algorithm is formulated in the Bayesian framework. As one kind of Monte Carl non-linear inversions, it can effectively integrate high frequency information of well logging data, and obtain inversion results with a higher resolution. Firstly, we get the priori information through fast Fourier transform moving average (FFT-MA) and gradual deformation method (GDM). Second, we structure likelihood function. Then we apply Metropolis algorithm in order to obtain an exhaustive characterization of the posteriori probability density. FFT-MA is a kind of efficient simulation method. Combined with GDM, it can constantly modify reservoir model and keep the spatial structure unchanged until it matches the observed seismic data. According to the model trial and real data processing, we can conclude that nonlinear inversion based on Metropolis sampling algorithm provide reasonable elastic parameter information, especially it improves the resolution of P-wave velocity. Even when the signal noise ratio (SNR) is relatively low, it can still show reasonable elastic parameter information, which proves the effectiveness of the proposed method. The inversion resolution of P-wave and S-wave impedances is higher than elastic parameters inversion if we do not consider the noise.
Sancevero S S,Remacre A Z,de Souza Portugal R et al.Comparing deterministic and stochastic seismic inversion for thin-bed reservoir characterization in a turbidite synthetic reference model of Campos Basin,Brazil.The Leading Edge,2005,24(11): 1168-1172.
[2]
Moyen R,Doyen P M.Reservoir connectivity uncertainty from stochastic seismic inversion. SEG Technical Program Expanded Abstracts,2009,28:2378-2382.
[3]
Sams M S,Saussus D.Comparison of uncertainty estimates from deterministic and geostatistical inversion.The 70th EAGE Conference & Exhibition,2008.
[4]
Francis A.Limitations of deterministic and advantages of stochastic seismic inversion.Canadian Society of Exploration Geophysicists Recorder,2005,30(2):5-11.
[5]
Francis A.Understanding stochastic inversion:Part 1.First Break,2006,24(11):69-77.
[6]
Francis A.Understanding stochastic inversion:Part 2.First Break,2006,24(12):79-84.
[7]
Dubrule O.Workshop report:“Uncertainty in reserveestimates” EAGE Conference,Amsterdam,2 June 1996.Petroleum Geoscience, 1996,2(4): 351-352.
[8]
Kjønsberg H,Hauge R,Kolbjørnsen O et al.Bayesian Monte Carlo method for seismic predrill prospect assessment.Geophysics, 2010,75(2):O9-O19.
Le Ravalec M,Noetinger B,Hu L Y.The FFT moving average (FFT-MA) generator:An efficient numerical method for generating and conditioning Gaussian simulations.Mathematical Geology,2000,32(6):701-723.
[11]
Hu L Y.Gradual deformation and iterative calibration of Gaussian-related stochastic models.Mathematical Geology,2000,32(1): 87-108.
[12]
John A S,Martin L S,Sven T.Introductory Geophysical Inverse Theory.Colorado and New England: Samizdat Press,2001.
[13]
Oliver D S.Moving averages for Gaussian simulation in two and three dimensions. Mathematical Geology,1995,27(8):939-960.
[14]
Duijndam A J W.Bayesian estimation in seismic inversion,Part II:Uncertainty analysis.Geophysical Prospecting,1988,36(8): 899-918.
[15]
Journel A G,Huijbregts C J.Mining Geostatistics.London,New York and San Francisco: Academic Press,1978.
[16]
Hu L Y, Blanc G.Constraining a reservoir facies model to dynamic data using a gradual deformation method.The 6th European Conference on the Mathematics of Oil Recovery,1998.
[17]
Hu L Y,Le Ravalec M,Blanc G et al.Reducing uncertainties in production forecasts by constraining geological modeling to dynamic data.SPE Annual Technical Conference and Exhibition,Society of Petroleum Engineers,1999.
[18]
Mosegaard K,Tarantola A.Monte Carlo sampling of solutions to inverse problems.Journal of Geophysical Research:Solid Earth (1978-2012),1995,100(B7):12431-12447.
[19]
Metropolis N,Rosenbluth A W,Rosenbluth M N et al.Equation of state calculations by fast computing machines.The Journal of Chemical Physics,1953,21(6):1087-1092.
[20]
Tarantola A.Inverse Problem Theory and Methods for Model Parameter Estimation.Paris:SIAM,2005.