Report

High resolution velocity analysis for resource plays - estimating eta (η) using DE method Bo Zhang, Tao Zhao, and Kurt J. Marfurt The University of Oklahoma-AASPI Outline • Motivation • Eta Estimation Without Picking • Application • Conclusion • Road-ahead 2 Motivation Example of RMS velocity and Eta picking Gather after moveout Velocity semblance Eta semblance http://www.crestoneseismic.com/index.php/seismic-software-toolkit/velocity-analysis/semblance-velocity-analysis Motivation The Disadvantages of current workflow for nonhyperbolic velocity analysis: • analysis at small apertures may be inaccurate. • Picking errors in introduce errors in picking η. • Simultaneous picking of and η is time consuming and tedious. Outline • Motivation • Eta Estimation Without Picking • Application • Conclusion • Road-ahead 5 Eta Estimation Without Picking There are three main issues to perform automatic nonhyperbolic velocity analysis: • The travel time equation. • The parameters and objective function. • Optimization engine. Eta Estimation Without Picking The travel time equation: 4 2 2 x x eff t 2 t02 2 2 2 2 vnmo vnmo t0 vnmo 1 2 eff x 2 In cases where VTI exists, the magnitude of ηeff in the NMO equation (Alkhalifah and Tsvankin, 1996) is responsible for both long offset and VTI effects. Eta Estimation Without Picking The parameters and objective function: m vint eff vrms n 2 Vi ti i 1 12 ti i 1 n Qm Si vrms , eff n i 1 is semblance for the th selected reflections events, and are respectively the interval velocity and effective eta model. Eta Estimation Without Picking Optimization engine: Initialize a set of models Mutation and crossover to generate trial models Compare the objective function of trial and initial models Better model survive to the next generation Differential evolutionary (DE) algorithm is an efficient and simple global optimization scheme. Eta Estimation Without Picking The workflow of eta estimation without picking: Seismic gathers Horizons Initial _0 discontinuity attribute Build theCompute initial interval velocity from _0 DE operation to get the a set of new interval velocity and Eta models. Evaluation the corrected gathers for each model All selected events are flattened? Yes New New interval velocity Effective Eta Outline • Motivation • Eta Estimation Without Picking • Application • Conclusion • Road-ahead 11 Application Location map of a 3D wide azimuth survey (Courtesy of Devon Energy) 45-12 Application Simplified stratigraphic column of the Fort Worth Basin in Wise County (modified from Montgomery et al., 2005) 13 Application NMO gathers based on 2-term hyperbolic velocity analysis (The Barnett Shale and maximum offset are respectively around 7500 and 14000 ft.) Application NMO gathers after automated 3-term non-hyperbolic velocity analysis. (The Barnett Shale and maximum offset are respectively around 7500 and 14000 ft.) Application Stacked section based on 2-term NMO corrected gather after muting 1000 ft Application Stacked section based on automated 3-term NMO corrected gather 1000 ft Application RMS velocity from 2 term velocity analysis Application RMS velocity from automated 3 term velocity analysis Application Effective eta from automated 3 term velocity analysis Application Interval velocity using Dix equation from original RMS velocity Application New interval velocity from automated 3 term velocity analysis Application Co-render initial RMS velocity with old stacked section 1000 ft Application Co-render new RMS velocity with new stacked section 1000 ft Application Co-render initial interval velocity with old stacked section 1000 ft Application Co-render new interval velocity with new stacked section 1000 ft Outline • Motivation • Eta estimation without picking • Application • Conclusion • Road-ahead 27 Conclusion • Two term velocity analysis is not capable for long offset velocity analysis. • Propose three term automatic velocity analysis algorithm can flatten the reflection events as much as possible. • The estimated effective eta η combine the long offset and VTI effects. • The estimated interval velocity model can be used for the following processing such reflection tomography. 28 Outline • Motivation • Eta estimation without picking • Application • Conclusion • Road-ahead 29 Road-ahead • Set interval eta as on of the parameters instead of effective eta. • Calibrate the estimated interval velocity with well logs. • Employ the estimated interval velocity as the input for reflection tomography. • Employ the estimated interval velocity to fill the low frequency gap in impedance inversion. 30 Acknowledgements • Devon energy for permission to use and show their data. • The industry sponsors of the University of Oklahoma AttributeAssisted Seismic Processing and Interpretation (AASPI) Consortium. • Dr. J. T. Kwiatkowski for the inspiring discussions. Backup The engine for automatic velocity optimization Differential evolutionary (DE) algorithm is an efficient and simple global optimization scheme. The basic features can be summarized as follows: Initialization Mutation Crossover Selection DE workflow The engine for automatic velocity optimization Problem statement and notation Suppose we want to optimize a function with D real parameters We must select the size of the population N (it must be at least 4) The parameter vectors have the form: xi ,G x1,i ,G , x2,i ,G x2 , i , G where G is the generation number. i 1,2, , N The engine for automatic velocity optimization Initialization Define upper and lower bounds for each parameter: x Lj x j ,i ,1 xUj Mutation Randomly select initial parameter values uniformly between the upper and lower bounds. Crossover Selection The engine for automatic velocity optimization Initialization Each of the N parameter vectors undergoes mutation, recombination and selection Mutation Crossover Selection Mutation expands the search space For a given parameter vector xi,G randomly select the three different vectors: xr1,G , xr 2,G , xr 3,G The engine for automatic velocity optimization Initialization Add the weighted difference of two of the vectors to the third to form the donor vector: Mutation vi ,G 1 xr1,G F xr 2,G xr 3,G The mutation factor F is a user defined constant Crossover Selection from [0, 2] The engine for automatic velocity optimization Initialization Crossover incorporates successful solutions from the previous generation Mutation The trial vector ui,G+1 is developed from the elements of the target vector, xi,G, and the elements Crossover of the donor vector, vi,G+1 Elements of the donor vector enter the trial vector Selection with probability CR The engine for automatic velocity optimization Initialization Mutation Crossover Selection v j ,i ,G 1 u j ,i ,G 1 x j ,i ,G 1 if rj ,i CR or j I random if rj ,i CR or j I random i 1,2, , N ; j 1,2, , D rj ,i ~ U 0, 1, Irandom is a random integer from [1,2,…D] The engine for automatic velocity optimization Initialization Mutation ui ,G xi ,G 1 x i ,G if f ui ,G 1 f xi ,G 1 otherwise i 1,2, , N Crossover rj ,i ~ U 0, 1 , Irandom is a random integer from [1,2,…D] Selection Mutation, crossover and selection continue until some stopping criterion is reached