2 SEISMIC DATA PROCESSING

Alteration of seismic data to suppress noise, enhance signal and migrate

seismic events to the appropriate location in space is termed as Seismic Processing.

It facilitates better interpretation because subsurface structures and reflection

geometries are more apparent.

2.1 OBJECTIVES

To obtain a representative image of the subsurface.

Improve the signal to noise ratio: e.g. by measurement of several channels

and stacking of the data (white noise is suppressed).

Present the reflections on the record sections with the greatest possible

resolution and clarity and the proper geometrical relationship to each other

by adapting the waveform of the signals.

Isolate the wanted signals (isolate reflections from multiples and surface

waves).

Obtain information about the subsurface (velocities, reflectivity etc.).

Obtain a realistic image by geometrical correction.

Conversion from travel time into depth and correction from dips and

diffractions

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2.2 PREPROCESSING

Preprocessing is the first and important step in the processing sequence and

it commences with the reception of field tapes and observers log .Field tape

contains seismic data and observers contains geographical data (shot/receiver

number, picket number, latitude and longitude etc).

2.3 DEMULTIPLEXING

Field tapes customarily arrive at the processing center written in multiplexed

format (time sequential) because that is the way generally the sampling is done in

field. In general the early stages of processing require channel ordered or trace

ordered data. Demultiplex is therefore done to convert the time sequential data into

trace sequential data.

Mathematically, Demultiplexing is seen as transposing a big matrix so that

the column of the resulting matrix can be read as seismic traces recorded at

different offsets with a common shot pint. At this stage, the data are converted in a

convenient format that is used throughout the processing. This format is

determined by the type of the processing system and individual company. A

common format used in seismic industry for data exchange is SEG-Y, established

by the society of exploration geophysicists. Nowadays demultiplexing is done in

the field.

2.4 REFORMATTING

The formats generally used for data recording are SEG-D (Demultiplexed

data) and SEG-B (Multiplexed data). Hence they are called field formats.

Demultiplexed is done on data recorded in SEG-D format. In this stage the data are

converted to a convenient format, which is used throughout processing. There are

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many standards available for data storage. Format differs with the manufarcturer,

type of recording instrument and also with the version of operating system.

2.5 FIELD GEOMETRY SET UP

Field geometry is created with the help of information provided by field

party. That is as follows.

1. Survey information

(I) X and Y coordinate of shot/vib. Points.

(II) Elevation of geophone/shot points

2. Recording instrument

(I) Record file numbers

(II) Shot interval, group interval, near offset and far offset

(III) Layout, no. of channels, foldage.

3. Processing information

(I) Datum statics

(II) Near surface model

(III) Datum plane elevation

2.6 EDITING

Edit traces, which consist of extremely noisy traces and muting the first-

arrivals on all traces. Traces from poorly planted geophones may show

sluggishness and introduce low frequency and sometimes cause spiky amplitudes

and therefore degrade a CMP stack. These traces are identified during manual

inspection/editing phase of all the shot records and flagged in the header so that

they will not be included (they are “killed”) in processing steps and in display.

Traces so noisy that they don’t visually correlate with strong arrivals on

adjacent traces should be killed. We have to be conservative in trace killing

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because the fold of this data is low and eliminating only a few traces may have

noticeable effect on the stacked traces.

Editing involves leaving out the auxiliary channels & NTBC traces and

detecting and changing dead or exceptionally noisy traces. Bad data may be

replaced with interpolated values. Noisy traces, those with static glitches or mono-

frequency high amplitude signal levels are deleted. Polarity reversals are corrected.

Output after editing usually includes a plot of each file so that one can see what

data need further editing and what type of noise attenuation are required.

Fig.2.1.1 (a) before editing (b) after editing

2.7 SPHERICAL DIVERGENCE CORRECTION

A single shot can be thought of a point source which gives rise to a spherical

wave field. There are many factors which affect the amplitude of this wave field as

it propagates through the earth.

Two important factors which have major effect on a propagating wave field

are spherical divergence and absorption. Spherical divergence causes wave

amplitude to decay as 1/r, where r is the radius of the wave front. Absorption

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results in a change of frequency content of the initial source signal in a time-

variant manner, as it propagates. Since earth behaves as a low pass filter so high

frequencies are rapidly absorbed.There are some programmes used for gain-AGC,

PGC, geometric spreading correction

2.8 STATIC CORRECTION

When the seismic observations are made on non flat topography, the

observed arrival times will not depict the subsurface structures. The reflection time

must be corrected for elevation and for the changes in the thickness of the

weathering layer with respect to flat datum. The former correction removes

difference in travel time due to variation of surface elevation of the shot and

receiver location. The weathering corrections remove differences in travel time to

the near surface zones of unconsolidated low velocity layer which may vary

thickness from place to place. These are also called static corrections, as they do

not change with time. The static corrections are computed taking into account the

elevation of the source and receiver locations with respect to seismic reference

datum (such as Mean Sea Level), velocity information in the weathering and sub

weathering layers. Often, special surveys (up hole surveys, shallow refraction

studies) precede the conventional acquisition to obtain the characteristics of the

low velocity layer.

2.9 TRACE BALANCING

To bring all the input data amplitudes in a specific range (necessary for

display), amplitude scaling is done. A separate balance factor is computed for and

applied to each trace individually. Now days, surface consistent amplitude

balancing is in use.

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2.10 MAIN PROCESSING

Main processing starts. It includes three major steps. They are as follows:

1. DECONVOLUTION

2. STACKING

3. MIGRATION

Fig 2.1.2 Seismic data volume represented in processing coordinate:

midpoint- offset-time (After Őz Yilmaz, etal 2001)

Deconvolution acts on the data along time axis and increase temporal

resolution.

Stacking compresses the data volume in the offset direction and yields the

plane of stack section (the frontal face of the prism)

Migration then move dipping events to their true subsurface position and

collapses diffraction and thus increases lateral resolution.

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2.11 DECONVOLUTION

Deconvolution is a process that improves the temporal resolution of seismic

data by compressing the basic seismic wavelet.

The need for Deconvolution In exploration seismology the seismic wavelet generated by the source

travels through different geologic strata to reach the receiver. Because of the many

distorting effects encountered the wavelet reaching the receiver is by no means

similar to the wave propogation by source.

Objective of deconvolution

Shorten reflection wavelets

Attenuate ghost , instrument effects , reverberation and multiple reflection

The convolutional model for deconvolution

(I) The earth is made up of horizontal layers of constant velocity.

(II) The source generates a compressional plane wave that impinges on layer

boundaries at normal incidence.

(III) The source wave form does not change as it travels in the surface.

(IV) The noise component n(t) is zero.

(V) The source waveform is known.

(VI) Reflectivity is a random series.

(VII) Seismic wavelet is minimum phase.

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There are two type Deconvolution

1) Deterministic Deconvolution

Deconvolution where the particular of the filter whose effects are to be

removed are known ,is called deterministic Deconvolution .The source wave

shape is sometime recorded and used in a deterministic source signature

correction .No random are involved for example where source wavelet is

accurately known ,we can do source signature Deconvolution.

2) Statistical Deconvolution

A statistical Deconvolution need to derive information about the wavelet

from the data itself where no information is available about any component of the

model .Statistical deconvolution is applied without prior application of

deterministic deconvolution in the case if land data taken with an explosive source.

In addition we make certain assumption about the data which justifies the

statistical approach

There are two type of statistical deconvolution

(I) Spiking Deconvolution –The process by which the seismic wavelet is

compressed into a zero lag spike is called Spiking deconvolution

(II) Predictive Deconvolution –The process uses prediction distance greater than

unity and yields a wavelet of finite duration instead of a spike. This is helpful in

suppressing multiples

Deconvolution parameter

Deconvolution can give best results only when accurate parameters are

chosen. Parameters associated with Predictive Deconvolution are:

(I) Operator Length-The total Operator Length is the sum of the “Prediction

operator length” (POL) and the “Prediction distance” (PD). The Deconvolution is

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ineffective if the POL is too short. Typically the prediction operator should exceed

two or three times the dominant period in the data.

(II)Prediction Distance (PD)- Prediction distance controls the extent to which

Deconvolution can compress the seismic wavelet. Deconvolved wavelets can have

pulse breadths no shorter than PD. Thus in general longer the prediction distance

‘milder’ the Deconvolution. “Spiking Deconvolution” is performed with PD of one

sample interval. As PD approaches unity, more contraction and consequently more

high-frequency noise is introduced. PD is to be chosen such that we get a good

compromise between resolution and signal-to-noise (S/N) ratio in the output trace.

(III)Percentage white noise- Compression of the seismic wavelet is also

controlled by the percentage white noise. The larger the percentage white noise,

the lesser is the compression. It is specified as a percentage of the total power in

the signal. The increase in the percentage white noise decreases the effect of

Deconvolution.

2.12 CMP Shorting

Seismic data acquisition with multifold coverage is done in shot-receiver

(s,g) coordinate. Seismic data processing, on other hand conventionally is done in

midpoint-offset (y, h) coordinates. The required coordinate transformation is

achieved by sorting the data into CMP gather based on the field geometry

information , each individual trace is assigned to the mid point between shot and

receiver location associated with that trace .Those traces with the same mid point

are grouped together , making up a CMP gather

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Fig 2.1.3 Seismic data in shot-receiver coordinates

Fig 2.1.4 Seismic in common midpoint gather

2.13 VELOCITY ANALYSIS

Velocity analysis is the most important and sensitive part of the processing.

Without velocity one cannot change seismic section into depth domain, which is

very necessary. For applying NMO correction one need NMO velocity. Thus one

performs the velocity analysis on each CDP gather but it is not feasible to perform

velocity analysis on each CDP gather. Hence one performs velocity analysis on

one CDP gather from a group of CDP points. There are several methods to do

velocity analysis like constant velocity scan; constant velocity stacks (CVS),

velocity spectrum method and horizontal velocity analysis. Out of these methods,

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now a day’s velocity spectrum method is most commonly used because it

distinguishes the signal along hyperbolic paths even with a high level of random

noise. This is because of the power of the cross correlation in measuring

coherency. The accuracy of the velocity is limited.

(I) Constant Velocity Stacks (CVS)

To obtain a reliable velocity function by the best stack of signal .Stacking

velocities often are estimated from the data stacked with range of constant

velocities on the basis of the stacked event amplitude and velocity. A portion of the

line of CMP gather has been NMO corrected and stack with constant range of

velocities. The resulting constant-velocity CMP stacks then displayed as a

panel .Stacking velocities are picked directly from the constant-velocity stack

(CVS) panel by choosing the velocity that yield the best stack response at a

selected event time

The CVS method is especially useful in areas with complex structure .In

such area this method allows the interpreter to directly chose the stack with best

possible event continuity .The constant-velocity stacks often contain many CMP

traces and sometime consist of an entire line.

(II) Velocity spectrum method

The velocity spectrum approach is unlike the CVS method. It is base on the

correlation of the traces in a CMP gather, and not on lateral continuity of staked

events. This method, compared with the CVS method, is more suitable for data

with multiple reflection problems. It is less suitable for highly complex structure

problems. Suppose we repeatedly correct the gather using constant velocity values

from 2000-4300 m/sec, then stack the gather and display the stacked traces side by

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side. The result is a display of velocity versus two-way time, called a “velocity

spectrum”.

There are two commonly used ways to display the velocity spectrum: power plot and contour plot

Fig 2.1.5 Two way of displaying velocity spectrum derived from the CMP gather (a),(b) power plot (c) contour plot ,( After Őz Yilmaz ,2001)

(III)Horizontal Velocity Analysis

One method to estimate velocities with enough accuracy for structural and

stratigraphic application to analyze the velocities of a certain horizon of interest

continuously. Such a detailed velocity analysis is called Horizontal Velocity

Analysis. The velocity is estimated at every CMP along the selected key horizon of

interest on the stacked section. The principle of estimating the velocities by this

method is the same as that of the velocity spectrum. The output coherency values

derived by hyperbolic time gates are displayed as a function of velocity and CMP

position.

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One of the applications of horizontal velocity analysis is to improve the

layered velocity variation along marker horizon, especially if these velocities are

used in post-stack depth migration.

2.14 NORMAL MOVEOUIT CORRECTION

Non zero offset data is characterized by a travel time increase with

increase in offset distance from the source to the reflector. The non zero offset to

zero offset conversion is achieved through a correction called NMO (normal move

out) correction.

For the single constant horizontal velocity layer the trace time curve of a

function of offset is a Hyperbola. The time difference between travel time at a

given offset and at zero offset is called normal moveout (NMO). The velocity

required to correct for normal moveout is called the normal moveout velocity. For

a single horizontal reflector, the NMO velocity is equal to the velocity of the

medium above the reflector.

For the simple case of single horizontal layer, the travel time equation as a

function of offset is

t2(x) = t2(0) + x2/v2 (2.1)

Where x is the distance (offset) between the source and receiver position. V is the

velocity of the medium above the reflecting interface. And f (0) is twice the travel

time along the vertical path. The NMO correction is given by the difference

between t(x) and t(0)

∆tNMO = t (x) – t (0)

= t (0) {[1- (x / vNMO.t (0)) 2]1/2 -1} (2.2)

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Fig 2.1.6 The simple geometry for NMO correction in single layer(After Őz Yilmaz ,2001)

NMO in a horizontal stratified earth

Now we consider a medium, composed of horizontal isovelocity layers each

layer have a certain thickness that can be defined in terms of two way trace time.

The layers have interval velocities (v1, v2, …. VN) where N is Number of layers.

Travel time equation for the path SDR is

T2(x) = c0 + c1x2 + c2x4 + c3x6 +…. (2.3)

Where c0 = t(0), c1 = 1 / v2rms and c2, c3, …… are complicated functions The

rms velocity vrms down to the reflector on which depth point D is situated is defined

as

V2rms = 1 / t(0) ∑ vi

2 ∆ti(0) (2.4)

Where ∆ti is the vertical two way time through the i th layer and t(0) = ∑ ∆tk.

By making small spread approximation the series in equation .We can be truncated

as follows:

T2(x) = t2(0) + x2 / v2rms (2.5)

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Here we see that the velocity required for NMO correction for a horizontally

stratified medium is equal to the rms velocity

Fig 2.1.7 NMO for horizontal layer(After Őz Yilmaz etal 2001)

Fig 2.1.8 Before and after NMO correction

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NMO StretchingIn NMO correction, a frequency distortion occurs, particularly for shallow

events and at large offset. This is called NMO stretching .The waveform with a

dominant period T is stretched so that its period becomes T’. Stretching is

frequency distortion in which events are shifted to lower frequencies. Stretching is

quantifies as

∆f / f = ∆tNMO / t (0) (2.6)

Where f is the dominant frequency. ∆f is change in frequency

Because of the stretched waveform at large offset, stacking the NMO corrected

CMP gather will severely damage the shallow events. This problem can be solved

by muting the stretched zone in the gather.

Fig 2.1.9 NMO Stretch

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2.16 RESIDUAL STATIC CORRECTION

They are statics deviation from a perfect hyperbolic travel time after

applying NMO and elevation statics corrections to this trace within the CMP

gather. These statics cause misalignment of the seismic events across the CMP

gather and generate a poor stack trace. Therefore one need to estimate the time

shifts from the time perfect alignment, then correct them using an automatic

procedure.

A model is needed for the moveout corrected travel time from a source

location to the point on the reflecting horizon, then back to a receiver location. The

key assumption is that the residual statics are surface consistent, meaning that

statics shift are time delays that depend on the sources and receiver on the surface.

Since the near-surface weathered layer has a low velocity value, and refraction in

its base tends to make the travel path vertical, the surface consistent assumption

usually is valid. However, this assumption may not be valid for high-velocity

permafrost layer in which rays tend to bend away from the vertical.

Residual static corrections involve three stages;

1. Picking the values.

2. Decomposition of its components, source and receiver static,

structural and normal moveout terms.

3. Application of derived source and receiver terms to travel times on the

pre-NMO corrected gather after finding the best solution of residual static

correction. These statics are applied to the deconvolved and sorted data, and the

velocity analysis is re-run. A refined velocity analysis can be obtained to

produce the best coherent stack section.

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2.17 DIP MOVE OUT (DMO) CORRECTION

The DMO correction says that-post-stack migration is acceptable when the

stacked data are zero-offset. If there are conflicting dips with varying velocities or

a large lateral velocity gradient, a prestack partial migration is used to attenuate

these conflicting dips. By applying this technique before stack, it will provide a

better stack section that can be migrated after stack. Prestack partial migration only

solves the problem of conflicting dips with different stacking velocities. Its

applications are;

I. Post-stack migration is acceptable when the stacked data is zero-offset. This

is not the case for conflicting dips with varying velocity or large lateral

velocity variations.

II. Pre-stack partial migration or dip Move out provides a better stack, which

can be migrated after stack.

III. PSPM solves only conflicting dips with different stacking velocities.

2.18 STACKING

I. Each common mid point gather after normal move out correction is summed

together to yield a stacked trace.

II. Stacking enhances the in-phase components and reduces the random noise.

III. Stacking yields Zero offset section (in the absence of dipping layers in the

subsurface)

Stacking is the combining two or more traces into one trace. This

combination takes place in several ways. In digital data processing, the amplitudes

of the traces are expressed as numbers, so stacking is accomplished by adding

these numbers together.

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Peaks appearing at the same time on each of the two traces combined to

make a peak as high as the two added together. The same is true of two troughs. A

peak and a trough of the same amplitude at the same time cancel each other, and

the stack trace shows no energy arrival at that time. If the two peaks are at the

different times, the combined trace will have two separate peaks of the same sizes

as the original ones. After stacking, the traces are “normalized” to reduce the

amplitude so that the largest peaks can be plotted.

Fig 2.1.10 Diagram for the stack processes

2.19 DECONVOLUTION AFTER STACK

NMO correction and Stacking also act as a high cut filter. Loss of high

frequencies results in loss of resolution. The Deconvolution after stack applied to

restore high frequency attenuated by CMP stacking and NMO correction.

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RANDOM NOISE ATTENUATION

Random noise is particularly common when the shot point is close to gravel,

boulders or buggy limestone, all of which can cause scattering of waves. Most of

random noise is reduced during stacking. The estimation of random noise is done

in frequency-space (F-X) domain. Each seismic trace in T-X domain is Fourier

transformed along the time axis to yield corresponding trace in F-X domain. Signal

energies, being sinusoidal, become predictable and can be removed in this domain

through a predictive deconvolution. Thus deconvolution in F-X domain removes

the signal content of the trace leaving behind the noise content. Total field minus

the estimated noise gives the signal field.

TIME VARIANT FILTER

Different parts of the section contain varying ranges of frequencies-

shallower part containing broader frequency than middle and lower part of the

section. Deconvolution enhances the bandwidth so a band pass filter has to apply

after deconvolution. So different parts of the seismic section have to be subjected

to different sets of band pass filters in a time variant manner. So the filter used at

this stage is time variant filter.

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3 MIGRATION

Migration is the process that moves the reflection energies from the apparent

locations to the true locations. The spatial velocity distribution is used here for the

identification of these true points in the subsurface. Migration improves the spatial

disposition of the reflecting layers and hence achieves ‘Imaging’.

3.1 Migration principles

The migration principles are

(I) The dip angle of the reflector in the geologic section is greater than in the time

section, thus migration steepens reflector.

(II) The length of the reflector, as seen in the geologic section is shorter than in

time section; thus, migration shortens the reflector.

(III) Migration move reflector in the updip direction.

0 A B x

C

True Dip C’

t D

D’

Apparent Dip

Fig 3.1.1 Migration principle

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3.2 MIGRATION STRATEGIES

CASE MIGRATION

Dipping Events Conflicting Dips with different

Stacking Velocities 3-D Behaviour of Fault Planes and

Salt Flanks

Time Migration Prestack Migration

3D Migration

Strong Lateral velocity variations Associated with complex overburden structures

Complex Non Hyperbolic Move out

3-D structures

Depth Migration

Prestack migration

3D MigrationNeed Based selection of type of Migration:

Fig 3.1.2 Simple structure and simple velocity Post Stack Time Migration

Fig 3.1.3 Simple structure and Complex velocity Post Stack Depth Migration

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Fig 3.1.4 Complex structure and simple velocity Pre Stack Time Migration

Fig 3.1.5 Complex structure and Complex velocity Pre Stack Depth Migration

3.3 Migration Parameters

After deciding on the migration strategy and the appropriate algorithm, the

analyst then needs to decide migration parameters

(I)Migration aperture-It is the parameter which is use in the Kirchhoff migration.

A small aperture causes removal of steep dips.

(II)Depth Step Size-It is the parameter which is use in finite difference method.

An optimum depth step size is the largest depth step with the minimum tolerable

phase errors. It depends on temporal and spatial sampling

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(III)Stretch Factor-It is the parameter which is used in Stolt migration .In a

constant velocity medium the stretch factor is one .The larger the vertical velocity

gradient, smaller stretch factor is needed.

3.4 BOW-TIE EFFECT

A concave-upward event in seismic data produced by a buried focus and

corrected by proper migration of seismic data. The focusing of the seismic wave

produces three reflection points on the event per surface location. The name was

coined for the appearance of the event in unmigrated seismic data. Synclines, or

sags, commonly generate bow ties.

Fig 3.1.6 A syncline might appear as a bow tie on a stacked section and can be

corrected by proper migration of seismic data.

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There are basically DIFFERENT TYPES of migration based upon the

domain in which the migration operates and the type of data on which it operates

(Stacked or Unstacked):

Fig 3.1.7 Different types of migration

3.6 Different Types of Migrations algorithm.

There are different types of migration algorithm

(I)Algorithms based on differential methods

Finite difference techniques implemented in t – x and f-x domains

(II)Algorithms implemented in the FK domain

FK, Phase shift, PSPC, and PSPI

(III)Algorithms based on integral methods

Kirchhoff’s method

3.7 KIRCHHOFF MIGRATION ALGORITHM

Kirchhoff migration is a non recursive method of seismic migration that uses

the integral form (Kirchhoff equation) of the wave equation. The Kirchhoff

migration method uses the same geometric and seismic wave-front principles as

the diffraction summation method .The Kirchhoff method considers the apex of the

diffraction curve to be the location of the true point reflector. The Kirchhoff

method is based on Huygens ‘Principle, according to which, the seismic reflector is

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Post-Stack

Pre-Stack3D Depth

2D Time

viewed as if it is composed of closely spaced point diffractions as shown in the

figure 3.1.8.The migration of a seismic section is achieved by collapsing each

diffraction hyperbola to its origin (apex). In this way, each point on the migrated

section is treated independently from the other points. Each point on the output

migrated section is produced by adding all data values along a diffraction that is

centered at that point.

Fig 3.1.8 Diffraction summation (collapsing each diffraction hyperbola to it apex)

The two methods differ, in the treatment of the data prior to summation.

Whereas the diffraction summation method sums the seismic event amplitudes as

recorded, Kirchhoff migration corrects the amplitudes and phase for three factors

before summing. In another way one can say that the diffraction summation

technique that incorporates the obliquity, the spherical spreading and wavelet

shaping factors is known as Kirchhoff migration.

First, the method corrects for the angle at which each event arrives at each

receiver. The energy from a point reflector arrives at the receivers at different

angles. The quantity of energy arriving at each receiver is dependent on the angle

of incidence. This phenomenon is called the obliquity factor. Figure 3.1.9 shows

the circular wave of energy generated from a point reflector. At every location

other than the image ray location, the event arrives at an oblique angle to the

receiver. When the energy arrives at the surface, the receivers near the point of

image ray arrival record greater amplitude than those receivers located at some

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distance from this location. Before the summation, we apply an obliquity, or

directivity, correction factor to the amplitudes. This correction factor is equal to the

cosine of the angle formed by the vertical axis and a line drawn from the location

of the point reflector to each receiver. In figure3.1.9, the correction for the receiver

at location R6 would equal cos β.

Fig 3.1.9 Showing the mechanism for obliquity factor

The second correction is the spherical divergence, or spreading factor. As

the wavefront travels away from the source or point reflector, energy dissipates. As

a result, amplitudes decrease as travel time or distance from the source increases.

In a CMP gather, a receiver located at the zero offset location is closer to the

reflector point than a receiver located at some point away from the zero offset

location. Thus, more energy reaches the zero offset receivers and consequently, it

records larger amplitude than a receiver located some distance away from the ZSR.

In a shot gather, the greatest amount of energy (and, therefore, the largest

amplitude) is recorded by the receiver nearest to the. So we may consider the

effects of spherical divergence. The energy density of a seismic wave decays by

the inverse of the square of the distance travelled from the source (1/r2). The

amplitude of a seismic wave in three-dimensional space decreases by the inverse of

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the distance travelled (1/r). In the Kirchhoff migration scheme, amplitudes in the

depth domain are corrected by a factor of 1/r before summing. In the time domain,

the amplitude correction applied equals to 1/t, where t is the travel time of the

particular seismic event.

The third factor in the Kirchhoff migration method is a correction to restore

amplitude and phase from distortions that occur during wavefront propagation.

This correction is called the wave shaping factor.

All methods of seismic migration involve the back propagation (or

continuation) of the seismic wave field from the region where it was measured

(Earth's surface or along a borehole) into the region to be imaged. In Kirchhoff

migration, this is done by using the Kirchhoff integral representation of a field at a

given point as a (weighted) superposition of waves propagating from adjacent

points and times. Continuation of the wave field requires a background model of

seismic velocity. Because of the integral form of Kirchhoff migration, its

implementation reduces to stacking the data along curves that trace the arrival time

of energy scattered by image points in the earth. Kirchhoff’s migration can perform

depth migration using an interval velocity model and ray tracing honouring Snell’s

law. The wave equation used in Kirchhoff migration can be expressed as:

(3.1)

Where t0 = t - (r / v). Equation (1) clearly contains the obliquity (cos Ø) and the

spherical divergence (1/ r) factors among its terms. The second term in this

equation, (1/r)u (r0,t0) is usually dropped, because it is proportional to 1/r2

Kirchhoff migration is defined by the formula:

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(3.2)

The non-zero-offset diffraction surface is plotted schematically in figure

shown below. This surface is often called the “Pyramid of Cheops”.

Fig 3.1.10 Diffraction surface for the finite offset case

Kirchhoff pre-stack depth migration involves summing input data samples

along the pre-stack diffraction curve and assigning the result to the apex (at zero-

offset). The actual ray path (from ray tracing) from every source to every receiver

is used to define the diffraction surface.

The advantages of the Pre Stack Depth Kirchhoff Migration scheme are its

simplicity and ability to handle steep dips. In fact, a recently developed algorithm

called Kirchhoff turning ray migration can handle interfaces that dip 90 degrees

and "beyond" .(Interfaces that dip beyond 90 degrees include those that overhang,

as in a salt dome, and those that overturn, as in a trusted anticline.)

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3.8 FINITE-DIFFERENCE MIGRATION

Finite Difference migration uses a formula that extends a field of data back

to an earlier stage. So, from the data received at the geophones, an entire new set of

data is calculated-the data as it was just a little time before it arrived at the

geophones. In effect, though not usually plotted, it is another seismic section, the

one that would have been recorded if the geophones were not on the top of the

ground, but buried a little way down. Then another section, in effect a little deeper,

is calculated, and so on, all the way down to the reflecting horizons, and on to the

bottom to the section. As data is retraced, things are put in adjusted directional

relationships i.e. they are migrated.

At each stage the data above has been migrated and the data below is not yet

migrated. The depth step and dip of reflector can effect the migration as follows:

a) Increasing depth step size causes more and more under migration at

increasingly steep dips.

b) The wave form along reflectors is dispersed at steep dips and large depth

steps.

c) Kinks occur along reflectors at discrete intervals that correspond to the depth

step size. Kinks are more pronounced at increasingly steeper dips.

The first inference results from the parabolic approximation, the second

from differencing approximations and the third from gradual under migration

towards the base of each depth step.

Advantages of this method are as follows:-

a) Non-degradation of reflection quality of the section.

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b) Handling of lateral velocity variations.

c) Non-formation of smiles in deeper part of section and hence better

imaging in deeper part.

A disadvantage of finite-difference migration is that it does not, in its pure form,

handle steep dips well.

3.9 F-K MIGRATION

F-K migration is a migration method that operates in the F-K domain. It is

therefore a constant velocity migration and thus by definition, a time migration. F-

K migration is usually the fastest and also the most accurate migration (for

constant velocity) because it uses only minimum approximations. F-K migration

has no dip limitations and can fully reconstruct the amplitude and the phase of the

data.

Some of the characteristic features of F-K migration are as follows:

a) This method is ideal when the velocities are constant.

b) It works very well when the velocities vary smoothly.

c) It gives excellent results on many marine lines.

d) It can give an accurate time migration when many constant velocities are

made.

Frequency-wave number migration can migrate dip up to 900

3.10 POST-STACK MIGRATION

Post-stack migration is the migration done on stacked section as indicated by

its name. This migration is based on the idea that all data elements represent either

primary reflection or diffractions. This is done by using an operation involving the

rearrangement of seismic information so that reflections and diffractions are

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plotted at their true locations. The variable velocities and dipping horizons cause

the data to record surface positions different from their subsurface positions. So,

migration is needed to move reflections to their true subsurface locations.

3.11 PRE-STACK MIGRATION

When the subsurface structure is complex and velocity variation is also

complex, reflection events are not hyperbolic and the stacking process does not

work very well. So, post stack migration does not give clear results.

Pre-stack migration, as the name suggests, is done on pre stack data i.e.on

CMP gathers and can be done in time or depth domain. Pre-stack migration is

applied only when the layers being observed have complicated velocity profiles, or

when the structures are just too complex to see with post-stack migration. Layer

velocity information is required by the user for running pre-stack Time or Depth

migration. It is an important tool in modelling salt diapers because of their

complexity and this has immediate benefits if the resolution can pick up any

hydrocarbons trapped by diapers.

Pre-stack migration is applied to avoid amplitude distortions due to CMP

smearing and non-hyperbolic move out. Hence, Pre-stack Time or Depth migration

is a valuable tool in imaging seismic data. In the past, the main constraints on pre-

stack migration were the computation requirement the time and skill required to

construct velocity model within a reasonable time. Advances in computing

technology and formation of new migration algorithms have eased these

constraints.

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3.12 PRE-STACK VERSUS POST-STACK MIGRATION

When the subsurface structures are simple, post-stack migration works well.

But post-stack migration is not faithful in areas with complex geology and

complex variations in velocities. Pre-stack migration is a better imaging tool which

works quite well in areas with complex structures and complex velocities.

In post-stack migration, hyperbolic moveout is assumed. Amplitude

distortions results when this assumption is not valid. Indeed, when ray paths from

near and far offsets travel through different layer with different velocities, moveout

is non-hyperbolic and stacking of the event after hyperbolic correction causes a

lack of focusing. To overcome this difficulty, pre-stack migration is required.

Post-stack migration algorithms deal mainly with rays traveling at moderate

angles from vertical. Rays traveling at large angles are required only to image

overturned reflectors. This is not the case with wide offset, pre-stack data. Even for

moderately dipping events, a ray from either source or detector may turn. The

intrinsic anisotropy in layered sedimentary sequences may result in horizontal

velocities 2-15% higher than vertical velocities. To image reflections from dipping

events recorded with today's wide offset acquisitions requires both faithful

handling of vertical velocity gradients and attention of anisotropy. These are taken

care of in pre-stack migration. However, post-stack migration is much faster than

pre-stack migration, because stacking reduces the number of traces that must be

processed. Also, post-stack migration is cheaper than pre-stack migration. But,the

pre-stack migration gives a better imaging quality and hence is the most preferred

migration.

3.13 PRE-STACK TIME MIGRATION

Though the vertical axis of the earth subsurface is measured in units of

distance, seismic images of the earth subsurface are usually presented in units of

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time. The process, referred to as time imaging, is practiced far more often than

depth imaging. The reason for the preference of time imaging over the depth one is

that we are simply unable to accurately position the reflectors in depth gap. In the

presence of dipping horizons, the sorting of traces into CMP gathers produces

gathers composed of many subsurface depth points, not just one depth point. When

the CMP stack is made, there is smearing in the subsurface coverage. In stacked

data, the steeply dipping tails of the diffractions usually cross flatter events, and are

thus lost due to conventional moveout and stack. The quality of the migrated

section suffers when all primary events and diffractions are not present on the input

stack. This situation in which two or more events with different dips exist at the

same time is the multivalued NMO problem. These problems are solved by Pre-

stack Time Migration.

Pre-stack time migration is done in common offset domain which results in

Pre-Stack Time Migration gathers. These gathers are also known as common

reflection point (CRP) gathers as they more or less refer to same subsurface point.

These Pre-stack time migrated gathers have multiple uses:

a) They can be muted approximately and stacked to get pre-stack migrated

section.

b) They can be used to refine the RMS velocity.

c) They can be used to estimate RMS velocity.

Carrying out a fresh velocity analysis on these gathers is more advantageous

as all the traces in the pre-stack time migrated gathers refers to the same point in

the subsurface. Also, a set of horizons can be identified on the pre-stack time

migrated stack, the process known as model building. Having built a model the

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RMS velocities can be either refined along these horizons or fresh RMS velocity

can be estimated along these horizons. This yields horizon based RMS velocity,

which will have more bearing on the structural aspects of the subsurface. Since, the

energies in a Pre-stack time migration gather are at correct migrated locations, the

estimated RMS velocity are bound to be better than the earlier velocities. Using

this refined RMS velocity section, a second pass of Pre-stack time migration is run

on CMP gathers.

The true earth coordinates are of course in depth, not time. Even so,

interpreters often need data in time coordinates, because the standard interpretation

system, log synthetics, and seismic-attribute techniques work with time and

frequency, not with depth and the wave-length. The most apparent difference

between time and depth migration occurs in the final display of migrated traces.

Time migration produces a time section, which interpreters can compare relatively

easily with unmigrated time sections. Time migrated section/image, following the

tradition of NMO and stack uses an imaging velocity field, i.e. one that best

focuses the migrated image at each output location. This velocity is free to vary

from point to point, so that time migration, in essence, performs a constant-velocity

migration at each image point. We can view pre-stack time migration as the

generalization of NMO that includes all dips, not just flat ones, while also

collapsing diffraction energy. This is true in the sense that a Pre-stack Time

Migration program restricted to imaging only flat dips at source-receiver midpoint

locations will yield an image that is identical to a stacked, unmigrated section

With diffraction summation migration, data values are summed along the

diffraction hyperbola and the result is assigned to its apex. This procedure, when

performed as a time migration, uses a RMS velocity value at each point and

assumes that diffraction curve is hyperbolic:

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t2 = t02 + 2(x-x0)2/ v2

RMS (3.3)

Where, t0 = Migrated time, x0 = Horizontal distance of diffraction point

Fig 3.1.11 Ray Path for diffraction using RMS velocity (Time migration)

Time migration is known to be a robust procedure, and less sensitive to the

velocity model than depth migration. When the velocity model is wrong, the depth

migration that computes the exact geometry of the diffraction curve may result in a

curve that is very different from the true curve. This would produce a very poor

image. In this the the lateral positioning of an event on a time migrated section

may be different than the lateral positioning on a depth migrated section. The

image rays provide the transformation of the image position between the time

migrated section and the depth migrated section

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Fig 3.1.12 True depth after migration

NMO+DMO+Stack+Post-stack Time Migration = Pre-stack Time Migration

Pre-stack time migration not only corrects for geometric distortions due to

refractions and diffractions of seismic waves but also provides following benefits:

Pre-stack migration facilitates velocity picking because it collapses

diffraction, focuses energy, and positions events in their corrected locations.

Velocities picked after pre stack migration are closer to the true positions

than those picked before the migration.

Pre-stack migration can correct some of the AVO problems if the migration

is performed in an amplitude-preserving manner.

Migration increases spatial resolution and hence, is also regarded as spatial

deconvolution. After migration, the lateral resolution is in the order of the

wavelength.

3.14 PRE-STACK DEPTH MIGRATION (PSDM)

If the structures are complex, reflections are non-hyperbolic and stacking

does not work very well. Pre-stack migration, when performed as a depth

migration, can handle move-outs that are not hyperbolic and significantly improve

the image quality. The problem of data mis-positioning in the pre-stack domain can

be illustrated using a simple example of a dipping reflector. For a dipping

interface, the reflection point changes for a different offset of the same CMP gather

(this effect is called reflection point dispersal). Migration corrects this mis-

positioning effect, so that after pre-stack migration, all traces of the same CMP

surface point refer to the same subsurface point. The pre-stack depth migrated

gather is called a CRP (Common Reflection Point) gather, and corresponds to the

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ray path geometry as shown in above figure. Pre-stack depth migration replaces

NMO & stacking and corrects the lateral mis-positioning of reflection events.

Prestack depth migration is however very sensitive to the accuracy of the velocity

model.

Fig 3.1.13 The generalized flowchart for Pre Stack Depth Migration

Pre-requisites for Depth Migration

Depth Migration essentially consists of two steps

1) Travel time computation & 2) Imaging

For computing travel times an accurate depth-interval velocity model is necessary.

This implies that accurate layer geometry in depth along with layer interval

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Signal conditioned CMP-gathers

Depth – Interval Velocity model

Pre Stack DepthMigration

Pick ResidualsFlat

gathers

YES

Final Image

Update the Interval Velocity model

NO

velocities and an efficient travel time computing method are pre-requisites for this

operation.

Advantages of pre-stack depth migration

Migration velocity analysis is performed in the correct migrated position

benefiting from higher signal to noise ratio due to the focusing of energy. Velocity

analysis after migration is not interfered with the diffraction energy, which gets

collapsed by the migration. In addition, velocities are obtained without assuming

hyperbolic move out. The disadvantage of Prestack depth migration is mainly due

to effort involved in preparation of interval velocity depth model and increase of

computation cost as compared to Prestack time migration.

3.17 Migration Effects

Using perpendicular reflection principle, some subsurface features and how

they will look when converted to sections with vertical traces can be considered.

Then some rules are formed for how the features of the section will have to change

to be migrated back to their correct configurations. For simplicity at this stage, it

will be assumed that the velocity of sound is constant all through the geologic

section, and the lines are shot in the direction of dip, so they do not have any

reflections from one side or the other of the line.

1 Reflections move up-dip.

2 Anticlines become narrower.

3 Anticlines may have less or the same vertical closure.

4 The crest of the anticline does not move.

5 Synclines become broader.

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6 The low point of the syncline does not move.

7 Synclines may have more or the same closure.

8 Crossing reflections may become a sharp syncline (Bow-tie effect)

9 An umbrella shape, diffraction, becomes a point.

10 The crest of diffraction does not move, and is the diffraction point.

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