Umesh Final Dissertation

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

2

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 3

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

4

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 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 monofrequency 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. 5

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 results in a change of frequency content of the initial source signal in a timevariant 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 6

applied to each trace individually. Now days, surface consistent amplitude balancing is in use. 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.

7

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.

8

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: 9

(I) Operator Length-The total Operator Length is the sum of the “Prediction operator length” (POL) and the “Prediction distance” (PD). The Deconvolution is 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

10

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, now a 11

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

12

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.

13

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}

14

(2.2)

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) ∑ vi2 ∆ti(0)

(2.4)

Where ∆ti is the vertical two way time through the ith 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

15

(2.5)

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 16

NMO Stretching In 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

17

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 preNMO 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.

18

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. 19

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.

20

 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 frequenciesshallower 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.

21

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 t

C’ D D’ Apparent Dip

Fig 3.1.1 Migration principle

22

3.2 MIGRATION STRATEGIES CASE

MIGRATION

 Dipping Events  Conflicting Dips with different Stacking Velocities  3-D Behaviour of Fault Planes and Salt Flanks  Strong Lateral velocity variations Associated with complex overburden structures  Complex Non Hyperbolic Move out  3-D structures Need Based selection of type of Migration:

Fig 3.1.2 Simple structure and simple velocity

Fig 3.1.3 Simple structure and Complex velocity 23

Time Migration Prestack Migration 3D Migration Depth Migration

Prestack migration 3D Migration

Post Stack Time Migration

Post Stack Depth Migration

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 24

(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.

25

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): 2D

Post-Stack

Time

3D

Pre-Stack

Depth

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 26

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 27

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 the 28

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: 29

(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 zerooffset). 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.)

30

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. 31

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. FK 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 32

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 prestack 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.

33

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 34

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 Prestack 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 35

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: 36

t2 = t02 + 2(x-x0)2/ v2RMS

(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

37

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 ray path geometry 38

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. Signal conditioned CMP-gathers

Depth – Interval Velocity model

Pre Stack Depth Migration

Update the Interval Velocity model NO

Flat gathers

Pick Residuals YES

Final Image

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 velocities and an efficient travel time computing method are pre-requisites for this operation. 39

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. 6 The low point of the syncline does not move. 7 Synclines may have more or the same closure. 40

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.

41