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
ONGC, KDMIPE Campus
Kaulagarh Road,
Dehradun - 248 195Phone : 91-135-2795536/2752088
Fax : 91-135-275028
E-mail : [email protected]
Website: www.spgindia.org
Printed at :
Allied Printers
Nehar Wali Gali,
Dehra Dun - 248 001
Phone : 2654505
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
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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
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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
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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)
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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.
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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.
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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.
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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.
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(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.
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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).
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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.
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Figure 7b : Wavelet shape and amplitude spectrum of seismic signal having different bandwidth.
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Figure 7c : Wavelet shape and amplitude spectrum of seismic signal in terms of Octave having different bandwidth
Band Pass 8-96 Hz
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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).
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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
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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.
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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.
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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.
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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).
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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
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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.
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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,
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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