review of kinematical inversion in prime software€¦ · processing accuracy estimation...

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


Input data




Isotropic inversion


Gradient analysis




Case study


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


Input data




Isotropic inversion


Gradient analysis




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



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.



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

10

Contents

11

Introduction


Input data




Isotropic inversion


Gradient analysis




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


Input data




Isotropic inversion


Gradient analysis




Case study


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


18

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

19

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


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


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


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


23

Illustration of a tomographic mesh and ray tracing process

Contents

24

Introduction


Input data




Isotropic inversion


Gradient analysis




Case study


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?


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

27

Contents

28

Introduction


Input data




Isotropic inversion


Gradient analysis




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


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


with overlaid model


Tomographic updating of intrusion

39


See next slide

Influence of intrusion shape

40




Local anomaly

Influence of intrusion shape

41


with overlaid model


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 vertical slice

44


with overlaid model


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

mailto:[email protected]

mailto:[email protected]

http://www.yandexterra.com/

Thank you for your attention!

yandexterra.com

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