why seismic processing ?

By:

Ali

Mis

aghi

Why seismic processing ?

Processing Steps

By:

Ali

Mis

aghi What’s a seismic trace?

Sandstone

Coal

Carbonate

Salt

Shale

* S(t) * R(t) Seismic trace + Noise (t) =Rf(t)

Filtering

Stacking

.

.

.

Deconvolution

By:

Ali

Mis

aghi

*

g(t)

f(t)

*

g(t)

f(t)

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Ali

Mis

aghi

Wave propagation

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Ali

Mis

aghi

By:

Ali

Mis

aghi Land dataMarine data

Split shot gather

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Ali

Mis

aghi

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000 2500

X (m)

T (s)

Direct

Ground roll

Head wave (refraction)First multiple

Primary

R1 R2

Seismic eventsNon-primary events

By:

Ali

Mis

aghi

Primary

Earth’s surface

Subsurface reflector

S R1

Ground roll Direct P-wave

R2

Head wave (refraction)

First multiple

Seismic eventsNon-primary events

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Ali

Mis

aghi

CDP Fold =Number of receivers x receiver interval

2 x shot interval

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Ali

Mis

aghi

CDP gather NMO Stack

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Ali

Mis

aghi

Migration

“The goal of migration is to make the stacked section appear similar to the

geologic cross-section”

Oz Yilmaz

By:

Ali

Mis

aghi

A step in seismic processing in which reflections in seismic data are moved to their correct locations in the x-y-time space of seismic data, including two-way traveltime and position relative to shotpoints

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

m

n

Zn Zm

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Ali

Mis

aghi

By:

Ali

Mis

aghi

Typical ProMax flow for velocity analysis.

By:

Ali

Mis

aghi

Examining the normal moveout equation, it is possible to analyze NMO velocities by plotting reflections in T2 X2 space

By:

Ali

Mis

aghi

Concept of Constant Velocity Stack as an aid to stackingvelocity estimation.

By:

Ali

Mis

aghi

One method to determine stacking velocity is to use a Constant Velocity Stack (CVS) for several CDP gathers

By:

Ali

Mis

aghi

Same CVS panel of traces as before switching to variabledensity color for the traces to utilize dynamic range

By:

Ali

Mis

aghi

Same as previous color panels with velocity range nowhalved to better pick correct velocities

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Ali

Mis

aghi

Another term for Normal Moveout Equation.

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Ali

Mis

aghi

Options in the ProMax Velocity Analysis Routine.

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Ali

Mis

aghi

Demonstration of the velocity spectra

By:

Ali

Mis

aghi


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Ali

Mis

aghi

CDP gather with NMO applied (center) surrounded by panelshaving progressively lower velocity (left) or higher velocity.

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Ali

Mis

aghi


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Ali

Mis

aghi

From left to right are panels for Semblance, Gather, DynamicStack, Flip Stacks, and Velocity Function Stack.

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Ali

Mis

aghi

The ProMax routine ‘Velocity Analysis’ has it all – from left toright: velocity spectra, interactive cursor with CDP gather,dynamic stack, and a variation on CVS

By:

Ali

Mis

aghi

The Semblance Panel shows the semblance plot, the pickedvelocity function, guide functions, and the interval velocitycomputed from the picked function.

By:

Ali

Mis

aghi

Dix equation converts stacking velocities to interval velocities.

By:

Ali

Mis

aghi However, you get RMS velocities, one can continue to

calculate interval velocities, interval thicknesses, and average velocities.

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Ali

Mis

aghi

Remaining three panels in Velocity Analysis routine.

By:

Ali

Mis

aghi

Use of ProMax routine Velocity Viewer and Editor

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Ali

Mis

aghi

A common problem with stacking is residual NMO on theCDP gathers resulting from imperfect velocity specification.

By:

Ali

Mis

aghi

Example of the data/velocity Interleave Display usingLandmark’s SeisCube program.

By:

Ali

Mis

aghi

Progressive Mute Analysis

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Ali

Mis

aghi

Prestack CDP gather with a horizon plotted along an eventthat is not perfectly flattened by NMO; other causes might bestatics, noise, and/or lithology that is affecting the phase.

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

ProMax routine CDP/Ensemble Stack vertically stacksinput ensembles of traces.

By:

Ali

Mis

aghi

Definition of multiplies as it applies to processingseismic reflection data using ProMax.

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Ali

Mis

aghi

Example of a surface multiple on left in red and intrabedmultiple on the right in blue.

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Ali

Mis

aghi

Comparison of short-path and long-path multiples.

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Ali

Mis

aghi

Conceptual abstraction of the Tau – P domain

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Ali

Mis

aghi

Organizing seismic reflection data into ray-parameter domainhas certain advantages that are elaborated here.

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Ali

Mis

aghi

Working definition of the Radon Filter commonly used for multiple suppression – working in the intercept-time (T) / ray parameter (p) or slowness domain.

By:

Ali

Mis

aghi

Use of the radon transform for the removal of multiples bydiscriminating on the basis of moveout – here no rejection.

By:

Ali

Mis

aghi

Use of the radon transform for the removal of multiples bydiscriminating on the basis of moveout – rejection shown.

By:

Ali

Mis

aghi

More on the use of the Radon Filter.

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

Migration

By:

Ali

Mis

aghi Migration

“Migration is an inversion operation involving rearrangement of seismic information elements so that

reflections and diffractions are plotted at their true locations.”

R.E Sheriff

“The goal of migration is to make the stacked section appear similar to the geologic cross-section”

Oz Yilmaz

By:

Ali

Mis

aghi

Unmigrated

By:

Ali

Mis

aghi

Migrated

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Ali

Mis

aghi

Migration

• Collapses diffractions

• Corrects for dip– Moves dipping events in the updip direction

• Removes effects of surface curvature– “unties the bowties”

By:

Ali

Mis

aghi Reconstructing the wavefield

By:

Ali

Mis

aghi

Constant velocity migration

By:

Ali

Mis

aghi Schematic that shows the imaging problem for a

simple anticline.

By:

Ali

Mis

aghi Schematic that shows the imaging problem for a

simple syncline.

By:

Ali

Mis

aghi

Schematic that shows the imaging problem for a vertical fault.

By:

Ali

Mis

aghi Schematic that shows the imaging problem for a 30-

degree fault.

By:

Ali

Mis

aghiSchematic that shows the imaging problem for a reef model.

By:

Ali

Mis

aghi

• Kirchoff migration (diffraction stacking)

• Finite difference method

• F-K migration

– integral solution of wave equation

– derivative solution of wave equation

– Fourier domain solution of wave equation

Migration Methods

By:

Ali

Mis

aghi

Kirchoff Migration(Diffraction Summation)

For every point (x,z), collapse all energy from hyperbola with vrms

AB

C O

t0

x

t

2

220

2 4rmsv

xtt

By:

Ali

Mis

aghi

Kirchoff Migration(Diffraction Summation)

Factors to consider before summing energy in diffraction:

• Obliquity factor– A cos

• Spherical divergence factor– A 1/r

• Wavelet shaping factor– phase correction

By:

Ali

Mis

aghi

Migration collapses diffractions to reveal structure

By:

Ali

Mis

aghi

Finite Difference Migration

• Solving the wave equation by stepping down discrete intervals from z=0

• Downward continue wavefield to “exploding reflector”

• Define an angle for width of cone for to be included in migration for each point– wider cone more accurate– narrow cone faster, better approximations

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

sintan a

Migration steepens and moves dipping reflectors

Apparent dip in time section is related to true dip:

(migrator’s equation)

By:

Ali

Mis

aghi Collapsing diffraction and relocating

dipping surface

Diffraction D Apex P

Reflector B A

By:

Ali

Mis

aghi

F-K Migration• Events can be separated by their

dips in F-K space

• Transform according to migrator’s equation tan a=sin

• Advantage: very computationally efficient!

• Disadvantage: only works for constant velocity (without modifications that compromise its efficiency)

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi Migration removes multiple-

branch reflections

• Synclines get broader

• Anticlines get narrower

By:

Ali

Mis

aghi

“Untying the bowties”

By:

Ali

Mis

aghi

Limitations of Migration• Insufficient spatial resolution will result in aliasing• 2-D slice of 3-D wavefield (need 3-D migration!)• Edge effects• Coherent noise• Requires knowledge of velocity structure• Time migration methods assume lateral velocity varies

slowly (otherwise need depth migration)

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

3-D Processing

• Binning by common midpoints in cells on a grid

• Migration can be two stage 2-D migration (in-line direction, then cross-line direction) or full 3-D wavefield solution

• Most other processing operations are unchanged

• Display is more difficult (and more fun!)

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

Why Deconvolution?

• Decreases ringing

• Increases resolution

• Improves appearance of stacked section and makes it easier to interpret

• Section is more like the earth and less like the seismic source

• Can remove multiples

By:

Ali

Mis

aghi

Convolutional model of a seismograms=w*e+n

source wavelet

11v

22v

33v

44v

55v

Earth response function seismogram

*

(+noise)

=

By:

Ali

Mis

aghi

Spiking Filter

• Take existing wavelet and transform to a unit impulse (delta function)

• Also called “whitening” because it aims to create a white spectrum

By:

Ali

Mis

aghi

Predictive Deconvolution

• Deconvolution with a built-in time lag

• Use to remove – Multiples– Bubble pulse

By:

Ali

Mis

aghi

Deconvolution Example

By:

Ali

Mis

aghi

Raw gather decon Bandpassfiltered

autocorrelograms

By:

Ali

Mis

aghi

Raw gathers

By:

Ali

Mis

aghi

After decon

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

Deconvolution

• Deterministic Inverse Filtering

• Deghosting

• Least Squares (Optimum) Filtering

• Spiking filter

• Wavelet shaping

• Predictive Deconvolution

By:

Ali

Mis

aghi Convolutional model of a

seismogram

s=w*e+n

One equation with 3 unknowns

How can we possibly find e?

We make assumptions:– e, n are white (random)– w is minimum phase

By:

Ali

Mis

aghi

w

e

s

By:

Ali

Mis

aghi

Am

plitu

deS

pect

rum

Aut

ocor

rela

tion

Am

plitu

deEarth response Wavelet Seismogram

By:

Ali

Mis

aghi

Deterministic DeconvolutionAssume that an operator f(t) exists such that

)()(*)( ttftw

In the Fourier domain:

1)()( FW

f

w

if

iw

eAF

eAW

)()(

)()(

wiw eA

F)(

1)( so

and

)()(

)(/1)(

wf

wf AA

The inverse operator f(t) has opposite phase and inverse amplitude spectrum from the source wavelet w(t)

By:

Ali

Mis

aghi

Deterministic Deconvolution

• Assumptions:1 source wavelet is minimum phase2 noise is zero3 wavelet is known

• Not true, especially 2

• In practice, the Fourier domain implementation is not very good if assumptions are not met

• Other methods are more stable

By:

Ali

Mis

aghi

Deghosting

• Eliminate source & receiver ghosts by considering them as time delayed copies of the source (and with known depths the time delays are known)

• Alternatively, hydrophones and geophones with different responses can be combined to eliminate ghosting effects

By:

Ali

Mis

aghi

Correlation

Autocorrelation

Cross-correlation

1,,1,01

)(1

0

Nkxx

Nxr

kN

tkttk

1,,1,01

),(1

0

Nkyx

Nyxg

kN

tkttk

By:

Ali

Mis

aghi

Wavelet Estimation

• In general, the source wavelet is unknown

• Source wavelet can be estimated from seismogram alone assuming:– minimum phase wavelet– white earth response spectrum

ewx rrr * autocorrelation

(with white earth response)wx rrr 0

Autocorrelation of seismogram is the autocorrelation of source wavelet (within a constant)

By:

Ali

Mis

aghi

Optimum Weiner Filters

Want to find the optimum filter components fi that minimize the error between the desired and actual outputs in a least-squares sense:

t

ttt xfdL 2)(

)1(,,2,1,0,0

nif

L

i

By setting

so 022

itt t

titti

xxfxdf

L

Recognizing the terms for auto- and cross-correlation,

ii grf

itt t

titt xdxxf

or

By:

Ali

Mis

aghi


ii grf

Or, in matrix form,

1

2

1

0

1

2

1

0

0321

3012

2101

1210

nnnnn

n

n

n

g

g

g

g

f

f

f

f

rrrr

rrrr

rrrr

rrrr

The autocorrelation matrix is a Toeplitz matrix, and can be inverted by Levinson recursion

are called the normal equations

By:

Ali

Mis

aghi


1

2

1

0

1

2

1

0

0321

3012

2101

1210

nnnnn

n

n

n

g

g

g

g

f

f

f

f

rrrr

rrrr

rrrr

rrrr

The gi terms are the cross-correlation of the desired wavelet with the input wavelet (seismogram).

0

0

0

1

1

2

1

0

0321

3012

2101

1210

nnnn

n

n

n

f

f

f

f

rrrr

rrrr

rrrr

rrrr

In the case of spiking deconvolution, the normal equations take the form

By:

Ali

Mis

aghi

Wavelet Processing

• Attempt to shift source wavelet to some other known wavelet, to accomplish one or more of:

• Reduce variation of source (between shots, between receivers)

• Shift to another known wavelet– e.g., hydrophone response to match seismometer

• Separate wavelet and earth response more clearly

By:

Ali

Mis

aghi

Wavelet Processing

By:

Ali

Mis

aghi

Wavelet Processing

Transform to zero phase and broaden spectrumIncrease resolution

By:

Ali

Mis

aghi

By:

Ali

Mis

aghi

1) Shots : 2 – 548

2) Minimum phase

3) Traces have been resampled (2ms >4ms) and decimated (384 > 192)

4) Fk filter

5) Geometry has been applied

6) Velocity file is available(By Geco)

Real data

12.5 m

91o

25 m

7.5 m 8.5 m

By:

Ali

Mis

aghi

Check the muteVelocity Analysis

NMO

Stack

Real data work flowSorting

Pick mute

True Amplitude Recovery

Deconvolution

Velocity Manipulation

Migration

Demultiple

By:

Ali

Mis

aghi Real data

-A report:

-Explanation of the processing steps with proper and related snap shots(Mute, TAR, Decon, NMO, Demultipling, Stacking, Migration,etc

-Final results(a comparison study)

-Brute-stack section(s)

-Demultipled stack section(s)

-Migrated section(s)

Project results:

why seismic processing ?

Documents