### High resolution velocity analysis for resources plays

```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
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
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
Qm    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
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
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
29
• 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
```