Resolution Geohorizons

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GEOHORIZONS July 2004 /1

GEOHORIZONSJournal of Society of Petroleum Geophysicists, India

Editor-in-chiefR.T. Arasu

Co-ordinatorS.K. Chandola

Editorial TeamAnand Prakash

Pradeep Kumar

V. Singh

Regional Editors

S.K. Bhandari, MumbaiP.H. Rao, Baroda

A.K. Sharma, Kolkata

A.K. Bansal, Jorhat

Arun, Chennai

D.N. Patro, Ahmedabad

Geohorizons, SPG, India1, Old CSD Building

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Kaulagarh Road,

Dehradun - 248 195Phone : 91-135-2795536/2752088

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Geohorizons is published by the Society of Petroleum Geophysicists

(SPG), India. Geohorizons welcomes your contribution and articles on latest

researches and investigations in the field of petroleum geophysics, related

geoscientific and engineering disciplines. News items about the Society,

announcements and other features containing information of interest to the

members of the Society are also welcome.

The statement of facts and opinions given in the articles published in

the journal are made on the sole responsibility of author(s) alone and the Society

or the Editor cannot be held responsible for the same.

EDITORIAL 2

PRESIDENTS PAGE 3

TECHNICAL ARTICLES

Understanding the Seismic Resolution and its Limit for Better 5Reservoir Characterization

V. Singh and A.K. Srivastava

Seismic Data Acquisition in Difficult Logistic Conditions 37

B.K. Singh and Neeraj Jain

SPG NEWS SECTION

Glimpses of Hyderabad 2004 43

DISC 2003 on Geostatistics in Petroleum Exploration 46

ONGC-SPG India Delegation at EAGE-2004 47

DISC 2004 on Deepwater Petroleum Systems 48

Conference on Non-Seismic Methods for Hydrocarbon Exploration 49

Participation of SPG India in APG 2004 Conference 50

ONGC-SPG Delegation at 74th SEG Meeting, Denver, Colorado, USA 51

DLP-2004 on Time Lapse Seismic (4D) for Reservoir Management 52

Australian News highlights the Geo-steering of high tech wells of 53

Mumbai High during SPG Conference at Perth, Australia

Participation of SPG India in AEG-2004 Conference 54

SPG NE-Chapter organizes a Lecture on Magnanetic data 55

interpretation

CALENDER OF EVENTS 56


2/61GEOHORIZONS July 2004 /2

EDITORS PAGE

Geophysics, an offshoot of Physics, has attracted lot many people from different

disciplines-Physicists, Geologists, electrical and electronic engineers, instrument engineers,

civil engineers, petroleum engineers, software and communication engineers, technologists,

etc. It is one of the few subjects with which the mysteries of the Mother Earth can be

unraveled. As it is not a basic science like physics or chemistry, Geophysics offers many-a-

solution for a given problem. It requires human intervention to pinpoint the one which suits the

best at the given time and space. That is where a geoscientist comes into the picture. Therehave been thousands of geoscientists who have toiled in the sun, rain, thick forests and

merciless deserts, mangroves and deep oceans, labs, computer centres and workstations to

capture and model the true nature of the earth beneath the surface. Their contributions led to the growth of geophysics

to the level as we see today.

Like other sciences, Geophysics heavily relies on data. Geoscientists speak through the medium of data.

Billions and Trillions of bits of data collected in the form of ones and zeros on the land, on the surface of the ocean

and at its bottom become an earth layer, an ore here, an oil sand there and gas sand elsewhere in the hands of

geoscientists. The inanimate data bits turn into a geological structure, a stratigraphic pinchout, a wedgeout, deep

inside the earth. What our geological friends perceived using scanty outcrops and well core data is converted into a

fact using this medium called geophysical data. The entire process involves-not an individual but an integration of

creative minds.

We need to pool up the creativity of human minds that work in nooks and corners of the land, on the ocean.

Petroleum exploration and exploitation being our core activity, we have to bring together the thought processes of the

people working in various work centres of oil companies, universities/institutes and other private companies from

India and abroad.

Geohorizons, a bi-annual journal published by the Society of Petroleum Geophysics (SPG), India is a

suitable medium through which people from the forward base to the head quarters, from the field camps and

onboard survey vessels to the labs and processing and interpretation centres, from academia to industries can

communicate with each other. Geohorizons has been serving the community of petroleum geoscientists for the past

nine years. Edited by able and experienced seniors in the past, it has traveled the length and breadth of the country

and has carried valuable information all along.

Friends, the new editorial board that has taken over this journal recently wishes that this medium be made

much stronger. The new board wishes to take this magazine to each and every geoscientist working in the country,

to serve as a medium of communication among all those who are practicing in geosciences, to serve as a platform

for exchange of ideas, innovations and inventions.

With this goal in mind may I request all my fellow geoscientists to come forward and contribute technical

articles, discussions and thought processes to Geohorizons. Let your knowledge not be in a closet, let it be brought

to an open forum. Let Geohorizons be a carrier, modulated by your Knowledge to reach the fellow geoscientists

across the globe.

(R.T. Arasu)

Editor-in-Chief



PRESIDENTS PAGE

It is heartening to communicate to the fellow society members through this maiden column

after taking over as the President of SPG, India in January 2004. Maintaining regular

communication with all the regional and student chapters has been the top priority of this

Executive Committee. It is this interaction and mutual cooperation through which the society

can achieve sustainable growth both in terms of knowledge dissemination and stature.

Looking back, the period of last one year has been satisfying in many ways. SPG-2004 at Hyderabad can be regarded as a milestone event in many ways. The remarkable

success of Students programmes has prompted many fellow societies to include such events

in their seminars. This is an encouraging trend and may go a long way in bridging the yawning gap between the

industry and academia, generate better employment opportunities for the aspiring geoscientists and also encourage

youngsters to take up Petroleum Geophysics as a career. The pre and post-conference workshops covering a wide

range of topics from 3D survey design to Geostatistics exposed the petroleum geoscientists to the expertise of

internationally renowned domain experts.

The DISC 2004 by Dr. Paul Weimer on Petroleum systems of deepwater settings held at Chennai in

August04 was a great success and would probably help in shaping up the future of deepwater exploration in the

country. Similarly DLP 2004 by Dr. Marcus Marsh on Use of 4D seismic in Reservoir Management held atDehradun during October04 also is particularly relevant in the context of the present efforts by the oil companies to

enhance recovery from the existing reservoirs to reduce the alarming demand-supply gap.

At the national level, lectures by domain experts were organized at Dehradun. This included enlightening

talks by Dr. Satish Singh and Prof. Christopher Liner. It has been our endeavor to distribute the SPG activities to the

various regional chapters to enhance their involvement. The pre and post-conference workshops and DISC 2004

were initiatives in this direction. Here, one must acknowledge the initiatives taken by some of our regional chapters

and I would like to make special mention of the Mumbai chapter in successfully organizing the symposium on Non-

seismic Methods in Hydrocarbon Exploration involving geoscientists from all the major E&P companies of India

and also the international domain experts and representatives from academia.

Our main concern as a society today is maintaining and enhancing our membership base and also ensuring

the timely publication of Geohorizons and the News Letter which form the lifeline of SPG. In order to improve

the quality of articles, we took a decision to change the periodicity of Geohorizons from quarterly to half-yearly.

We have also constituted special interest groups to generate quality articles in different streams of petroleum

exploration. Time and again, we have requested the regional chapters to come forward and contribute to these

publications by way of papers, articles and news items. But the response, to be honest, has been lukewarm barring

a few exceptions. We must understand that no professional society can sustain without a good communication link

with the members and the outside world, however successful our biennial conventions might be. I once again request

you all through this column, specially the regional and student chapters, to write regularly for these publications.

One of the decisions that were taken in the EC meetings included sending of two delegates (in place of one)

to the SEG/EAGE conventions. Representatives from Chennai and Mumbai chapters attended the EAGE and SEG

conventions respectively at Paris and Denver, in addition to one representative from SPG, India. I hope the trend will

continue and more and more of our geoscientists shall be exposed to these conventions to bring back cutting edge

Geophysical technologies which can be adopted by the Indian E&P industry for finding more oil and gas.

At SEG-Denver, a new dimension was added to SPG-SEG cooperation by formal agreement on signing of

enhanced Level-III support by SEG for SPG-2006, Kolkata. As a part of the agreement, the event shall be called

SEG-SPG International Conference & Exposition with technical support from SEG in scrutinizing the papers,

deputing a technical programme co-chairperson, assisting in organizing the event and participation of a larger delegation

including President-SEG. In return, SPG has agreed to share 10% of the profits earned from the event with SEG. It



was also agreed to extend the duration of DISC for two days instead of one starting from 2005 and to hold the DISC

2006 during SPG-2006, Kolkata. SEG also agreed to consider empanelment of geoscientists from SPG to deliver

continuing education programmes in Asia-Pacific regions. We hope that these initiatives shall pave way for greater

cooperation between the two societies. We have also taken initiatives to further improve our relationship with EAGE

and Dr. Olivier Dubrule, President-EAGE has assured us of all possible cooperation on his part.

SPG also realizes the importance of maintaining close interaction and cooperation with other Geophysical

societies, particularly in the South-East Asian region. It gives me pleasure to share with you that SBGf, the

Brazilian Geophysical Society has responded well by offering a free both along with a complementary registration attheir forthcoming International Convention to be held in 2005. SPG shall reciprocate the gesture during Kolkata-

2006.

So all in all, there has been some forward movement on all fronts, but a lot remains to be done. Today, SPG

can take pride in being the premier Geophysical society in India with wide international recognition, contributing

consistently to the cause of Petroleum Geophysics and Petroleum Geoscientists. We must try our might, both as

individuals and as teams, to further broaden and enhance our membership base, infuse a new life into our publications

and keep disseminating knowledge to ensure a bright future for Petroleum Geophysics in India.

I extend my heartiest wishes to all the fellow members on the festive season of Dipawali, Id, Guruparb,

Christmas and the New Year to follow and hope that SPG will have much larger representation at EAGE and SEG-

2005 by way of technical papers.

(Apurba Saha)



INTRODUCTION

From their first use in 1928, surface seismic surveys

have been lauded for their effect on exploration success,

reducing risk appreciably. During the years since, surveys

have expanded from two-dimensional (2D) to three

dimensional (3D) to four dimensional (4D) and expanded to

encompass the development and production as well asexploratory phases of reservoir life. Likewise, advances in

seismic data processing utilizing massive parallel computers

and integrated reservoir imaging software have improved the

reliability of data interpretation and thereby drilling accuracy

itself. Good quality of seismic data and its higher resolution

is of paramount importance for its cost-effective utilization in

various aspects of hydrocarbon E & P activities. There are

still numerous practical problems related to subsurface

imaging and reservoir development such as detection and

resolution of thinly laminated sand-shale sequences,

distribution of faults, fault type, magnitude of throw and

characteristics, discrimination between sealing and

nonsealing faults, detection and delineation of fracture zones,

macro and microscopic heterogeneity, subsalt and subbasalt

imaging, imaging of the subsurface in complex geological

set-ups (deep water, gas chimney, volcano, karst), fluid and

permeability predictions which are unsolved and require

further attention of practising geoscientists (Pramanik et al.,

1999).

It is well known that the acoustic impedance contrast,

rugosity and continuity of the individual reflector, properties

of stratified systems and sharpness of the seismic pulse

control the reflection of seismic waves from an interface. The

combined effects of all factors quantify the overall resolution

of the seismic data. The sharpness of the reflected pulse is

directly related to the signal to noise spectral bandwidth of

seismic data which lies somewhere between 10-100Hz in ideal

conditions. In most of the real seismic data sets the spectral

bandwidth falls much below to above given range (between

10-60Hz with dominant frequency of 30 to 35Hz). Therefore,

the seismic data of such narrow signal to noise spectral

Understanding the Seismic Resolution and its Limit for Better

Reservoir CharacterizationV.Singh and A.K.Srivastava

Geodata Processing and Interpretation Centre

Oil and Natural Gas Corporation Limited, Dehradun-248195, U.A., India

SUMMARYIn recent years, seismic surveys have provided more clearer subsurface images, finer details related to reservoircharacterisation and management. This has considerably reduced the risk associated with drilling of wells in existing

fields and also in new exploratory areas. Optimum resolution of seismic data is a prerequisite for obtaining these detailed

and accurate geologic information. This warrants the understanding of various aspects of seismic resolution, which can

be achieved in seismic surveys and the physical factors those limit the seismic resolution. Subsurface reflectivity, convolution

theory, theoretical and practical limits of seismic resolution, effect of earth stratification on seismic response, maximum

attainable signal bandwidth, seismic data acquisition and processing techniques are some of the important aspects which

affect seismic resolution. The foundation of seismic technique is based on earth reflectivity and its convolution with source

wavelet. Earth reflectivity and partitioning of energy at an interface are offset dependent phenomenon where as wavelet

characteristics changes as it propagates in the earth and get further distorted by various types of noises present in the

subsurface and during recording and processing stages. A theoretical background of these aspects is elaborated before

dealing with resolution. Vertical and lateral resolution limits are dependent on wavelet characteristics and elastic

parameters of subsurface layers. Synthetic modelling approach has been adopted to demonstrate the estimation of layer

thickness and limit of vertical resolution from seismic amplitude and wavelet time period. Concept of Fresnel zone radiusand its variation for smooth plain, curved and rugged reflecting surfaces is also visualised. Absorption and attenuation

are the inherent properties of the medium of energy propagation. The earth attenuates higher frequencies very fast thus

limiting the resolution. Estimation of frequency loss due to attenuation provides basis for the true amplitude recovery. A

theoretical estimation of maximum attainable signal bandwidth and its impact on resolution are elaborated. Apart from

attenuation, earth stratification generates interbed multiples and background noise. Interbed multiples lower the frequency

where as background noise fixes the practical limit for highest corner frequency. In seismic prospecting, efforts are

always on to improve the resolution and thereby to see the response of as much thin layer as possible. Below the limit of

seismic resolution, we get the composite response of closely spaced interfaces. The effect of variation in spacing and

magnitude of reflection coefficient of interfaces on amplitude and phase of composite response has been studied through

extensive synthetic modelling. Knowledge of well data acquisition, its evaluation, quantification of phase variations in

seismic wavelet is also very crucial in obtaining precise calibration between borehole and seismic data Recently, interpretive

application of spectral decomposition technique in frequency domain has emerged as a powerful tool for analysing the

properties of extremely thin reservoirs which are well below the conventional quarter-wavelength resolution of seismicdata. This work emphasises that the understanding of basic principles related to seismic resolution and their limits in

achieving high resolution seismic data is of paramount importance before making any attempt of accurate subsurface

imaging, reservoir characterisation and management.



bandwidth having limited seismic resolution may not be able

to provide the satisfactory solutions of these specific

subsurface imaging, reservoir development and hydrocarbon

production related problems and require high resolution

seismic data. Further, seismic resolution also becomes a major

hurdle especially for the imaging of deeper horizons where

effectiveness of seismic reflection techniques generally

deteriorates with increasing overburden depth. Since high

resolution is a prerequisite for extracting the detailed and

accurate geologic informations from seismic data. Therefore,in order to get full appreciation of the seismic data and its

limitations from an interpreters point of view, it becomes

necessary to have thorough understanding of the subsurface

reflectivity, convolution theory, theoretical and practical limits

of vertical and lateral seismic resolution, estimation of

maximum achievable signal bandwidth, effect of stratification

on seismic response, seismic data acquisition and processing

techniques.

Interpretation starts from the finally processed

seismic data, which requires best possible calibration with

borehole data for extracting meaningful information from it.

Good calibration requires the basic understanding of well

data acquisition and its evaluation. Keeping the importance

of all these aspects in view, an attempt has been made to

elaborate the basic aspects of seismic resolution and their

elaboration through synthetic modelling. This starts with the

theoretical background of seismic reflection kinematics given

in section (2) to understand the relationship between

subsurface reflectivity for P-waves with angle of incidence.

The significance of seismic reflection amplitude is well

established for understanding the nature of the stratigraphy.

For inferring the stratigraphic details from the seismic

reflection, it becomes necessary to have the understanding

of convolution theory along with various factors which affect

seismic response and limits of vertical and lateral resolutions.

They have been discussed in sections (3) and (4) respectively.

It has been illustrated that signal spectral bandwidth i.e.,

wavelength holds the key for both vertical and lateral

resolution and defines the theoretical limits of resolution.

Vertical resolution determines the capability to quantify

properties of individual layers from the interference pattern

of a multi-layered response. This has been illustrated through

synthetic modelling. Lateral resolution determines the

capability to quantify the lateral changes of those properties.

The effect of rugosity of reflection surface on Fresnel zone

has also been discussed. As estimation or measurement ofsignal spectral bandwidth is a direct assessment of resolving

power, it becomes necessary to know its maximum attainable

limit of signal bandwidth in practice. This aspect has been

demonstrated in section (5) through synthetic modelling.

Results show that the very nature of earth crust layering

itself puts a natural limit on signal bandwidth by generating

interbed multiples along with background noise.

Synthetic modelling also enables us to understand

the effect of layer parameter variations such as thickness,

velocity and density. Their seismic response of these

variations can be analysed for better understanding of theirinfluence. The effect of interference on seismic reflection

response by removal and insertion of an interface at target

horizon can be analysed more effectively through synthetic

modelling and have been discussed in section (6) with some

examples. Various aspects of seismic data acquisition and

processing which affect the seismic resolution have been

described in section (7). Velocity resolution depends on

Fresnel zone considerations. A change of velocity in seismics

can be distinguished only when object size is greater than

Fresnel zone. Well data provide a variety of information such

as lithology, mineralogy, porosity, morphology of porespaces, the fluid content and detailed depth constraints to

geologic horizons. Therefore, careful use of calibration at

well location with all the available information and expertise

is very vital in deriving meaningful information from the

seismic attributes and to have confidence in the results

obtained from interpretation of the seismic data. This aspect

has also been critically discussed in this section. In recent

years, a new technique Spectral decomposition has been

developed which has helped interpreter to analyse the

extremely thin reservoirs, well below what has traditionally

been considered the quarter-wavelength resolution of

processed seismic data (Partyka et al., 1999, Partyka, 2001,Castagna et al., 2003). This technique makes use of variousfrequency components within a band-limited seismic wavelet

in the frequency domain via the discrete Fourier Transform

(DFT) or maximum entropy method (MEM) or Continuous

wavelet transforms (CWT). Spectral decomposition provides

a robust and phase independent approach to seismic

thickness estimation. Although, it builds on the concept of

traditional techniques documented by Widess(1973) and

Kallweit and Wood(1982). The traditional techniques for

estimating thin reservoirs thickness require zero-phase data

and careful picking of temporally adjacent peaks and troughs,

whereas thickness estimates derived from spectral

decomposition require only one guide pick within the seismiczone of interest.

Finally, It has been emphasised that the

understanding of basic principles related to seismic resolution

and its limit is essential for effective utilisation of 3-D seismic

surveys in accurate subsurface imaging, reservoir

characterisation and management. The integration of seismic

information with petrophysical, geological and reservoir data

using state-of-art technologies is extremely important in

finding out the solutions of reservoir development and

production problems. The adoption of newly emerged

technologies along with multi-disciplinary approach, theirstretching to new boundaries which are beyond conventional

limits will also be required ultimately to utilise the full potential

of seismic data in coming years.

THEORETICAL BACKGROUND OF

SEISMIC REFLECTION

When a plane acoustic wave strikes obliquely at an

interface, the situation becomes more complicated. An incident

P-wave generates four waves: reflected and transmitted shear

waves and reflected and transmitted compressional waves.

Figure (1) shows the partitioning of incident compressionalwave energy at a specific interface into four different waves.



The reflection and transmission coefficients depend on angle

of incidence as well as on the material properties of the two

layers.

The angle of incident, reflected and transmitted rays

are related by Snells law which is written as

p = (sini/V

P1) = (sin

t/V

P2) = (sin

i/V

S1) = (sin

t/V

S2) (1)

where p is the ray parameter. The subscripts 1 and

2 represent parameters corresponding to upper and lower

layers respectively. Here VPand V

Sare the P-wave and shear

wave velocities in homogeneous, isotropic linear and elastic

media. They are defined as

VP= [{K+ (4/3)}/](1/2) = [(+ 2)/](1/2) (2)

VS

= [/](1/2) (3)

where is density, K is bulk modulus, is shearmodulus and is Lames constant.

The energy and amplitude of these four waves may

vary greatly as a function of incident angle. This variation

for all the four reflected and transmitted waves is shown

graphically in Figure (2). Some of the important points of

energy partitioning are:

1. At the angle of incidence = 0 degree, most of theincident energy is transmitted as compressional, very

little energy is reflected as compressional. No shear

energy neither reflected nor transmitted, is generated.

2. At the angle of incidence = 90 degree, only reflectedcompressional energy is generated; no shear wave or

transmitted compressional wave energy is generated.

3. At the critical angle, the partitioning of energy changes

radically. At the angle of incidence less than criticalangle, some of the incident energy is transmitted as

compressional energy and may be further partitioned

at the next interface. At incident angle greater than

critical angle, no compressional energy is transmitted

and as a result seismic reflection method fails. At critical

angle, there is no reflection of shear waves but minor

shear energy is transmitted. With further increase in

angle of incidence, the shear energy reflection and

transmission becomes maximum and then it starts

decreasing with further increase of angle of incidence.

The maximum value of shear wave reflection and

transmission depends on ( Vp/Vs) ratio.

Figure 1 : Schematic diagram showing energy partitioning.

Figure 2 : Graphs of reflected and transmitted compressional and shear waves with angle of incidence (After Dobrin, 1960).


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where G = (Rp- 2R

s)

= (1/2) [{ (Vp/ V

p) - (/ ) - 2 (V

s/ V

s)}]

= Gradient term and depends on (Vp/V

s) ratio.

This equation (10) represents a simple straight line

which provides Rp

as intercept and G as slope (or gradient) if

R() is plotted against sin2. In deriving the aboveexpression of P-wave reflection coefficient R

pp() given in

equation(10), following assumptions were made:

1. The medium of seismic wave propagation is isotropic

and homogeneous.

2. The values, Vp

andVsare small compared to, V

p

and Vs.

3. Angle of incidence is less than critical angle.

4. Shear wave velocity is assumed half of the P-wave

velocity i.e.,(Vp/V

s) = 2.

5. For angle of incidence range 0 to 30 degree, the value

of tanand sinwill be approximately same therefore;the contribution of third term in P-wave reflection

coefficient equation (8) becomes insignificant and hence

ignored for all practical purposes.

Analysing the variation of reflection coefficient with

angle of incidence may be helpful in providing insight for

identifying specific AVA/AVO anomalies. The intercept and

gradient computed from equation (10) are the two basic AVO

attributes being extensively used for inferring the lithology,

porosity, pore fluid content and saturation directly from P-

wave seismic data through different version of cross-plots

between them directly or with some of their combinations

(Castagna et al., 1998, Goodway et al., 2001, Mahob and

Castagna, 2003).

INTERACTION BETWEEN SEISMIC

WAVELET AND SUBSURFACE REFLECTIVITY

Understanding the interaction of seismic wavelet

with subsurface reflectivity and the generation of amplitude

as a result of this interaction are of importance in application

of seismic technology for hydrocarbon exploration. For simple

understanding of seismic reflection response, mostly, the

noise free seismic trace S (t) is assumed to be a function of

the wavelet w(t) convolved with a reflectivity series r (t) i.e.,

S(t) = r(t) * w(t) (11)

where * symbolises convolution. The graphical

representation of a seismic trace in time and frequency

domain, its relation with lithology and acoustic impedance is

clearly demonstrated in Figure (3). Here the reflectivity series

r(t) is assumed effectively random, sparse in time and contains

all frequencies equally. But in reality, as the seismic wavelet

travels through the earth, it encounters geological interfaces

(or boundaries) where it is partially reflected back towards

the surface. The field seismic response at a given location is

treated as a series of wavelet amplitudes recorded at various

travel times. Each amplitude/ travel time pair is a function of

numerous parameters including but not limited to:

1. Subsurface reflectivity

2. Target depth

3. Structural dip

4. Overburden structural complexity including anisotropy

and heterogeneity

5. Angle of incidence

6. Source and receiver geometry7. Seismic source type

8. Noise

Seismic wave propagation is a three-dimensional

phenomenon. Therefore, in reality, a seismic reflection signal

is a much more complex waveform and can be represented in

three dimension as S = S(x, y, t). But for simplicity, it has been

considered here as S = S(t) only. Using convolutional model,

a segment of seismic reflection trace S(t) is written as

S(t) = S (r (t), zt,, c (t), (t), O(t), w (t), n (t)...) (12)

Where r(t) = Reflectivity series

zt

= Target depth

= structural dipc (t) = Structural complexity including macro-

velocity field

(t) = Angle of incidenceO(t) = Source-Receiver offset

w(t) = Seismic wavelet and

n(t) = Noise.

Equation (12) shows that there are several

phenomena that have deterious effects on the recordedseismic wavelet. Each component mentioned in equation (12)

contributes its own seismic response so that the finally

recorded seismic wavelet is the convolution of all the

individual responses. This means that the wavelet emerged

from the subsurface and the recorded one is not the wavelet

Figure 3 : Graphical representation of a seismic trace in time and

frequency domain, its relation with lithology and acoustic

impedance.



that was generated at the seismic source. Hence seismic

reflection data will have amplitudes that are related to

phenomena other than subsurface geology, i.e., reflectivity

series r(t). Combined in the reflected arrivals are the travel

time and amplitude information, from which the geoscientist

infers subsurface structure using travel time, and subsurface

stratigraphy, lithology and pore fluid content using amplitude.

In order to infer the finer details from seismic reflection data,

it becomes important to understand the different phases of

the seismic signal through which it passes since its generation

from the source to final processing. These aspects are divided

into five major components and are summarized in Figure (4).These components suggest that the real wavelet of seismicdata is very far away from being an ideal spike and is bothtime-varying and complex in shape. For practicalunderstanding, broadly these wavelets are divided into three

types:

(1) Minimum phase wavelet- All impulsive sources

(dynamite or air gun) generate minimum phase wavelet.

This wavelet has positive time values with no componentprior to time zero and sharpest leading edge as close to

origin as possible.

Figure 4 : Schematic diagram showing major components affecting seismic wavelet.



(2) Zero phase wavelet-This wavelet is perfectly symmetrical

and it is assumed that reflection occurs exactly at the

center of the wavelet. A zero phase wavelet is physically

impossible but can be fabricated in the computer by

adding together a series of appropriate cosines or by

altering the phase of a minimum phase wavelet.

(3) Mixed phase wavelet-This is a hybrid wavelet that is

neither zero phase nor minimum phase. It usually results

either from filtering of a minimum phase wavelet with adevice that has non-minimum phase properties or by

incorrect wavelet processing.

For an interpreters point of view, the important

aspect of various wavelets is the question where in time is

the event that caused the reflection. The description of

different wavelets suggests that zero phase seismic data is

easier to interpret because for a positive or negative reflection

coefficient, there will be a maximum either peak or trough

depending upon the data polarity. Minimum phase wavelet

will impart an apparent time shift to the reflection events and

split the initial energy into large peak and troughs at the startof the wavelet. This makes data polarity issue more

complicated. For subsequent illustrations in this work,

Standard Ricker and Ormsby zero phase band-pass wavelets

have been used as and when required.

SEISMIC RESOLUTION

It has been observed that majority of the reservoirs

are thin in the vertical direction and seismic trace gives the

resultant of superimposed wavelets reflected from closely

spaced interfaces giving rise to problem of resolution. Similar

problem is encountered in defining the lateral extension ofwedge-out prospects, and mapping of thin and narrow

channels. For detailed and accurate delineation of such

reservoirs, efforts are made to increase the resolving power

of the seismic data during acquisition and processing level.

Thus, it becomes necessary to understand the fundamental

concepts of resolvability. The term resolution can be defined

as the ability to distinguish the separate features, and is

commonly expressed as the minimum distance between two

features such that the two can be defined rather than one.

The resolving power of the seismic reflection data is always

measured in terms of the seismic wavelength, which can be

defined by a basic relation in terms of velocity and frequency

as

Wavelength () = Velocity (V) / Frequency (f) (13)

Seismic velocity increases with depth because rocks

are older and more compacted at deeper level. The

predominant frequency of the seismic signal decreases with

depth because higher frequencies in the signal are more

quickly attenuated. Therefore, wavelength generally increases

with depth because (1) velocity increases and (2) frequency

becomes lower (Figure 5). At deeper depths, due to larger

wavelength, geological features have to be much larger in

comparison to shallower depths to produce similar seismic

expression. Seismic resolution has two dimensions:

(a) Vertical and

(b) Lateral

a. Vertical Resolution

Vertical resolution refers to the distinct identificationof close seismic events corresponding to different depth

levels. It may be explicitly defined as the minimum separation

between two nearby reflectors, which can be identified as

two separate interfaces rather than a single one. The yardstick

for vertical resolution is the dominant wavelength. Several

authors have treated the concept of vertical resolution in the

past because it forms the basis of reflection seismology

(Sheriff, 1977, Koefoed, 1981, Widess, 1982, Berkhout, 1985,

Sheriff, 1985, Siraki, 1993). Kallweit and Wood (1982) have

discussed several definitions to resolvable limit as they apply

to zero phase wavelets. The most common definitions of

resolvable limit are those attributable to Lord Reyleigh (whostudied resolution as applied to visible light), to Ricker (1953)

and to Widess (1973). Rayleighs limit of resolution occurs

when images are separated by peak-to- trough time interval

( TD) of the pulse. This minimum thickness (T

D) represents

the maximum resolving power in time domain and can be

defined in terms of dominant wavelength () of the pulse as

TD/4 = V/ 4f (14)

This minimum vertical separation is commonly known

as Tuning thickness. At tuning thickness the reflections

from upper and lower interfaces interfere and form composite

Figure 5 : Schematic diagram showing variation of velocity,

frequency and wavelength with depth.



reflector. The maximum or minimum value of composite

amplitude at tuning thickness with respect to seismically

resolved layer can be observed depending upon the polarity

of the top and bottom reflection. For reflectors separated by

less than /4 thickness, the amplitude of the compositereflection depends on reflector separation, i.e., directly on

the thickness of the reflecting layer. This composite amplitude

variation can be used for estimating the net thickness

calculations for arbitrary thin beds. In depth domain, maximum

resolving power can be defined as

Zr= (V/2) . T

D(15)

Rickers limit of resolution occurs when images are

separated in a time interval equal to the separation between

inflection points (Figure 6). Widess (1973) has demonstrated

that the limiting separation for wavelet stabilisation occurs

when the bed thickness is equal to 1/8 of a wavelength of the

predominant frequency of the propagating wavelet. This /8wavelength separation of thin bed is known as Critical

Resolution Thickness and also the Widess limit of

resolvability. This critical resolution thickness (CRT) in terms

of predominant wavelength is expressed as

CRT =/8 = V/8f (16)

Thus, the values of resolvable limit given by these

two definitions (one by Rayleigh and other by Widess) are

respectively 1/4 and 1/8 of the dominant wavelength. While

Rayleigh criterion is appropriate one to apply for the

continuous waves encountered in optics, Koefoed(1981) and

Widess(1982) have argued that this criterion should be

modified to incorporate the wavelet shape when discussing

seismic resolution. Vertical resolution is then controlled by

three factors: the width of the central lobe of the pulse, the

ratio of the central lobe to side lobe and the side-tail

oscillations. Based on this analysis, Widess(1982) has

identified several characteristics associated with a pulse.

These include the width of the major lobe, the minimum

apparent separation between pulses, the tuning separation,

and Widess definition of the limit of resolution Tr .

Widess

limit of seismic resolution is defined as

Tr

= E / am

2 (17)

Where E is the total energy content of the signal

pulse and am

is the amplitude of the central lobe. Here noise

has been ignored in derivation of this formula.

Claerbout (1985) has related time frequency

resolution to the uncertainty principle of quantum mechanics.

For any function, the time pulse width (L) and the signal

spectral bandwidth (f = fmax

- fmin

, where fmax

is highest

frequency and fmin

is lowest frequency) are related by

L.f1 (18)

This equation states that a given pulse width has a

certain minimum bandwidth and vice versa; a given

bandwidth has a certain minimum pulse width of the wavelet.

Thus, a given bandwidth has a certain maximum resolution

potential. The effects of phase distortion cause the inequality

of equation (18). In applying these formulas for computation

of resolution it is very important to distinguish clearly the

difference between different frequencies and their relation

with wavelength. The maximum frequency corresponds to

minimum wavelength, minimum frequency corresponds to

maximum wavelength, peak frequency corresponds to peak

wavelength and predominant frequency corresponds to

predominant wavelength. The peak frequency is that

Figure (6) : Diagram showing the different limits of vertical resolution (After Kallweit and Wood, 1982).



frequency at which the value of amplitude will be maximum in

Fourier amplitude spectrum. The predominant frequency can

be computed using interval time between the wavelets two

side lobes. In other words, it is equal to inverse of wavelet

breadth time L. Thus, predominant frequency is different

from the peak frequency.

To visualise the relation between wavelet shape and

frequency bandwidth and its impact on seismic resolution

parameters, a suit of wavelets and amplitude spectra areshown in Figures (7a, 7b & 7c). The analysis of these wavelets

and amplitude spectra show that high frequency component

of the spectrum is essential for obtaining small width of the

central lobe and the low frequency content of the spectrum

plays an essential part in causing a low value of the side lobe

ratio required for higher resolution. In absence of high

frequencies the width of the central lobe becomes broader

and in the absence of low frequency, side lobes become too

prominent. This results in poor resolution. The values of

tuning thickness and critical resolution thickness have been

computed for the wavelets shown in Figures (7a, 7b & 7c)

and are summarised in Table-1.

Although, the width of the central lobe (2T0) and

tuning thickness (TD) is minimum for frequency bandwidth

56-92 Hz as compared to other frequency bandwidth shown

in Figures (7a, 7b & 7c), but for this bandwidth the ratio of

amplitude between central lobe and side lobe is very less and

has very prominent side tail oscillations which results in poor

resolution. On the other hand, the width of the central lobe

for 8-96 Hz frequency bandwidth is slightly higher than that

of 56-92Hz bandwidth. But ratio of amplitude between central

lobe and side lobe is very high and side tail oscillations are

very minimal. This shows that for achieving higher resolution,

it is desired to have a signal bandwidth, which contains lower

as well as higher frequencies in its spectrum.

To understand the Rayleighs seismic resolution

limit, a 1-D model of the seismic response of a pinchout having

equal amplitude from top and bottom interface with similar

polarity is generated using a Ricker wavelet of 35 Hz and is

shown in Figure (8a & 8b). This synthetic model demonstrates

the seismic response of two reflectors as a function of the

vertical separations between the two. At sufficiently large

separations the two reflections are independent of each other,

at smaller separations the two reflections merge, and thereafter

it is no longer possible to distinguish them as separate

reflections. This shows that thickness between two interfacesis below the limits of seismic resolution. In analogy with the

Rayleigh criterion, a value of /4 is quoted as the resolutionlimit, the minimum vertical separation of the two reflectors at

which the compound reflection can be identified as consisting

Table 1: Computed Tuning thickness and Critical resolution thickness for different signal bandwidth

Sl. Band (Hz) Band Band Central lobe Trough to Tuning Critical Tuning CriticalNo. f

min, f

maxRatio Width zero crossing Trough time thickness resolution thickness resolution

(Octave) (Hz) 2T0

L in Time thickness in Depth thickness(ms) (ms) (peak to in Time Z

r for in Depth

trough) CRT V=2500m/s V=2500m/sT

D (ms) (ms) (m) (m)

1 Ricker 35Hz ---- ---- 13.8 22.0 11.0 05. 5 14.0 07.0

2 6, 34 >2 28 24.6 43.0 21.5 10.7 27.0 13.5

3 24, 52 >1 28 13.8 24.6 12.3 06.1 15.2 07.6

4 56, 92 ---- 36 07.7 15.4 07.7 03.8 09.6 04.8

5 8, 90 >3 82 10.8 17.0 08.5 04.2 10.6 05.3

6 8, 16 1 8 41.5 72.3 36.1 18.0 44.6 22.3

7 8, 32 2 24 24.6 40.0 20.0 10.0 25.0 12.5

8 8, 64 3 56 13.8 24.6 12.3 06.1 15.2 07.2

9 8, 96 3.5 88 10.8 15.4 07.7 03.8 09.6 04.8

Figure 7a: Wavelet shape & amplitude spectrum of Ricker wavelet of frequency 35 Hz.



Figure 7b : Wavelet shape and amplitude spectrum of seismic signal having different bandwidth.



Figure 7c : Wavelet shape and amplitude spectrum of seismic signal in terms of Octave having different bandwidth

Band Pass 8-96 Hz



of two components, where is the dominant wavelength ofthe pulse. Figure (8c) shows the variation of apparent

thickness (trough- to- trough time) and maximum absolute

amplitude of the composite wavelet with true wedge thickness

for a 35Hz Ricker wavelet. For thicknesses greater than /2,the true and apparent bed thickness exactly follow the 45-

degree line, below /2 thickness the thickness curve deviatesupward from the 45-degree line and at /4 value thicknesscurve again crosses 45-degree line and then rapidly

approaches to a limiting value below /4 thickness values.This shows that below tuning thickness, it may not be possible

to extract meaningful information about thickness of bed fromthe apparent thickness. The value of maximum absolute

amplitude of composite wavelet decreases slowly below /2thickness and becomes minimum at tuning thickness /4.With further decrease in bed thickness, composite amplitudestarts increasing and finally becomes double at the limit of

zero thickness.

To understand the Widess limit of seismic resolution,

a synthetic seismic model of a pinchout having two spikes

of equal amplitude and opposite polarity is being generatedusing standard zero phase Ricker wavelet of 35 Hz and is

shown in Figure(9a & 9b). It has been observed in this figure

Figure 8c : Resolution and detection graphs for two spikes ofequal amplitude and equal polarity convolved with35 Hz Ricker wavelet ( After Kallweit and Wood,1982).

Figure 8a : Geological wedge model bounded by two different

formations.

Figure 8b : Synthetic seismic response of wedge model shown

in Figure (8a).

Figure 9a : Geological wedge model bounded by similar formation.

Figure 9b : Synthetic seismic response of wedge model shownin Figure (9a).

Figure 9c : Resolution and detection graphs for two spikes ofequal amplitude and opposite polarity convolved

with 35 Hz Ricker wavelet ( After Kallweit andWood, 1982).



that the convolved wavelet converges to the derivative of

the convolving wavelet as spike separation decreases. The

limiting separation for wavelet stabilisation occurs when bed

thickness is equal to /8 of a wavelength of the propagatingwavelet. For bed thickness less than /8, there is no furtherchange in the peak-to- trough times and only a change in

amplitude of the composite waveform is observed. Figure(9c)

shows the variation of maximum amplitude and apparent

thickness (trough-to- peak time) with true bed thickness for

the synthetic response given in Figure(9b). For thicknesses

greater than /2, The true and apparent bed thickness exactlyfollow the 45-degree line, below /2 thickness the thicknesscurve deviates downward from the 45-degree line and at /4value thickness curve again crosses 45-degree line and then

rapidly approaches to a limiting value below /4 thicknessvalues. The value of maximum absolute amplitude of composite

wavelet increases slowly below /2 thickness and becomesmaximum at tuning thickness /4. With further decrease inbed thickness, composite amplitude starts decreasing and

finally becomes zero at the limit of zero thickness.

These theoretical limits and synthetic seismic models

shown in Figures (8&9) demonstrate that use of composite

amplitude seismic response of wavelet can be made for

analysing the effect of individual thin bed in actual practice.

But in real seismic data, due to presence of noise and wavelet

shape variation it may not be always possible to derive direct

relation between individual bed thickness and composite

amplitude response.

b. Lateral Resolution

In addition to having limited vertical resolution,

reflection seismology also possesses finite lateral resolution.

Thus, it is not possible to generate perfectly sharp seismic

images of the subsurface; rather some blurring and lateral

smearing of such images occurs. This is primarily due to the

wave nature of the seismic signal. Migration of seismic data

attempts to compensate many wave effects. Thus, it becomes

important to understand lateral resolution separately on

stacked and migrated data.

b.1. Unmigrated data

In ray theory, a reflection from a subsurface of

acoustic impedance contrast is considered as coming from a

point described by the geometrical laws of Snell relating to

subsurface geometry, velocities and source- receiver

positions. This point of reflection is defined by tracing rays

from source to reflector to receiver. According to wave theory,

seismic method does not produce a reflection from one

individual point on a reflecting horizon but it gets generated

by integration over an area. Mathematically, convenient ray

tracing defines a point of reflection that is at the center of

this area of reflection integration. Energies from incremental

areas surrounding this reflection point having less than half

wavelength ray path difference at the receiver location interfere

constructively to generate the visible reflection event. This

area of constructive reflection accumulation surrounding the

ray theory reflection point is known as FRESNEL ZONE

(Lindsey, 1989).

Claerbout (1985) has defined Fresnel zone as the

distance across the hyperbola at the time when time of the

first arrival has just changed the polarity. He has illustrated

this through a synthetic seismic response generated from a

small geological anomaly. The generated seismic response

follows the hyperbolic path with offset and is shown in Figure

(10). The flat portion of the hyperbola produces a spatial

smear that may obscure the geological features. The size of

this lateral smear is referred as Fresnel zone. Sheriff (1985)

has defined Fresnel zone as the portion of a reflector from

which reflected energy can reach a detector within one-half

wavelength of the first reflected energy.

Figure 10 : Claerbouts definition of the Fresnel zone

(Claerbout, 1985).

Lateral resolution refers both to the lateral extent of

the reflecting surface which contributes to the seismic

reflection observed at the surface (i.e., the Fresnel zone for

unmigrated data) and also to the lateral spreading of the

seismic image, even of a sharp discontinuity. The size of the

Fresnel zone establishes the lateral resolution of the seismic

data. If the reflectivity changes take place in a distance less

than the Fresnel zone, they tend to be obscured in their

seismic expression. The ability to observe such important

phenomena as tidal channel cuts in sands, lateral facies

changes, spatial porosity variations etc., from seismic data is

a function of Fresnel zone size and hence lateral resolution.

In order to compute the Fresnel zone radius, wavefronts have

been considered rather than rays. Figure (11) shows an

isotropic spherical wavefront incident on a flat, horizontal

reflector. S is a coincident source and receiver, Z is the reflector

depth and R1and R

2are radii of the first Fresnel zone. The

limit of the constructively interfering reflection response is

the locus of points on the reflection surface where the increase

in one way path length from the centroid is one-quarter

wavelength.

The distance H from the source (S) to the edge of

the Fresnel zone will be thus equal to



H = Z+ /4 (19)

where is the wavelength of the wave. UsingPythagorass theorem

(Z+ /4)2 = Z2 + R2 (20)

Solving for R= R1= R

2gives

R = ( Z. /2 + 2/16 )1/2 (21)

Assuming Z>> , then Fresnel zone radius R will begiven by

R (Z. /2) 1/2 (22)

This equation can be expressed in terms of average

RMS velocity V, dominant frequency f and two way traveltime t to the reflecting horizon as

R (V/ 2) ( t/f) 1/2 (23)

The above equation shows that Fresnel zone radius

will not be of same size for all the frequencies in the observed

seismic passband. This concept of Fresnel zone is strictly

valid for monochromatic waves. Since seismic waves are never

strictly monochromatic, several workers have attempted to

develop analogs of the Fersnel zone for broad band wavelets

(Kallweit and Wood, 1982, Knapp, 1991, Buhl et al., 1996).Recently , Ebrom et al, (1997) have demonstrated that

broadband Fresnel radius can be easily calculated for zerophase wavelets using Pythagorean theorem and is equivalent

to the Rayleigh criterion for lateral resolvability in unmigrated

reflection seismic data. The expression for the Fresnel zone

radius for smooth, flat and horizontal reflector is rewritten as

R (L.Z.V/ 2)1/2 (24)

where L = 2 (TD)

and is equal to trough to trough

period of the zero phase wavelet and Z is depth of the reflector.

Here TD

is the distance between main lobe and first side

lobe. If a reflector is rugged, three different situations can be

visualised (Rocksandic, 1985):

1. Low amplitude reflector relief rests within one quarter

wavelength:In this case reflected waves result from

the constructive interference of all the energy reflected

within Fresnel zone like flat and horizontal reflector

shown in Figure (11), but the Fresnel zone is irregularly

shaped, has a different size and now time lag is not the

function of the distance from the central point only.

Lateral changes of the reflector relief will cause lateral

changes of the reflection strength ( Figure 12).

Figure 11: Fresnel zone for spherical waves from a flat and

horizontal reflector.

Figure 12: Fresnel zone for spherical waves from a rugged reflector,

the relief of which rests within /4 wavelength.

2. The reflector relief is low wavelength-high amplitude

in comparison with one-quarter wavelength:As shown

in Figure (13), certain flat portion in this case may be

larger than the Fresnel zone especially for higher

frequencies, and reflection will occur as in the case of a

flat reflector. However, because such portions are

oriented differently, interference of reflected wave willoccur.

3. Reflector of high wavelength- high amplitude relief:

In this case as illustrated in Figures (14a & 14b), every

high will generate a diffracted wave. If such highs are

close enough, interference of diffracted waves will

create a continuous reflection; if they are not close

enough diffractions will be present on the seismic

response. On migration diffraction will collapse to point

like reflections.

Figure 13 : Fresnel zone for spherical waves from a rugged reflector

with a low wave number high amplitude relief.



From the analysis of Fresnel zones of rugged

reflector it is found that the seismic response is frequency

dependent and the same relief may belong to different cases

for different frequencies. Lateral changes of the reflection

strength, loss of high frequencies, and diffractions are the

manifestations of a rugged surface. The significance of the

Fresnel zone is that a reflection observed at single point on

the surface samples the subsurface reflector over an area of

radius R. This results in smoothing process on a lateral scale

of length 2R and hence provide minimum lateral dimension

for an observed reflection.

b.2. Migrated data

Migration process improves the lateral resolution

by collapsing diffraction pattern associated with a reflector

discontinuity and so enhances and sharpens the seismic

image of the subsurfaces. Now to understand the lateral

resolution of migrated data let us consider a point diffracter

at lateral position X0

and two way travel time T0

. On a CMP

stack this point generates a hyperbolic diffraction pattern.

After migration with exact migration velocity Vmig

, it is found

that the migrated image is not a point but has a finite width.

This limit of migrated image is entirely due to limited aperture

used in the migration process and provides a theoretical limit

to the sharpness with which an image can be reconstructed.

Without going into further mathematical details, the expression

for the radius of migration aperture of migrated data can be

computed by expression ( OBrien and Lerche, 1988)

Rmig

= (1/4) Z / Xmax

(25)

where Z is reflector depth, Xmax

is the maximum

migration aperture. The migration aperture is that spatial

extent in which actual hyperbolic path spans during migration

and is measured in terms of number of traces. The migration

aperture for a dipping reflector having dip angle at depthZ can be defined as

Xmax

= Z tan (26)

The expression of Fresnel zone radius after migration

given in equation (25) clearly demonstrates that lateral

resolution of migrated data depends on reflector depth,

migration aperture and signal wave length. On the migrated

section an area having diameter 2Rmig

contributes towards

the reflection observed at a surface location. Fresnel zone

radius R for unmigrated seismic data given in equation (24)

and Rmig

for migrated data for a reflector at depth 2.5Km.

using migration aperture of 2.5 Km. have been computed for

different wavelets shown in Figures (7a, 7b & 7c) and are

summarised in Table-2.

Thus, to obtain a given lateral resolution implies

using a certain migration aperture recorded for CDPs out to

a distance of Xmax

beyond the target being imaged. To attain

the desired lateral resolution it is necessary that CDPs be

spaced sufficiently closely. To avoid aliasing, the moveout

between adjacent CDPs along the diffraction curve must be

less than the half wavelet period. Applying this criterion at

the edge of the migration aperture, where diffraction moveout

is maximum, one finds

CDPspacing

< Rmig

(27)

On a 2D migrated section, the lateral resolution in

the in-line direction is determined by Rmig

as given in equation

( 25). However, at right angles to the seismic line the method

still samples the full Fresnel zone of radius R as given in

equation (24) which can be significantly greater than the

resolution achieved in the in-line direction (Table-2). This

can be seen clearly in Figure (15). Through 2D-migration

process (1) dipping events are accurately moved updip if the

2D seismic line is oriented in the structural dip direction (2)

diffractions are effectively collapsed to their generating

positions if the 2D seismic profile is normal to the line of

diffraction and (3) amplitudes are restored for reflections only

for the curvature components in the direction of 2D seismic

profile. Thus, if the subsurface is believed to have a simple

geometry i.e., 2D structures then only 2D migration will be

effective up to certain extent in achieving the desired lateral

resolution. If the subsurface structures have a significant

3D component it may not be possible to achieve desired lateral

Figure 14a: Fresnel zone for spherical waves from a rugged reflector

with a high wave numberhigh amplitude relief.

Figure 14b: Fresnel zone for spherical waves from a rugged reflector

with a high wave number high amplitude relief.



resolution by simple orientation of 2D seismic lines which

makes a strong argument for performing 3D seismic surveys

for better lateral resolution. Since seismic wavefronts travel

in three dimensions, 3D migration for 3D seismic surveys

has proved to be useful in reducing the Fresnel zone into asmall circle instead of an ellipse as in case of 2D migration.

3D migration has been very helpful in achieving desired lateral

resolution and correct positioning of deep 3D structures

having arbitrary orientation.

In a nut-shell, it has been seen that frequency and

velocity are the key factors which determine the resolving

power of seismic data. Since nothing can be done with the

velocity of the medium which is assumed constant for

isotropic and homogeneous medium - it is the frequency of

the wavelet that finally holds the key for both vertical and

lateral resolution. Although, the assumption of isotropic andhomogeneous earth subsurface is very far away from the

reality. Several evidences have shown that most of the

sedimentary rocks are anisotropic and seismic velocities

change with direction (Singh and Kumar, 2001, Pramanik

et al., 2001, Winterstein and De, 2001). Presence of anisotropy

changes the shape of wavefront from spherical to

nonspherical and affect overall vertical and lateral seismic

resolution. The limits of vertical resolution and the size of

Fresnel zone diameter would be significantly different from

that determined by assuming isotropic medium (Okoye and

Uren, 2000). The variation in seismic resolution will depend

on the positive and negative values of anisotropic parameters

of the medium. In the above discussion of vertical and lateral

resolution it is assumed that seismic signal is noise free. The

presence of noise such as ambient noise, ground roll,multiples, events which do not satisfy velocity model and

migration noise caused by coarse sampling all have

detrimental effect on resolvability of reflected events. This

indicates that the seismic resolution achieved in practice will

be always less than the theoretically estimated seismic

resolution for a given source wavelet. Thus,the efforts to

maximise vertical and lateral resolution is the effort to

reduce the noise, increase the velocity accuracy and

maximise the bandwidth of reflected signal.

ESTIMATION OF MAXIMUM ATTAINABLE

SEISMIC SIGNAL BANDWIDTH

Estimation or measurement of signal bandwidth is

a direct assessment of resolving power and ultimately provide

an objective means of assessing the value of a seismic data

set. Therefore, it will be interesting to know whether there

is any limit in achieving maximum signal bandwidth or a

signal bandwidth very close to source can be obtained in

seismic reflection data. The process by which signal comes

to dominate noise over the certain frequency band is complex

and not fully understood. The various factors which influence

the shape of seismic wavelet have already been summarised

in Figure (4). It is important to note that we can put frequencies

from 0-10, 000Hz in to the ground through available efficient

sources but we still get back a usable range of signal

bandwidth something like 10-90Hz. This is the result of

various processes in the earth that eat up high frequencies

and our need to work with portable devices also contributes

to this direction. In other words, the earth introduces changes

in the nature of wavelet, which becomes broader and more

asymmetric with increasing travelled distance. Therefore, it

becomes important to understand the effect of stratification

of earth on seismic signal bandwidth and its maximum

attainable limit if any, before considering various aspects of

Table.2: Computed Fresnel zone radius at depth Z=2.5Km. and V=2500m/s for different signal bandwidth

Sl. Band (Hz) Band Band Central lobe Trough to Tuning Fresnel Zone Fresnel Zone

No. f min

, fmax

Ratio Width zero crossing Trough time thickness Radius R for Radius Rmig

(Octave) (Hz) 2T0

L in Time V=2500 m/s for Xmax

=2.5 Km

(ms) (ms) (peak to trough) at t=2sec & z=2.5 Km.

TD using eqn. (24) using eqn. (25)

(ms) (m) (m)

1 Ricker 35 Hz 13.8 22.0 11.0 264.0 14.0

2 6, 34 >2 28 24.6 43.0 21.5 369.0 27.03 24, 52 >1 28 13.8 24.6 12.3 276.0 15.2

4 56, 92 36 07.7 15.4 07.7 219.0 09.6

5 8, 90 >3 82 10.8 17.0 08.5 230.0 10.6

6 8, 16 1 8 41.5 72.3 36.1 472.0 44.6

7 8, 32 2 24 24.6 40.0 20.0 354.0 25.0

8 8, 64 3 56 13.8 24.6 12.3 276.0 15.2

9 8, 96 3.5 88 10.8 15.4 07.7 219.0 09.6

Figure 15: Effect of 2-D and 3-D migration on Fresnel zone size.



data acquisition, processing, interpretation and reservoir

characterisation.

Experimental evidences show that the earth

attenuates seismic signal in a frequency dependent manner

so that amplitude of a frequency component is reduced by a

constant factor per wavelength. The origin of attenuation

phenomenon in the earth subsurface is different from other

processes, which make amplitude decay, such as geometrical

spreading, reflection/ transmission losses and diffraction. It

is an intrinsic property of the subsurface materials quantified

by the seismic quality factor Q and related to internal

friction and anelasticity; as opposed to perfect elasticity

where waveform indefinitely travel without changing the

shape because all the frequencies are equally retained.

Different mechanisms have been proposed in the literature

to explain the attenuation phenomenon. Among them

Constant Q theory is one of the most extensively used

mechanism for understanding attenuation phenomena in

the earth (Kjartonson, 1979). For constant Q theory, the

amplitude spectrum A(f, t) of a nonstationary propagating

wavelet is given by

A (f, t)= Ao(f, t)exp (- f t / Q) (28)

Here Q is known as the Quality factor and is inversely

proportional to the attenuation, Ao (f, t) is the source

amplitude spectrum. Equation (28) states that at some travel

time t after the source explosion, the amplitude spectrum of

the waveform of the primary wavefront will be an exponentially

attenuated version of source amplitude spectrum. In order to

visualise the magnitude of attenuation problem the expression

for total attenuation ( f

) at frequency f is defined as

f= f t (29)

Here product of time t and frequency f gives the

number of wavelength in the reflection path and is

absorption constant in dB/wavelength. Various methods

utilised for estimation of attenuation have indicated that the

total average attenuation coefficient varies between 0.1 to

0.3 dB/wavelength. To demonstrate the effect of attenuation

at different frequencies of the seismic signal, a value of 0.15

dB/ wavelength has been taken and the variation of amplitude

at different time is shown in Figure (16). From this figure it is

clear that lower frequencies have less attenuation than higher

frequencies. At 3.0 sec and 100 Hz, the amplitude of reflection

component is 36dB below the amplitude of 20Hz component

of the same reflection. Therefore, increasing the resolution

of a seismic reflection requires inverting the attenuation by

restoring the amplitude of the higher frequencies. This figure

can be utilised to estimate the limit of restoration of attenuated

reflection coefficient. Further, the presence of low and high

frequency noise still complicates the seismic signal

bandwidth. Noise present in the original seismic data can be

divided in to three types: (1). Ambient (2) recording system

and (3) source-generated noise.

The ambient noise can be reduced substantially by

simple improvements in field operations during data

acquisition. Recording system noise is generated much lower

in amplitude than the other types and can be measured quite

accurately. Source generated noise is the most difficult to

deal with. Low and high frequency coherent noise can be

effectively attacked during acquisition and processing. More

difficult problem is scattered energy from the seismic source.

In some areas, the irregularities in geology, especially near

the surface, which return energy to the seismic detectors

over the unpredictable reflection and diffraction path. But

such areas are not very common. Most of the sedimentary

basins of the world have geology, which is quite close to the

ideal horizontal uniform layers of sediments, but there is still

a background of apparently random source-generated noise

which limits the resolution of seismic data. In 1978,

Schoenberger and Levin tried to explain the loss of high

frequencies due to the effect of short period multiples. But

Figure 16: Attenuation of seismic signal at different two-way time assuming attenuation constant 0.15 dB/ wavelength

( After Denham, 2000).



they could not explain the universal presence of background

noise after a particular frequency in all the seismic data sets.

In 1981, Denham has given an empirically derived relation for

obtaining the maximum attainable frequency in a seismic

reflection, which is written as

fmax

= 150/t (30)

where t is two-way travel time of the reflected signal.

Thus, if the reflection time is 2.5 sec, the maximum frequency

would be 60Hz. From the constant Q theory, Figure (16) shows

that attenuation at 60Hz and 2.5 sec. is about 23dB which can

be restored. If we assume that we can just see the data when

signal to noise ratio is 1:1; this implies that source generated

noise is about 23dB below the highest amplitude component

in the source. In deriving this empirical relation, Denham (1981)

has assumed that the most likely source of this source-

generated background noise was the distortion of geophones

combined with distortion introduced by geophone arrays and

geophone ground coupling as an added factor. Later on it

was realised that the distortion of advanced geophones as

specified by the manufacturers is much below to the observed

level of background noise and can not be the soul cause for

its presence in the recorded seismic data. Very recently,

Denham (2000) has suggested that the earth layering itself

generates the short period multiples as well as introduces

source-generated background noise. As a result of short

period multiple generations loss of high frequencies occur

and when combined with the presence of background noise,

it places a very real limit to attainable signal bandwidth in

seismic imaging. To explain this, Denham has generated a

synthetic section consisting of 20,000 layers in 6.0 km. thick

sedimentary section with velocity varying randomly from 2500

to 3500m/s. The largest absolute value of reflection coefficient

in the model was taken 0.024. Each layer has thickness

equivalent to 0.1 msec one-way travel time. The geological

model was made on the basis of well log data used by

Schoenberger and Levin (1978). Using acoustic theory, spike

transmission response of the model was computed including

multiples upto 300 layers for 5,000, 10,000, 15,000 and 20,000

layers and seismic responses are shown in Figure (17). As

number of layers increases in the model , the seismic pulse

gets widened and time delay of peak value increases. The

rms amplitude of the tail after first zero crossing goes below

the amplitude of initial spike and varies between 23 to 26 dB

depending upon the number of layers. Consideration of

elastic model with mode conversion phenomena may further

introduce more and more background noise. These modelling

results shown in Figure ( 17) clearly demonstrate that even

in absence of all other noises, the very nature of the

sedimentary crust as it approximates a finely layered stack

of horizontal beds introduces a practical limit of achievable

seismic resolution.

Thus, using Denhams(2000) approach, the

estimation of maximum achievable signal spectral bandwidth

can be made in real seismic data if Q structure of the study

parameters. Many sophisticated laboratory facilities have

been developed for measuring Q in dry, partially and fully

saturated cores under simulated environmental conditions

as a function of frequency and strain amplitude but Q value

obtained in the laboratory may not be directly applicable to

surface seismic data. It has been widely accepted that in-situ

borehole experiments are most suitable for reliable estimation

of the seismic quality factor Q. As a result, many case studies

of estimating Q from VSP data have been reported in the

literature. Very recently, an attempt has been made by

Pramanik et al., (2000) to estimate Q using zero offset VSP

and sonic log data. This estimated Q structure was used indesigning inverse Q filter for application to compensate

attenuation losses in surface seismic data. This inverse Q

filtering has improved amplitude, frequency and phase

stability of seismic data significantly and resulted in broader

signal to noise spectral bandwidth. This estimated Q structure

also can be utilised to estimate the limit of restoration of

attenuated reflection coefficient and maximum achievable

signal spectral bandwidth in surface seismic data by using

constant Q theory as demonstrated by Denham(2000).

The concept of constant Q theory together with a

simple model of background noise processes as having aconstant power level; leads to the expectation shown in Figure

(18) . Here the curve labelled as theoretical attenuated

spectrum depicts the constant Q model while the horizontal

line at - 50dB is a possible background noise level. The

expected observable spectrum follows the theoretical Q model

until it drops below the noise level and then follows the noise.

Thus, this simple constant Q model predicts a corner

frequency which is an indicator of the frequency at which

signal has been swamped by the noise. Such corner

frequencies are observable in real data though care must be

taken to account for the shape of any recording filters affecting

the higher frequencies. This observed highest corner

Figure 17: Effect of earth filtering on transmission responseincluding short period multiples up to 300 layers

(After Denham, 2000).

area is accurately known. But, inspite of tremendous

advancement in seismic related technologies , so far, there is

no direct method available for the accurate measurement of

attenuation and it remains one of the least understood seismic



frequency in the recorded data fixes the practical limit of

seismic resolution. Beyond this frequency, the enhancement

of seismic signal spectral bandwidth is not possible at any

cost during seismic data processing.

EFFECT OF EARTH STRATIFICATION ONSEISMIC REFLECTION RESPONSE

A sedimentary sequence, in general is a stratified

system of a wide band nature consisting of a large but finite

number of layers. Acoustic properties within a layer may be

either constant or variable , the variation being either parallel

to the stratification or perpendicular to it. Both types of

variation may be present simultaneously resulting in an

oblique variation. A boundary between two strata is

expressed by more or less abrupt changes of acoustic

properties and seismic response is influenced by stratification

in two ways: by the properties of individual reflector and bythe properties of stratified systems. Due to band limited nature

of seismic waves, the spectrum of a seismic record contains

information only on that part of the spectrum of the stratified

system which corresponds to the wavelets bandwidth. This

accounts for impossibility to determine the complete

spectrum of a stratified system from reflection seismic data.

In order to understand the influence of stratified systems on

the seismic reflection response the forward synthetic

modelling is being extensively used as an excellent tool in

increasingly challenging pursuit of reservoirs in the petroleum

industry. Forward stratigraphic modelling begins with

geological data. Well logs are the primary source for these

geological data. The sonic and density logs are of particular

importance because these logs are mathematically related to

the seismic data through acoustic impedance. Well logs, cores

and cuttings have excellent vertical resolution but very limited

lateral resolution. On the other hand, seismic provide excellent

lateral resolution but very limited vertical resolution. Thus,

integration of seismic and well log data sets through synthetic

modelling can provide both vertical and lateral description of

the subsurface. The presence of various fluids in the reservoir

like gas, oil and water and effect of their replacement on

synthetic seismic can also be analysed. This modelling

analysis forms the basis for conducting time lapse or 4-D

seismic surveys in hydrocarbon producing fields. Two

mathematical approaches are being utilised for synthetic

modelling (1) wave theory and (2) ray theory. In wave theory

approach, spherical wavefronts of advancing and reflected

waves are used to model the seismic response. In ray theory

approach, minimum travel time ray tracing is used to calculate

the seismic response from the input model.

In order to understand the influence of stratified

systems on the reflection seismic response, synthetic

seismograms for a few simple stratified systems have been

calculated for normal incidence having zero source-to-receiver

offset distance using 30Hz zero phase Ricker wavelet. Interbed

multiples were neglected because their effect is small for

simple stratified systems, which are studied. The

methodology adopted for generating synthetic seismograms

for stratified systems closely follows to that of

Rocksandic(1985). It has been most oftenly observed from

well logs that there is no sharp contrast between two

formations and log properties (for example velocity and

density) change slowly. This zone of slow change is known

as transition zone. To study the effect of transition zone on

reflection seismic response, synthetic seismograms were

generated for a model of linear variation of acoustic impedance

and are shown in Figure (19). The thickness of the transition

zone is defined in terms of two way propagation time and

related to the predominant period of the incident wavelet. It

is observed that the presence of transition zone causes

changes in amplitude, apparent period and time lag. The

reflected wavelet amplitude decreases, whereas its apparent

period increases with the increase of transition zone thickness

up to about 70% of the predominant period of the incident

wavelet and then remains constant as shown in Figure (20).

The change of signal shape becomes quite distinct when the

thickness of transition zone approaches predominant period

of the incident wavelet. Two sets of geological models

consisting one, two, four, six and eight interfaces of equal

reflection coefficient generated from sand layers of equal

thickness encased in shale in respective set are taken for

generation of synthetic seismic response (Figures 21 & 22).

The reflection coefficient of sand layers in second set (Figure

22) is higher in comparison to first set (Figure 21). Two-way

propagating times are the same for the models having similar

sand layers with both reflection coefficients, but the

thicknesses are different because of different velocities. The

seismic responses for those models are similar in form but

the reflection strength depends upon the reflection

coefficient. In case of thick layer the impedance contrast

boundary is represented at amplitude maxima and wavelet

remains symmetric, where as in case of presence of thin sand

and shale intercalations, there is no definite relation with

acoustic impedance contrast boundary and amplitude maxima/

minima and wavelet becomes asymmetric.

Figure (23) shows the synthetic seismic reflection

responses for geometrically similar models as shown in

Figure 18: Amplitude spectrum showing corner frequency

estimation using constant Q theory in presence of

background noise.



Figure 19 : Reflection responses of transition zones (After Rocksandic, 1985).

Figures (21 & 22) but with very high reflection coefficients.

In this case not only the reflection strength, but also the

shape of the seismic signals is different due to decreased

transmission of seismic energy. In such cases most of the

energy is reflected from the top of the first layer and lower

layers are practically unseen due to poor energy transmission

below layer one and destructive interference. Figure (24)

demonstrates the seismic reflection amplitude variations due

to different stratification patterns of layers having similar

reflection coefficients. Some stratification patterns will

reinforce the seismic signal by a constructive interference,

where as others will attenuate it by a destructive interference.

Figure (25) shows the synthetic seismic responses for four

geometrically similar geological models where two sand layers

are encased in an acoustically homogeneous medium. The

bed spacing between two layers is sufficiently large to

prevent the interference of reflected waves from first layer to

second layer. For low and moderately high reflection

coefficients, the difference between the amplitudes of the

reflections from the first and second layers is small. However,



Figure 20: Variation of the reflection strength, apparent period and time lag with transition zone thickness

variation ( After Rocksandic, 1985).

for very high reflection coefficients, the reflection strength

corresponding to the first layer is considerably higher than

that corresponding to the second. This is an effect of

decreased transmission of seismic energy through the first

layer. Figure (26) illustrates the predominant influence

Resolution Geohorizons

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