High Resolution Velocity Analysis for Resource Plays Bo Zhang and J. T. Kwiatkowski

Outline Factors that affect the fidelity of velocity analysis High resolution velocity spectrum The engine for automatic velocity optimization Automatic interval velocity analysis based on DE (workflow) Synthetic and Real data examples Conclusion Road-ahead

Factors that affect the fidelity of velocity analysis The resolution of velocity spectrum. 0.5 1.0 1.5 0.0 12000 14000 Time (s) Velocity (ft/s) 1000 Semblance 12000 14000 Velocity (ft/s) 1000 SN based on PFA Vs.

Factors that affect the fidelity of velocity analysis Manually picking velocity at CDP location? Manually picking velocity for each reflection events? Conventional velocity analysis Dense velocity analysis (http://www.slb.com/services/westerngeco/services/dp/technologies/time/technology/dva.aspx)

Outline Factors that affect the fidelity of velocity analysis High resolution velocity spectrum The engine for automatic velocity optimization Automatic interval velocity analysis based on DE (workflow) Synthetic and Real data examples Conclusion Road-ahead

High resolution velocity spectrum The seismic trace d(t) can be written as where d(t) is the seismic traces, s(t) is the reflection signal, and n(t) is the noise. Suppose we have M traces in one CDP gather, then Construction the correlation matrix between each traces d_corr

High resolution velocity spectrum Assume the noise and reflected signals are uncorrelated, then the eigenstructure of d_corr has the following properties: d_corr is not sensitive to amplitude variation (AVO) In the ideal case, d_corr is a rank 1 matrix. The maximum eigenvalue of d_corr is corresponding major underline factors which is regards as the reflected signals. Those two properties suggest giving an estimated signal-to-noise ratio (S/N) to the corrected gather

High resolution velocity spectrum 0.5 1.0 1.5 0.0 3000 6000 9000 Time (s) Offset (ft) Synthetic gather with random noise added

High resolution velocity spectrum 0.5 1.0 1.5 0.0 12000 14000 Time (s) Velocity (ft/s) 10000 semblance

High resolution velocity spectrum 0.5 1.0 1.5 0.0 12000 14000 Time (s) Velocity (ft/s) 10000 SN based on PCA

Outline Factors that affect the fidelity of velocity analysis High resolution velocity spectrum The engine for automatic velocity optimization Automatic interval velocity analysis based on DE (workflow) Synthetic and Real data examples Conclusion Road-ahead

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: Mutation Initialization 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: where G is the generation number.

The engine for automatic velocity optimization Define upper and lower bounds for each parameter: Mutation Initialization Crossover Selection Randomly select initial parameter values uniformly between the upper and lower bounds.

The engine for automatic velocity optimization Each of the N parameter vectors undergoes mutation, recombination and selection Mutation expands the search space For a given parameter vector xi,G randomly select the three different vectors: Mutation Initialization Crossover Selection

The engine for automatic velocity optimization Add the weighted difference of two of the vectors to the third to form the donor vector: Mutation Initialization Crossover Selection The mutation factor F is a user defined constant from [0, 2]

The engine for automatic velocity optimization Crossover incorporates successful solutions from the previous generation The trial vector ui,G+1 is developed from the elements of the target vector, xi,G, and the elements of the donor vector, vi,G+1 Elements of the donor vector enter the trial vector with probability CR Mutation Initialization Crossover Selection

The engine for automatic velocity optimization if or Mutation Initialization Crossover Selection if or , Irandom is a random integer from [1,2,…D]

The engine for automatic velocity optimization if Mutation Initialization Crossover Selection otherwise , Irandom is a random integer from [1,2,…D] Mutation, crossover and selection continue until some stopping criterion is reached

Outline Factors that affect the fidelity of velocity analysis High resolution velocity spectrum The engine for automatic velocity optimization Automatic interval velocity analysis based on DE (workflow) Synthetic and Real data examples Conclusion Road-ahead

Automatic interval velocity analysis Conventional migration velocity analysis on the coarse grid Initialize the population set based on the conventional velocity model Get the trail interval velocity set by DE operation Define the analysis time grids along t0 axis for each CDP Prestack time migrated gather after reverse NMO Output the best member Compare the semblance value of trail and target interval model. The one with greater semblance value survives into next generation More generations Yes No

Outline Factors that affect the fidelity of velocity analysis High resolution velocity spectrum The engine for automatic velocity optimization Automatic interval velocity analysis based on DE (workflow) Synthetic and Real data examples Conclusion Road-ahead

Synthetic data examples Time (s)

Synthetic data examples 0.5 1.0 1.5 0.0 3000 6000 9000 Time (s) Offset (ft) Synthetic gather

Synthetic data examples 0.5 1.0 1.5 0.0 12000 14000 Time (s) Velocity (ft/s) 10000 semblance

Synthetic data examples 0.5 1.0 1.5 0.0 12000 14000 Time (s) Velocity (ft/s) 10000 SN based PCA

Synthetic data examples

Synthetic and Real data examples

Synthetic data examples 0.5 1.0 1.5 0.0 3000 6000 9000 Time (s) Offset (ft) NMO correction based velocity model from DE

Synthetic data examples 0.5 1.0 1.5 0.0 3000 6000 9000 Time (s) Offset (ft) NMO correction based manual picking velocity model

Synthetic data examples 0.5 1.0 1.5 0.0 3000 6000 9000 Time (s) Offset (ft) Synthetic gather with random noise added

Synthetic data examples 0.5 1.0 1.5 0.0 12000 14000 Time (s) Velocity (ft/s) 10000 semblance

Synthetic data examples 0.5 1.0 1.5 0.0 12000 14000 Time (s) Velocity (ft/s) 10000 SN based PCA

Synthetic data examples

Synthetic data examples

Synthetic data examples 0.5 1.0 1.5 0.0 3000 6000 9000 Time (s) Offset (ft) NMO correction based velocity model from DE

Synthetic data examples 0.5 1.0 1.5 0.0 3000 6000 9000 Time (s) Offset (ft) NMO correction based manual picking velocity model

Real data examples Location map of the Chicontepec foredeep in East-Central Mexico(Sarkar, 2011)

Real data examples 0.0 0.5 1.0 1.5 2.0 1 100 50 Time (s) CMP number high low Interval velocity from Dix inversion based on RMS velocity

Real data examples Interval velocity based on de search 0.0 0.5 1.0 1.5 2.0 1 100 50 Time (s) CMP number high low Interval velocity based on de search

Real data examples Manually picking RMS velocity 0.0 0.5 1.0 1.5 2.0 1 100 50 Time (s) CMP number high low Manually picking RMS velocity

Real data examples RMS velocity from DE optimization 0.0 0.5 1.0 1.5 2.0 1 100 50 Time (s) CMP number high low RMS velocity from DE optimization

Real data examples 0.0 0.5 1.0 1.5 2.0 1 100 50 Time (s) CMP number stacked section based on the RMS velocity from manual picking

Real data examples 0.0 0.5 1.0 1.5 2.0 1 100 50 Time (s) CMP number stacked section based on the RMS velocity from DE optimization

Real data examples Model based Impedance inversion 0.0 0.5 1.0 1.5 2.0 100 50 Time (s) CMP number high low Model based Impedance inversion

Outline Factors that affect the fidelity of velocity analysis High resolution velocity spectrum The engine for automatic velocity optimization Automatic interval velocity analysis based on DE (workflow) Synthetic and Real data examples Conclusion Road-ahead

Conclusion Interval velocity from RMS velocity strongly suffers the errors contained in the RMS velocity model From the synthetic testing, interval velocity model from DE optimization is superior to that generated from RMS velocity. In the real case study, the optimized interval velocity model has more detail than that inverted from RMS velocity By employing Gardner’s equation, high resolution interval velocity model can be used for model based impedance inversion Multiples will strongly damage the the optimized interval velocity

Road-ahead Consider the analysis time location on the section instead of each CDP alone. Integrate the interpreted horizons into the analysis. Testing on other surveys.

Acknowledgements PEMEX for permission to use and show their data The industry sponsors of the University of Oklahoma Attribute-Assisted Seismic Processing and Interpretation (AASPI) Consortium.