review of kinematical inversion in prime software€¦ · processing accuracy estimation...
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Review of kinematical inversion
in Prime software
Contents
2
Introduction
Components of kinematical inversion
Input data
Model types of layer
Inversion techniques
Recalculation to layer top
Isotropic inversion
Layer reconstruction
Gradient analysis
Anisotropic inversion
Tomographic inversion
Simplified workflow of kinematical inversion
Case study
Introduction
3
Depth-
velocity
model
Statics
Migration
Multiples
Topography
accounting
Signal
processing
Accuracy
estimation
Depth-velocity model is a central element of the whole seismic processing workflow in Prime software. Firstly we will
introduce main terms and inversion techniques and then describe simplified workflow of depth-velocity model
building.
The place of a depth model in the processing workflow structure
Contents
4
Introduction
Components of kinematical inversion
Input data
Model types of layer
Inversion techniques
Recalculation to layer top
Isotropic inversion
Layer reconstruction
Gradient analysis
Anisotropic inversion
Tomographic inversion
Simplified workflow of kinematical inversion
Case study
Components of kinematical inversion
5
Inversion consists of three components:
Input data – observed wave field and its kinematical characteristics, other a priori data
Depth-velocity model – a tool of describing the real media
Techniques of model parameters estimation for a chosen type of model
Contents
6
Introduction
Components of kinematical inversion
Input data
Model types of layer
Inversion techniques
Recalculation to layer top
Isotropic inversion
Layer reconstruction
Gradient analysis
Anisotropic inversion
Tomographic inversion
Simplified workflow of kinematical inversion
Case study
Kinematical characteristics
of observed wavefield
7
In Prime software all tools of extracting kinematical characteristics are horizons-based. This feature makes
inversion more stable and geologically reasonable.
Hyperbolic analysis in the time domain (t0 and Vcmp)
In simple cases it is acceptable to use horizons based stacking velocity analysis in the time domain for describing
wavefield kinematics.
Illustration of a wavefield kinematical parameterization by a hyperbolic curve
Kinematical characteristics
of observed wavefield
8
Analytical hodograph + trend of static corrections
In complex cases with a poor data caused by low density of seismic observations it is possible to use surface-
consistent description of wavefield kinematics. It is extremely useful for working with shallow part of a land data but it
can be used for marine data also. The main advantage of this approach – it works well even when the migration fails.
It’s. The disadvantage – it is applicable only when static corrections simplifies seismic events.
Illustration of a wavefield kinematical parameterization by a surface-consistent approach.
Resulting times are a combination of a fitted hyperbolic curve and a smooth component
of surface-consistent static corrections.
Migration velocity analysis in a migrated domain
The most common technique consists in using the residual moveout analysis in the depth migrated domain after
migration in a priori model. Usually it is being carried out by layer to layer, that makes residual moveout
curves/surfaces simpler after inversion for each previous layer. In most cases the residual moveout can be
approximated by hyperbola for each next layer.
Kinematical characteristics
of observed wavefield
9
Illustration of a wavefield kinematical parameterization by picking events in depth
migrated domain and its recalculation to time domain for each offset plane
For controlling the inversion process and delivering more information
Wells markers
Interpretation of horizons
VSP data
Constraints of model parameters
A priori input data
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Contents
11
Introduction
Components of kinematical inversion
Input data
Model types of layer
Inversion techniques
Recalculation to layer top
Isotropic inversion
Layer reconstruction
Gradient analysis
Anisotropic inversion
Tomographic inversion
Simplified workflow of kinematical inversion
Case study
Generalized layer-based model
12
Generalized layer-based model is a standard layer-based isotropic model with extended classes of layers
parameterization and special techniques for its building. We can use the following (from left to right):
Inhomogeneous layer consisting of two layers
Layer with vertical gradient of velocity
Anisotropic layer
Isotropic layer with a conformal mesh
Anisotropic layer with a conformal mesh
Illustration of extended classes of layer model
Contents
13
Introduction
Components of kinematical inversion
Input data
Model types of layer
Inversion techniques
Recalculation to layer top
Isotropic inversion
Layer reconstruction
Gradient analysis
Anisotropic inversion
Tomographic inversion
Simplified workflow of kinematical inversion
Case study
Recalculation to layer top
14
For simplifying an inverse problem in each layer the measured time field can be recalculated to its top. This method is
a common place for all types of inversion techniques which we use in practice. It requires derivatives of time fields
from source and receiver sides. This allows to turn the global problem into the problem in a single layer.
Illustration of recalculating data to layer top from source and receiver sides
Isotropic inversion
15
The process of kinematical inversion always starts with an isotropic assumption. It is possible to find geometry of
layer bottom and velocity distribution simultaneously. It is proved that such problem have a unique solution in a single
isotropic layer. There are two approaches implemented in Prime software for solving this problem:
R-method
Iterative method
Both of them are non-linear and use assumption about locally homogeneity of media. That means that it is possible to
assume constant velocity at local small area.
Isotropic inversion
R-method
16
R-method additionally uses assumption about local linearity of
reflection surface. In such case four unknowns have to be found: 𝑉 –
interval velocity, ℎ - depth of surface, 𝑛𝑥, 𝑛𝑦 - components of surface
normal. For doing that R-method uses recalculated data to top of
layer for constructing and solving system of many non-linear
equations for all pairs of source ( Ԧ𝑆) and receiver (𝑅) in some local
area which is called inversion base:
𝑡(𝑆𝑖, 𝑅𝑖) =1
𝑉𝑆𝑖 − 𝑅𝑖
2+ 4 𝑆𝑖 , 𝑛 + ℎ 𝑅𝑖, 𝑛 + ℎ .
This method is extremely fast what allows to get solution in each
CMP point during a short time. Also this method can be used for
building a special criterion for checking correctness of assumption
about local homogeneity.
Illustration of R-method principle
Isotropic inversion
Iterative method
17
Iterative method is a non-linear method which solves minimization
problem:
min𝑉
𝐺 𝑉 − 𝑇 1 .
For doing that it creates map migration of 𝑡0 surface for assumed
value of locally constant velocity and solves direct problem 𝐺 𝑉 .
Comparison with observed time field gives a new assumption about
velocity value. Such process is repeated until convergence. This
method much slower than R-method and can’t be done at each CMP
point for producing huge statistics but it can take into account
anisotropic and gradient parameters and to invert them too. Also it
can use data at day surface without recalculating them to layer top.
This can be useful for very complex near-surface model when time
fields derivatives calculation is poor.
Illustration of an iterative method principle
Layer reconstruction
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Layer reconstruction is a technique for building a compensational
model of layer consisting of two sub layers. It is quite useful in cases
of existing strong refraction boundary with poor visibility. Method
requires geological interpretation of layer bottom as a constrain and
it is based on uniqueness solution of problem of refraction boundary
reconstruction by information about velocity distribution above/below
it and 𝑡0 surface. It is usually used for salt shape reconstruction etc.
This technique solves minimization problem
min𝑉1,𝑉2
𝐺 𝑉1, 𝑉2 − 𝑇 1
which can be divided into two stages:
refractor surface reconstruction for assumed values of 𝑉1, 𝑉2direct problem solving and new assumption about 𝑉1, 𝑉2.
Illustration of a layer reconstruction method principle
Gradient analysis
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For estimation of parameters of layer with a vertical gradient of
velocity special technique exists. For solving that inverse problem
time fields of several horizons inside layer are required. Using patch
horizons is valid. At each horizon for each pair of velocity and
parameter of gradient 𝑡0 map migration is being performed and
direct problem is being solved. Misfits with observed data are being
added to special spectrum. Such spectrum shows whether layer can
be characterized by linear law of velocity and allows to pick solution
if assumption is true.
Illustration of a gradient analysis spectrum
Anisotropic inversion
20
Anisotropic model is useful for compensating both effects of true anisotropy and missed layering. Anisotropic
inversion hasn’t a unique solution. Some constrains are required. In our point of view the best and the most
controlled constrain is a geological interpretation of layer bottom boundary which can be based on an isotropic
solution. Anisotropic inverse problem can be formulated in next manner.
Input data
Surfaces of layer top and bottom
Time field 𝑡 𝑥𝑆, 𝑦𝑆 , 𝑥𝑅 , 𝑦𝑅 recalculated to a layer top
Surfaces 𝑡0𝑥′ 𝑥, 𝑦 , 𝑡0𝑦
′ 𝑥, 𝑦 and t0 𝑥, 𝑦 recalculated to a layer top
Problem
Find parameters 𝜐0 𝑥, 𝑦 , 휀 𝑥, 𝑦 , 𝛿 𝑥, 𝑦 , 𝑎𝑥 𝑥, 𝑦 , 𝑎𝑦 𝑥, 𝑦 such that misfit between predicted and observed
time fields will be minimum
Anisotropic inversion
21
Two sub tasks have to be solved
Solve optimization problem with parameters 휀 and 𝛿 in assumption of a locally homogeneity by minimization of
cost function:
min,𝛿{ 𝐽 𝛿 ≔ 𝐺 휀, 𝛿 − 𝑇 + 𝜆 휀 − 휀0 2
2+ 𝜆 𝛿 − 𝛿0 2
2}
Solve optimization problem with parameters 𝜐0,𝑎𝑥,𝑎𝑦 (usually VTI case assumed i.e. 𝑎𝑥 = 𝑎𝑦 = 0) in assumption
of locally homogeneity using fixed values of 휀 and 𝛿 solve by minimization of cost function:
min𝑥, 𝑦
𝐽𝜐0𝑎𝑥𝑎𝑦 = ൝𝐺 𝜐0, 𝑎𝑥, 𝑎𝑦 − 𝑇 ,Δ𝑡0𝑃 ≤ Δ𝑡0𝑃𝑚𝑎𝑥
𝑝𝑒𝑟𝑟 ⋅ Δ𝑡0𝑃, Δ𝑡0𝑃 > Δ𝑡0𝑃𝑚𝑎𝑥
Anisotropic inversion
22
In a point of normal reflection the wavefront has to
be tangent to the surface. Velocity has to be
consistent with 𝑡0 value.
𝑡0𝑥′ and 𝑡0𝑦
′ values can be used for penalization of
undesirable points
Tomographic inversion is useful when it is required to use time fields
of several horizons simultaneously and to update arbitrary part of the
model. For example it is quite frequent scenario when shallow part of
the model is being updated after inversion of deeper horizons when
shallow part prints are observed. Deeper horizons has more larger
offsets what leads to more robust inversion. The tomography in the
Prime software can work in layers with conformal mesh which
parameterized in a layer-based manner. It uses input data in time
domain and produces internal iterations, i.e. it implements non-linear
approach. This approach is based on iterative ray tracing and solving
system of linear equations:
𝐽𝑇𝑊𝑇𝑊𝐽 + 𝜆𝑘𝐸 + 𝛼 ∙ 𝑑𝑖𝑎𝑔 𝐽𝑇𝑊𝑇𝑊𝐽 ∆𝑚𝑘 = 𝐽𝑇𝑊𝑇𝑊Δ𝑇𝑘 + 𝜆𝐸 𝑚0 −𝑚𝑘
𝑚𝑘 + ∆𝑚𝑘 ∈ 𝑀
min𝛼≥0
𝛼 : ∆𝑚𝑘 ≤ ∆𝑘
Tomographic inversion
23
Illustration of a tomographic mesh and ray tracing process
Contents
24
Introduction
Components of kinematical inversion
Input data
Model types of layer
Inversion techniques
Recalculation to layer top
Isotropic inversion
Layer reconstruction
Gradient analysis
Anisotropic inversion
Tomographic inversion
Simplified workflow of kinematical inversion
Case study
Simplified workflow of kinematical inversion
25
Kinematical inversion in Prime software implements a layer-by-layer approach. We will describe
simplified workflow of depth-velocity model building by using migration velocity analysis (MVA)
technique for input data extraction as the most common method. The usage of other tools for time
field measurement is quite simple and similar to MVA.
Set a priori velocity below the last existent horizon in model, i.e. for the half-space. The horizon, which must to
be inversed, is located in this half-space
Run a pre-stack migration below the last existent horizon
Correlate the depth of the horizon, which must to be inversed, on the depth cube
Compute and correlate the spectrum of residual moveout parameter of the horizon, which must to be inversed
(or run automatic picking)
Solve a direct problem using correlated depth and residual moveout surfaces for measuring time field and its
characteristics
Solve an inverse problem in the assumption of isotropic layer
Smooth out surface of resultant velocity and recompute depth surface while data misfit is acceptable
Check a resultant depth surface. Is mis-tie with wells markers acceptable? Is the shape acceptable?
Simplified workflow of kinematical inversion
26
If mis-ties is unacceptable then correct depth surface according to wells data and perform anisotropic or
tomographic inversion
If shape of depth surface is unacceptable then make geological assumption and correct it. Perform a layer
reconstruction or tomographic inversion.
If chosen layer consists patch horizons with significantly other residual moveout then correlate it and its
spectrum and conduct gradient analysis or tomographic inversion
If after all possible variations misfit with data is quite big then you could lose some horizon. Try to find it and
repeat the inversion for it
If there are no lost horizons then try to update upper part of model by tomography
When inversion for current horizon is done repeat all steps for next horizon
Finally, perform a global tomography if necessary
Simplified flowchart of kinematical inversion
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Contents
28
Introduction
Components of kinematical inversion
Input data
Model types of layer
Inversion techniques
Recalculation to layer top
Isotropic inversion
Layer reconstruction
Gradient analysis
Anisotropic inversion
Tomographic inversion
Simplified workflow of kinematical inversion
Case study
Topography accounting
29
Raw map of topography Map of smoothed topography
(smoothing radius 1000 m)
Problem description
30
Example of time migration result (has been received from client)
Surface corresponding to top of intrusion Map of surface corresponding to top of intrusion
The third floor
Building top of intrusion by layer inversion
31
For accounting of intrusion influence frame model has been build using kinematical inversion techniques.
The second floor
The first floor
Surface corresponding to bottom of intrusion Map of surface corresponding to bottom of intrusion
The third floor
Building bottom of intrusion by layer inversion
32
For accounting of intrusion influence frame model has been build using kinematical inversion techniques.
The second floor
The first floor
Frame model
33
Example of the frame model which used in further non-linear tomography
Frame model
34
Example of the frame model which used in further non-linear tomography
Tomographic updating above intrusion
35
Map of velocity before tomography Map of velocity after tomography
Tomographic updating of intrusion
36
Map of velocity before tomography Map of velocity after tomography
See next slide
Velocity local anomaly of intrusion
37
Example of time migration result
(has been received from client)
Example of depth migration result
Local anomaly
Velocity local anomaly of intrusion
38
Example of depth migration result
with overlaid model
Example of depth migration result
Tomographic updating of intrusion
39
Map of velocity before tomography Map of velocity after tomography
See next slide
Influence of intrusion shape
40
Example of time migration result
(has been received from client)
Example of depth migration result
Local anomaly
Influence of intrusion shape
41
Example of depth migration result
with overlaid model
Example of depth migration result
Result of tomography
Maps comparison of target horizon
42
Map of horizon from target area before tomography Map of horizon from target area after tomography
Example of vertical slice
43
Example of time migration result
(has been received from client)
Example of depth migration result
Example of vertical slice
44
Example of depth migration result
with overlaid model
Example of depth migration result
General Director –
Mosyakov Dmitriy
Chief Geophysicist –
Silaenkov Oleg
Head of R&D Department –
Finikov Dmitriy
Head of Seismic Data Processing
Department –
Kuznetsov Ivan
Marketing Director –
Solovyeva Inna
e-mail: [email protected]
Office address:
Off. B-307, bld. 42/1, Bolshoy Bulvar, Technopark Office Center, Skolkovo Innovation Center,
Moscow, Russia, 143026
Phone: +7 (495) 943-47-70
E-mail: [email protected]
www.yandexterra.com
45
Thank you for your attention!
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