seismic inversion

2015
MODEL-BASED INVERSION
IN NORTH SEA
F3-BLOCK DUTCH SECTOR
By
Hassan Hussien Hassan
Khalid El-Maghawry
Wafaa Mohamed Hassan
B.Sc. Students 2015
To
Geophysics Department
Faculty of Science
Ain Shams University
Supervised by
Dr. Azza Mahmoud Abd El-Latif El-Rawy
Lecturer of Geophysics
Geophysics Department- Faculty of Science- Ain Shams University
Cairo - 2015

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Acknowledgement
We would like to express our gratitude and many thanks to our
supervisor Dr.Azza El-Rawy for her help, guidance, patient,
understanding, continuous support and efforts with us to complete this
work.
We are also thankful to Mr.Ahmad Hosny from Rashid Petroleum
Company for his help and advices.
Finally, we would like to appreciate all department staff members
they always had time for question and discussion.

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ABSTRACT
The location of project is in North Sea in Dutch sector where a 3D
seismic acquisition. As determination of lithology and fluid content
distribution is a desirable objective for reservoir characterization and
subsequent reservoir management, we adopt AVO inversion and post-
stack impedance inversion methods to achieve this goal. Due to the access
to available inversion methods, it is advisable on finding out the best
method. To this end, we present a comparative performance of the
available model based seismic acoustic impedance inversion methods. In
this study, we start with the traditional model based seismic acoustic
impedance inversion and compare its result with equivalent results from
elastic impedance, the separate or independent impedance inversion
carried out as a post stack process and simultaneous inversion.

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Contents
Acknowledgement........................................................................................................................................I
ABSTRACT.................................................................................................................................................II
Contents.......................................................................................................................................................III
List of Figures..............................................................................................................................................V
1. INTRODUCTION...............................................................................................................................1
1.1. Topographic location..................................................................................................................1
1.2. Objective of inversion.................................................................................................................2
1.3. Available data..............................................................................................................................2
1.4. Methodology................................................................................................................................5
2. GENERAL GEOLOGICAL SETTINGS .........................................................................................6
2.1. Introduction.................................................................................................................................6
2.2. Stratigraphy.................................................................................................................................7
2.2.1. Paleozoic (about 590 - 250 million years ago)......................................................................7
2.2.2. Mesozoic...............................................................................................................................8
2.2.3. Cenozoic .............................................................................................................................11
2.3. Petroleum system ......................................................................................................................11
2.4. Structural setting ......................................................................................................................15
2.5. Tectonic history.........................................................................................................................20
3. THEORITICAL BACKGROUND OF SEISMIC AMPLITUDE INVERSION ........................22
3.1. Introduction...............................................................................................................................22
3.1.1. Seismic velocity inversion ..................................................................................................22
3.1.2. Seismic Amplitude Inversion..............................................................................................23
3.2. Post-stack Inversion Methods..................................................................................................33
3.2.1. Colored inversion................................................................................................................33
3.2.2. Sparse spike inversion.........................................................................................................34
3.2.3. Model-based inversion........................................................................................................36
3.2.4. Stochastic inversion ............................................................................................................40
4. SEISMIC INVERSION USING HAMPSON-RUSSELL SOFTWARE......................................42
4.1. Introduction...............................................................................................................................42
4.2. Available Data...........................................................................................................................43

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4.3. Inversion Concepts....................................................................................................................44
4.4. Model-Based Inversion Workflow on F3-Block Seismic Cube.............................................47
4.4.1. Data Importing....................................................................................................................47
4.4.2. Identifying Target Reservoir in F3-Block Cube .................................................................52
4.4.3. Depth-Time Conversion and Check Shot Correction .........................................................57
4.4.4. Wavelet Extraction and Synesthetic Trace .........................................................................59
4.4.5. Initial Model Building.........................................................................................................62
4.4.6. Quality Control (QC) ..........................................................................................................64
4.4.7. Running Inversion...............................................................................................................67
4.4.8. Results.................................................................................................................................68
Summary....................................................................................................................................................71
References..................................................................................................................................................73

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List of Figures
Figure 1.1: Location map of Dutch Sector, showing F3 Block noted above (from Remmelts, 1995) -------- 3
Figure 2.2: stratigraphic column (modified from Glennie, 1997a) --------------------------------------------------10
Figure 3.2: Geologic Provinces Total Petroleum System (403601). -------------------------------------------------13
Figure 4.2: Petroleum System Glennie (1998)----------------------------------------------------------------------------14
Figure 5.2: structure features of North Sea (Ziegler, 1990)-----------------------------------------------------------18
Figure 6.2: Geological cross section ziegler (1978)----------------------------------------------------------------------19
Figure 7.3: velocity inversion R. Kamei, R.G. Pratt and T. Tsuji-------------------------------------------------------22
Figure 8.3: Modeling and Inversion Rasmussen KB Brunn A and Pedersen JM (2004)-------------------------26
Figure 9.3: Porosity vs Impedance, Salter R Et al (2005)---------------------------------------------------------------27
Figure 10.3: Porosity Prediction, Salter R etal (2005) ------------------------------------------------------------------28
Figure 11.3: Seismic Inversion------------------------------------------------------------------------------------------------30
Figure 12.3: Synthetic trace and wavelet extraction Buiting,J . J. M. & Bacon,M . (1999) --------------------32
Figure 13.3: Colored inversion vs Seismic data (Lancaster and Whitcombe 2000) -----------------------------34
Figure 14.3: Sparse spike inversion (modified after Ronghe and Surarat 2002). --------------------------------36
Figure 15.3: Model based inversion (Goffe et al.1994, Duboz et al. 1998)----------------------------------------38
Figure 16.3: Correlation between check shots and impedance log veeken 2006 -------------------------------38
Figure 17.3: Seismic vs Impedance, Veeken 2006-----------------------------------------------------------------------39
Figure 18.3: Stochastic inversion (modified after TorresVerdin et al. 1999).-------------------------------------41
Figure 19.4: combination between the geology and seismic data in inversion----------------------------------44
Figure 20.4: Seismic Inversion Components------------------------------------------------------------------------------45
Figure 21.4: Step 1 --------------------------------------------------------------------------------------------------------------46
Figure 22.4: Step 2 --------------------------------------------------------------------------------------------------------------46
Figure 23.4: Comparison between Input Seismic and Model Based Inversion-----------------------------------47
Figure 25.4: Opened Database List------------------------------------------------------------------------------------------47
Figure 24.4: HR Opened Database List -------------------------------------------------------------------------------------47
Figure 26.4: Hampson-Russell Interface -----------------------------------------------------------------------------------48
Figure 27.4: Well Explorer Window-----------------------------------------------------------------------------------------48
Figure 28.4: Importing Logs---------------------------------------------------------------------------------------------------48
Figure 29.4: Identifying unknown logs -------------------------------------------------------------------------------------49
Figure 30.4: STRATA Project Selection Mode-----------------------------------------------------------------------------49
Figure 31.4: Importing Data---------------------------------------------------------------------------------------------------50
Figure 32.4: SEG-Y Seismic File Open---------------------------------------------------------------------------------------51
Figure 33.4: Geometry Grid Page--------------------------------------------------------------------------------------------51
Figure 34.4: Well to Seismic Map Menu-----------------------------------------------------------------------------------52
Figure 35.4: GR-Porosity Cross plot-----------------------------------------------------------------------------------------53
Figure 36.4: Well F020-1 Cross Section ------------------------------------------------------------------------------------53

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Figure 37.4: GR-Impedance Cross Plot -------------------------------------------------------------------------------------54
Figure 38.4: F02-2 Cross section for GR-Impedance cross plot ------------------------------------------------------55
Figure 39.4: FS8 the target reservoir ---------------------------------------------------------------------------------------55
Figure 40.4: Picking Horizon FS8---------------------------------------------------------------------------------------------56
Figure 41.4: Actual Picks of FS8 ----------------------------------------------------------------------------------------------56
Figure 42.4: Difference between Time logs and Depth logs ----------------------------------------------------------57
Figure 43.4: Depth time table ------------------------------------------------------------------------------------------------58
Figure 44.4: Check Shot Correction -----------------------------------------------------------------------------------------59
Figure 45.4: Wavelet with different phases (0, 90,180 and 270) ----------------------------------------------------60
Figure 46.4: Wavelet 270 correlation in well F02-1---------------------------------------------------------------------61
Figure 47.4: Wavelet zero correlation in well F03-4--------------------------------------------------------------------61
Figure 48.4: Initial Model Building ------------------------------------------------------------------------------------------62
Figure 49.4 ------------------------------------------------------------------------------------------------------------------------62
Figure 50.4 ------------------------------------------------------------------------------------------------------------------------62
Figure 51.4 ------------------------------------------------------------------------------------------------------------------------63
Figure 52.4: Initial Model for F3-Block Seismic Cube-------------------------------------------------------------------63
Figure 53.4: Inversion Analysis for Post-stack Data---------------------------------------------------------------------64
Figure 54.4: Number of Iteration--------------------------------------------------------------------------------------------65
Figure 55.4: Error Plot----------------------------------------------------------------------------------------------------------66
Figure 56.4: Inversion Analysis Cross plot---------------------------------------------------------------------------------66
Figure 57.4: Inverted Inline ---------------------------------------------------------------------------------------------------67
Figure 58.4: Inverted Xline ----------------------------------------------------------------------------------------------------67
Figure 59.4: Inverted Arbitrary Line-----------------------------------------------------------------------------------------68
Figure 60.4: Reflectivity (Right) Impedance (Left) Slice-750 (upper) Slice-780 (lower) ------------------------69
Figure 61.4: Reflectivity (Right) Impedance (Left) Slice-950 (upper) Slice-1600 (Lower) ----------------------70

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CHAPTER 1:
1. INTRODUCTION
1.1. Topographic location
The North Sea is a marginal, shallow sea on the European continental shelf.
It is more than 970 kilometers from north to south and 580 kilometers from east to
west, with an area of around 750,000 square kilometers. The North Sea RAC area is
larger, because it includes the Skagerrak and Kattegat which connect the North Sea
proper to the Baltic. The North Sea is bordered by England, Scotland, Norway,
Denmark, Germany, the Netherlands, Belgium and France. In the southwest, beyond
the Straits of Dover, the North Sea becomes the English Channel which connects to
the Atlantic Ocean. The North Sea is a fairly shallow coastal sea and depths in the
southern basin do not exceed 50m. The northern areas are deeper but are still
generally less than 200m except in the Norwegian Trough, in the north-east, which
is the only region of very deep water.
The Dutch part of the North Sea (NCP) occupies an area of 57,000 km2 which
is larger than the mainland of The Netherlands. In addition to traditional activities,
like fishery and shipping, since the 1960s there have been new activities such as oil
and gas exploration and exploitation, and extraction of sand from the seabed. New
plans for installation of wind turbines and coastal extensions are in progress. In
addition the area forms part of a valuable marine ecosystem. Knowledge of the
morphology of the seafloor and the sediment properties is important, both to
understand the ecosystem as well as for developing infrastructural activities.

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1.2. Objective of inversion
The principle objective of seismic inversion is to transform seismic reflection
data into a quantitative rock property, descriptive of the reservoir. In its most simple
form, acoustic impedance logs are computed at each CMP... In other words, if we
had drill and logged wells at the CMP’s, what would the impedance logs have looked
like? Compared to working with seismic amplitudes, inversion results show higher
resolution and support more accurate interpretations. This in turn facilitates better
estimations of reservoir properties such as porosity and net pay. An additional
benefit is that interpretation efficiency is greatly improved, more than offsetting the
time spent in the inversion process. It will also be demonstrated below that
inversions make possible the formal estimation of uncertainty and risk
1.3. Available data
The project is a prospect in North Sea specified in Dutch sector place offshore
Netherlands F3 Block (Figure 1.1) with coordinates N 54°52′0.86″ / E 4°48′47.07
this project was held in 1987 and that by making 3d seismic survey and drilling of 4
wells in different area to cover our cube which has 24*16 km square our target is at
late Jurassic early cretaceous for very rich gas prospect.
The available data is:
Seismic Data:
• A 3D seismic cube that consists of 740 in lines and 949 xlines and it is post
stack cube

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Figure 1.1: Location map of Dutch Sector, showing F3 Block noted above (from Remmelts, 1995)

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Horizons
• Demo0 (FS4)
• Demo1 (MFS4)
• Demo2 (FS6)
• Demo3 (Top_Foresets)
• Demo4 (Truncation)
• Demo5 (FS7)
• Demo6 (FS8)
• Demo7 (Shallow)
Wells and available logs
• F02–1 (Caliper, Density, GR, P-Wave, Porosity)
• F03–2 (Density, GR, P-Wave, Porosity)

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1.4. Methodology
The 3D seismic cube is inputted in the Hampson-Russell software then we
start to input the wells in the area and recognize the logs in each wells then start to
input the tops and the check shots after that we start to input the seismic data as cube
and the horizons then start to extract wavelet to get synthetic seismogram and
correlate it with seismic after that the selected wavelet is used to make model based
inversion to our cube to get inverted one.
Benefits of seismic inversion
The benefits of seismic inversion include
• Compensation for and reduction of the effects of wavelet tuning
• Presentation of output as geologic layers rather than reflection edges
• Merging of known low frequency geologic and geophysical information with
seismic data
• Modelling and inclusion of layer stratigraphy
• Inclusion of geophysical constraints from known information or analogues.
• Calibration to well log data
• Improved interpretability of seismic horizons
• Increased bandwidth in the inversion output
• Attenuation of random noise

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CHAPTER 2:
2. GENERAL GEOLOGICAL SETTINGS
2.1. Introduction
Netherlands with coordinates N 54°52′0.86″ / E 4°48′47.07 this project was held in
1987 and that by making 3d seismic survey and drilling of 4 wells in different area
to cover our cube which has 24*16 km square. Our target is at late Jurassic early
cretaceous for very rich gas prospect.
To be reliable, Earth models used for mineral exploration should be consistent
with all available geologic and geophysical information. Due to data uncertainty and
other aspects inherent to the underdetermined geophysical inverse problem, there
are an infinite number of models that can fit the geophysical data to the desired
degree (i.e. the problem is no unique). Additional information is essential to obtain
a unique and useful solution. Incorporating prior geologic knowledge, and
combining several complimentary types of geophysical data collected over the same
Earth region, can reduce ambiguity and enhance inversion results, leading to more
reliable Earth models. There are two areas of research that are important to help
achieve the goal of more reliable Earth models: development of geophysical
inversion methods that
1) Increase the kinds of geologic information that can be incorporated
2) Can combine several complimentary types of geophysical data collected over the
same Earth region

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2.2. Stratigraphy
2.2.1. Paleozoic (about 590 - 250 million years ago)
The configuration of Lower Paleozoic crystalline and metamorphic basement
rocks that underlie the North Sea sedimentary basins was assembled during the
Caledonian Orogeny (about 420 - 390 million years ago) to form the Caledonian
basement. This was achieved through the closure of the Iapetus Ocean and the
Tornquist Sea, at the Iapetus Suture and ‘Trans-European Fault Zone’, respectively
(e.g. Andrews et al. 1990; Johnson et al. 1993; Gatliff et al. 1994; Glennie and
Underhill 1998). Many of the major faults within the Caledonian basement formed
lines of weakness that experienced significant reactivation during subsequent phases
of earth movements.
During the Devonian (about 410 -360 million years ago), there was
widespread red-bed molasse and lacustrine sedimentation as the newly-formed
Caledonian mountain ranges were eroded. Mid-Devonian (about 375 million years
ago) marine limestones in the south of the Central North Sea were probably formed
during an early rift phase. This was a precursor to the main phases of Permo-Triassic
(about 290 - 210 million years ago) and Late Jurassic rifting (about 160 - 140 million
years ago) and associated strike-slip movements.
During the early Carboniferous (about 360 - 325 million years ago),
fluviodeltaic and shallow-marine sediments and local volcanic accumulated in parts
of the Central North Sea at times of regional crustal extension, though the Northern
North Sea area was mainly source of clastic sediments. As in England, these
Carboniferous rocks were gently folded, faulted, uplifted and eroded during the Late
Carboniferous Variscan Orogeny approximately 300-290 million years ago.

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During the Late Permian (about 270 - 250 million years ago) redbeds and local
volcanic (Rotliegend Group) accumulated within the widespread Northern Permian
Basin. Following marine transgression, cyclical evaporitic successions (Zechstein
Group) were deposited and locally reach over 1000 m in thickness. The evaporites
have been deformed by halokinesis intermittently since mid-Triassic times (about
230 million years ago), leading to the widespread growth of salt pillows and salt
diapirs, especially in the Central North Sea
2.2.2. Mesozoic
For the ages of the geological systems and events in this section the reader is
referred to (Figure 2.1) In the Triassic there was a return to arid, continental climate
conditions and both sandstone- and mudstone-dominated redbed successions were
laid down. During the Early Jurassic there was a spread of marine deposits over
much of the North Sea during a phase of thermal subsidence following Permo-
Triassic rifting.
During the Middle Jurassic, regressive, paralic sediments accumulated when
a major subaerial thermal dome formed within the Central North Sea probably due
to the development of a warm, diffuse and transient mantle-plume head (Underhill
and Partington 1993). The Late Jurassic was a time of major extensional faulting.
The rifting was initially most intense at the extremities of the present graben system
and as time elapsed it propagated back towards the center of the dome (Rattey and
Hayward 1993; Fraser 1993). The onset of major rifting probably occurring in the
middle Oxfordian to early Kimmeridgian (approximately 157 - 155 million years
ago) (Underhill 1991; Glennie and Underhill 1998).
Seismic data reveal that the Upper Jurassic sedimentary successions
commonly thicken dramatically towards syndepositional faults. This pattern of

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sediment thickness variation is in contrast with that formed during the ‘thermal sag’
phase of basin development (e.g. McKenzie 1978) in Early-mid Jurassic times, when
the basin was more ‘saucer-shaped’ and the thickest deposits accumulated at its
center. Rift styles vary substantially between the northern and the central North Sea
and there were two principal controlling factors. Firstly, differences in the basement
composition and tectonic grain between the two regions strongly influenced
structural development. In the central North Sea, the rifts are more complex and were
segmented along NE ‘Caledonide’ and NW ‘Trans- European Fault Zone’ trends
(e.g. Errat et al. 1999; Jones et al. 1999). Secondly, in the northern North Sea, Upper
Permian salt is largely absent, and there is no major detachment between basement
and cover rocks. In contrast, the Zechstein evaporites in the central North Sea
provide a major detachment level that essentially separates the basement rocks from
the cover sequence of rocks or ‘carapace’ (e.g. Hodgson et al. 1992; Smith et al.
1993; Helgeson 1999).
This structural contrast is reflected in the smaller size of the oil and gas fields
discovered within the pre- and syn-rift successions of the central North Sea. Local
inversion of central North Sea depocentres during the Early Cretaceous is considered
to be a response to strike-slip faulting (Pegrum and Ljones 1984). Transpressional
pulses are believed to have triggered the halokinesis of Zechstein salts within the
Central Graben, which exerted an additional control on the patterns of subsidence
and sedimentation (Oakman and Partington 1998; Gatliff et al. 1994).

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Figure 2.2: stratigraphic column (modified from Glennie, 1997a)

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2.2.3. Cenozoic
Thermal subsidence in response to Late Jurassic rifting, dominated much of
the Cenozoic, with some relatively minor pulses of earth movements (e.g. Pegrum
and Ljones 1984). Regional patterns of sedimentation changed dramatically in early
Paleocene times, with the influx into the basinal areas of huge volumes of coarse
clastic detritus including debris flows and turbidities. This detritus was shed from
the uplands of northern Scotland and the Orkney-Shetland Platform, which were
undergoing thermal uplift in response to the development of the Iceland Plume
(White 1988; White and Lovell 1997).
2.3. Petroleum system
Upper Jurassic syn-rift, organic-rich marine mudstones (the Kimmeridge Clay
Formation) provide the source material for most of the region’s hydrocarbons
(Brooks et al. in press). Cretaceous and Cenozoic post-rift thermal subsidence and
burial has enabled the source rocks to become mature for hydrocarbon generation
along the rift axes from Paleocene times onward (Johnson and Fisher 1998).
Hydrocarbon migration has been mainly vertical, but with significant lateral
migration restricted to the Upper Jurassic and Paleocene successions. Hydrocarbons
extraction is from almost every clastic and carbonate sedimentary succession,
ranging in age from, and including, Devonian and Eocene strata. Pre-rift producing
fields comprise Paleozoic, Triassic to Lower Jurassic and Middle Jurassic categories
(Brooks et al. in press).
The Middle Jurassic tilted fault-block play is best developed in the East
Shetland Basin and is one of the most productive in the North Sea. Syn-rift reservoirs
within producing fields comprise Upper Jurassic to Lower Cretaceous sandstones
according to Brooks et al. (in press), though many authors prefer to interpret the

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Lower Cretaceous succession as post-rift deposits formed during a phase of local
strike-slip tectonism (e.g. Rattey and Hayward 1993; Oakman and Partington 1998).
The producing Upper Jurassic reservoirs include both shallow and deep marine
sandstones, though Lower Cretaceous reservoirs were almost exclusively formed
within deep marine settings. The syn-rift hydrocarbons producing fields display a
wide variety of trapping mechanisms, including tilted fault blocks, domes, and
stratigraphic closures. Thick, post-rift Lower Cretaceous mudstones also provide a
regional seal for many traps. Post-rift thermal subsidence has continued from
Cretaceous times to the present day. Within the UK sector, the Upper Cretaceous
Chalk is relatively insignificant as a producing reservoir.
Mass-flow sandstone reservoirs of Paleocene age are estimated to contain
about 20% of the oil province’s proven hydrocarbon reserves (Pegrum and Spencer
1990). Virtually all of the UK sector Paleocene sand systems become progressively
distal to the east or SE. There was an evolution from the emplacement of laterally
extensive sheet sands on the basin floor during the early Paleocene, to restriction of
sand bodies into narrow, elongate channels intercalated within mud-dominated slope
facies during the mid-Eocene.
The Central North Sea and includes many important producing hydrocarbon
fields. These fields mainly produce from syn-rift Upper Jurassic and/or post-rift
Lower Cretaceous or Paleocene reservoir sandstones. Halokinesis has generally not
exerted a major influence on the structural development.
Many of the Upper Jurassic and some of the Lower Cretaceous hydrocarbons
traps are located within either the footwall or hanging wall blocks of major faults
(e.g. the Piper and Brae fields). Other, younger Lower Cretaceous hydrocarbons
traps include a larger component of stratigraphic trapping (e.g. the Britannia Field).

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Figure 3.2: Geologic Provinces Total Petroleum System (403601).
all the Mesozoic traps are deeply buried by the thick Cenozoic successions which
occur within or overlie the rift-basins. In contrast, many of the Paleocene traps are
buried at relatively shallow depths. For example, the Balmorals Oilfield lies at about
2150 m depth (Tonkin and Fraser 1991).

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Figure 4.2: Petroleum System Glennie (1998)

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2.4. Structural setting
In the northern Dutch offshore Yore dale-type cycles were deposited from the
Middle Visean to the Early Namurian in relation to northern source. Continued
normal faulting resulted in a gradual basin deepening during the course of the Early
Carboniferous. Towards the end of the Visean differential subsidence had resulted
in a complex series of deep-water basins characterised by faulted basin-floor
topography. This caused local stagnation of deep-water circulation at the transition
from the Visean to the Namurian and resulted in the deposition of a thick bituminous
shale: the Geverik Member (UK: Bowland Shale). Within the Dutch sector, this
organic-rich shale was only encountered in proximity to the Brabant Massif;
extrapolating its extent into the main basin seems premature. Correlations of the
overlying Namurian deltaic show that the organic-rich Geverik Member just
northeast of the London Brabant Massif accumulated in a basin that was 200 meters
deeper than a similar location north of the London Brabant Massif where Visean
carbonates became exposed. The fact that the Geverik Member overlies a Dinantian
carbonate sequence suggests that the depositional location was part of the northern
flank of the London-Brabant Massif during the Early Carboniferous, instead of the
adjacent graben. This observation challenges the interpretation of Middle
Carboniferous organic rich shales as deep-water deposits and sheds doubt on its
presumed basin wide extent.
Fault orientation and Late-Carboniferous sediment-distribution patterns on
the pre-Permian sub crop map show that Early Carboniferous extension may have
dominated the entire eastern Netherlands. Similar patterns are observed in the
northern offshore. Namurian - Thrust loading during the Namurian resulted in high
subsidence and in the formation of a foreland basin north of the London-Brabant
Massif. Correlations of the overlying Namurian deltaic cycles suggest that the

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faulted topography of the Variscan back-arc basin had been leveled by the Early
Namurian. The thickness of the Namurian succession increases away from the
massif but subsequently decreases over the Mid- Netherlands Zandvoort-Krefeld
High, a NW-SE aligned structural element of low subsidence until well into the
Tertiary. The high is represented on the sub crop map by the major NW-SE
lineament separating the Lower Westphalian in the north from the Upper
Westphalian in the south. Another deep basin extended northward from the
Zandvoort- Krefeld High to the Texel-Ijsselmeer High, a structural element that may
be traced across the North Sea towards the northern basin margin. In the northern
Dutch offshore the Namurian is characterised by thick fluvial sandstones. Basal
turbidity fans, characteristic of the lowermost Namurian in some of the northern sub-
basins in the UK were not deposited in the southern part of the Southern North Sea
Basin. Westphalia – The lithological transition from the Namurian to the
Westphalian is placed at the first level of regional occurrence of coal beds. Across
the onshore Netherlands this is a characteristic series of three coals, interbedded thin
shales and sands, which shows that the entire basin
The Mid-Netherlands High has since long been regarded as an area of intra-
Westphalian uplift. Its southwestern boundary is defined by the Zandvoort-Krefeld
High. Uplift of the Mid-Netherlands High is attributed to transpressional movements
along its southern boundary faults. Evidence of intra-basinal sediment supply is
presented by the stacked fluvial sandstones. These sands were found to contain
reworked coal fragments of which vitrinite-reflectance data show that they were
previously buried at intermediate depths.
F3 is a block in the Dutch sector of the North Sea. The block is covered by
3D seismic that was acquired to explore for oil and gas in the Upper-Jurassic – Lower
Cretaceous strata, which are found below the interval selected for this demo set. The

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upper 1200ms of the demo set consists of reflectors belonging to the Miocene,
Pliocene, and Pleistocene. The large-scale sigmoidal bedding is readily apparent,
and consists of the deposits of a large fluviodeltaic system that drained large parts
of the Baltic Sea region (Sørensenetal, 1997; Overeemetal, 2001).
The deltaic package consists of sand and shale, with an overall high porosity
(20–33%). Some carbonate-cemented streaks are present. A number of interesting
features can be observed in this package. The most striking feature is the large-scale
sigmoidal bedding, with text-book quality downlap, toplap, onlap, and truncation
structures. Bright spots are also clearly visible, and are caused by biogenic gas
pockets. They are not uncommon in this part of the North Sea. Several seismic facies
can be distinguished: transparent, chaotic, linear, shingles. Well logs show the
transparent facies to consist of a rather uniform lithology, which can be either sand
or shale. The chaotic facies likely represents slumped deposits. The shingles at the
base of the clinoforms have been shown to consist of sandy turbidites.

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Figure 5.2: structure features of North Sea (Ziegler, 1990)

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Figure 6.2: Geological cross section ziegler (1978)

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2.5. Tectonic history
The North Sea area was the site of a triple plate collision zone during the
Caledonian orogeny Four major tectonic events influenced the area since the
Cambrian: (i) the Caledonian collision during Late Ordovician to Early Silurian, (ii)
subsequent rifting and basin formation mainly identified in the Carboniferous to
Permian, (iii) Mesozoic rifting and graben formation and (iv) inversion during Late
Cretaceous to Early Tertiary (Ziegler, 1990). The Caledonian collision involved two
large continents,
The tectonic regime changed from general extension and subsidence in The
Devonian to a strike-slip regime during the late Carboniferous to early Permian.
During the late Variscan cycle northwestern Europe was transected by a system of
conjugate shear faults, which in the Danish area resulted in the development of the
Tornquist Fan of faults that form links between NNE to SSW trending graben
structures (Thybo, 1997). At the late Carboniferous, the Variscan orogeny collapsed
and uplift caused truncation of the Devonian–Carboniferous successions.
The late Carboniferous and early Permian extensional wrench tectonics
caused crustal thinning and subsidence of the Northern and Southern Permian
Basins, which are separated by the Mid-North Sea-Ringkøbing Fyn High. The
crustal thinning was associated with magmatic activity, evidenced in Rotliegendes
volcanic deposits and associated sedimentary rocks. The Rotliegendes or top pre-
Zechstein reflector marks a regional unconformity between pre-rift and syn-rift
deposits and defines the traditional acoustic basement in most reflection seismic data
from the North Sea. From the Triassic to the Jurassic
The NNW_SSE striking Central, Viking and Horn Grabens developed with
extensive normal faulting in the basin areas. In the graben areas the Jurassic and

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Triassic sediments attain thicknesses in excess of 4 km (Vejbaek, 1992). During the
Late Cretaceous Laramide phase of the Alpine orogeny compressional stresses
caused inversion and deformation throughout the Danish and the North Sea area.
Since the Early Tertiary the geological evolution has been characterized by regional
subsidence in the North Sea area and uplift of the Baltic Shield.

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Figure 7.3: velocity inversion R. Kamei, R.G. Pratt and T. Tsuji
CHAPTER 3:
3. THEORITICAL BACKGROUND OF SEISMIC AMPLITUDE
INVERSION
3.1. Introduction
3.1.1. Seismic velocity inversion
The first type of inversion, velocity inversion, sometimes known as travel time
inversion, is used for depth imaging. Using seismic traces at widely spaced locations,
it generates a velocity-depth earth model that fits recorded arrival times of seismic
waves. The result is a relatively coarse velocity-depth model extending over several
kilometers in depth and perhaps hundreds of kilometers in length and width. This
solution is applied in data-processing steps such as migration and stacking,
eventually producing the type of seismic image that is familiar to most readers.
Seismic interpreters use these images to determine the shape and depth of subsurface
reflectors.

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3.1.2. Seismic Amplitude Inversion
The second type of inversion, amplitude inversion, is the focus of this
article. This approach uses the arrival time and the amplitude of reflected seismic
waves at every reflection point to solve for the relative impedances of formations
bounded by the imaged reflectors. This inversion, called seismic inversion for
reservoir characterization, reads between the lines, or between reflecting
interfaces, to produce detailed models of rock properties.
In principle, the first step in model-based seismic inversion—forward
modeling—begins with a model of layers with estimated formation depths,
thicknesses, densities and velocities derived from well logs. The simplest model,
which involves only compressional (P-wave) velocities invert for P-wave, or
acoustic, impedance.
The simple model is combined with a seismic pulse to create a modeled
seismic trace called a synthetic. Inversion takes an actual seismic trace, removes the
seismic pulse, and delivers an earth model for that trace location. To arrive at the
best-fit model, most inversion routines iterate between forward modeling and
inversion, seeking to minimize the difference between the synthetic trace and the
data.
In practice, each of these steps may be quite involved and can depend on the
type of seismic data being inverted. For vertical-incidence data, creating the initial
model requires bulk density measurements from density logs and compressional
velocities from sonic logs, both spanning the interval to be inverted. Unfortunately,
the necessary logs often are acquired only in the reservoir. In the absence of sonic
logs

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Borehole seismic surveys—vertical seismic profiles (VSPs)—can provide
average velocities across the required interval. If no borehole velocity data governs
reflection-driven changes in normal interface through the acoustic impedance
contrast; reflectivity is the ratio of the difference in acoustic impedances to their
sum.3 the result in depth-based reflectivity model is converted to a time-based model
through the velocities combining the time-based model with a seismic pulse creates
a synthetic trace. Mathematically, this process is known as convolution. The seismic
pulse, or wavelet, represents the packet of energy arriving from a seismic source. A
model wavelet is selected to match the amplitude, phase and frequency
characteristics of the processed seismic data. Convolution of the wavelet with the
reflectivity model yields a synthetic seismic trace that represents the response
of the earth as modeled to the input seismic pulse. Additional steps are needed when
Models that include noise, attenuation and multiple reflections are to be included in
the modeled trace.
The inverse operation starts with an actual seismic trace because the amplitude
and the shape of each swing in the seismic trace affect the outcome it is vital that the
processing steps up to this point converse signal phase and amplitude. Different
types of inversion start with different types of traces the main distinction is between
performed before stacking and inversion after it. Prestack and post stack. Most
seismic surveys provides images using data that have been stacked. Stacking is a
signal enhancement technique that averages many seismic traces the traces represent
recording from a collection of different sources and receivers offset with common
reflecting midpoint each trace assumed to minimal random noise and with signal
amplitude equal to the average of the signal in the Stacked traces the resulting
stacked trace is taken to be the response of normal- incidence reflection at the
common midpoint (CMP).

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Stacking is a reasonable processing step if certain assumptions hold: the
velocity of the medium overlying the reflector may vary only gradually, and the
average of the amplitudes in the stacked traces must be equivalent to the amplitude
that would be recorded in a normal- incidence trace. In many cases, these
assumptions are valid, and inversion may be performed on the stacked data in other
words, post stack. In contrast, when amplitude varies strongly with offset, these
assumptions do not hold, and inversion is applied to unstacked traces pre stack.
Before discussing pre stack situations in detail, we continue with the simpler case of
posts tack inversion.
A stacked trace is compared with the synthetic trace computed from the model
and wavelet. The differences between the two traces are used to modify the
reflectivity model so that the next iteration of the synthetic trace more closely
resembles the stacked trace. This process continues, repeating the generation of a
synthetic trace, comparison with the stacked trace, and modification of the model
until the fit between the synthetic and stacked traces is optimized. There are many
ways to construct synthetic traces, and various methods may be used to determine
the best fit. A common approach for determining fit is least-squares inversion, which
minimizes the sum of the squares of the differences at every time sample. This
inversion technique operates on a trace-by-trace basis.
In the simplest case, inversion produces a model of relative reflectivity at every time
sample, which can be inverted to yield relative acoustic impedance. To obtain
formation properties such as velocity and density, a conversion to absolute acoustic
impedance is necessary. However, such a conversion requires frequencies down to
near 0 Hz, lower than contained in conventional seismic data. An absolute acoustic
impedance model can be constructed by combining the relative acoustic impedance

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Figure 8.3: Modeling and Inversion Rasmussen KB Brunn A and Pedersen JM (2004)
model obtained from the seismic frequency range with a low-frequency model
derived from borehole data.
Relating seismically derived acoustic impedance to formation properties
makes use of correlations between logging measurements. For example, cross
plotting acoustic impedance and porosity measured in nearby wells establishes a
transform that allows seismically measured acoustic impedance to be converted to
porosity values throughout the seismic volume. An example from a carbonate
reservoir in Mexico demonstrates the power of this technique (Figure 9.3).

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Figure 9.3: Porosity vs Impedance, Salter R Et al (2005)
Seismic inversion or stratigraphic deconvolution tries to put a spiked response
at geological boundaries (lithology changes) and the main reservoir characteristic
interfaces. This is done by the inversion of the seismic cube into an Acoustic
Impedance cube (Figure 10.3). The link between the seismic cube and the AI cube
is the seismic wavelet. Seismic inversion is a rather confusing expression. Inversion
in itself means to undo an operation, but here in fact it is used for the transformation
of a seismic amplitude cube into an acoustic (or elastic) impedance cube. One of the
benefits of inversion is that the seismic resolution is increased (e.g. Veeken et al.
2004). Hill (2005) has investigated this phenomenon and found an improvement in
thickness prediction that was clearly beyond the seismic tuning thickness.
In the stratigraphic inversion scheme a comparison is made between the
synthetic trace at the well and the seismic trace. A wavelet is established by applying

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Figure 10.3: Porosity Prediction, Salter R etal (2005)
cross correlation techniques. Or the wavelet is derived from the shaping filter that
permits transformation of the reflection coefficient trace into the seismic trace. This
wavelet is then used to perform the seismic inversion, whereby the seismic traces
are transformed into blocky AI traces. The spiked response is expressed by the limits
of these AI units (Veeken et al. 2002a). These spikes are assumed to correspond
better to meaningful geological boundaries and reservoir characteristic interfaces. If
all works well there is relation between acoustic impedance and reservoir
characteristics like porosity, permeability, net-to-gross, HC saturation. Even if the
well trends are not exactly honored, the filtered well average may follow the general
picture provided by the inversion and that gives the possibility to delineate ‘sweet
spots’. A simple relationship often does not exist (Dvorkin and Alkhater 2004), but
in individual cases it can be different. For instance in the Kraka field, located
offshore Denmark, the Chalk porosity is linear correlated with AI (Klinkby et al.
2005) and this can be used in later prediction.

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3.1.2.1. Principles
The reflection coefficient series is convolved with the seismic wavelet to give
the seismic trace. Inversion aims to start from the seismic trace, remove the effect of
the wavelet to get back to the reflection coefficient series, and from them derive the
layer impedances. It has to assume that starting seismic data are free from correlated
noise (e.g. Multiples).Also, the wavelet presenting the data has to be estimated many
inversion methods derive the wavelet from a well tie and have to assume that it does
not change laterally away from the well. There is also an amplitude calibration to be
taken into account real seismic traces are not directly output as reflection coefficient
values, but are scaled to give some convenient but arbitrary RMS average over a
trace. At least over a limited time-gated, the Ratio of reflection coefficient of trace
amplitude has to be constant if inversion is going to work. Care is needed during
seismic processing to avoid steps that might introduce artificial amplitude changes
vertically or horizontally. However, locally variable effects in the overburden (e .g.
shallow gas) can reduce the Seismic energy penetrating to deeper reflectors and so
reduce the reflected signal left to itself, the inversion process would try to interpret
this as a decrease in impedance contrast across the deeper interfaces. To remove such
artefacts, a long-gate AGC may be applied, which scales amplitudes so as to remove
lateral variation when averaged over a TWT interval of 1s, for example.
Another issue is that the seismic traces contain data of limited bandwidth; the
frequencies Present depend on the rock properties and the seismic acquisition
technique, but might be in the range from 5 to 50 Hz. This means that the low
frequencies in particular, which are critical for the estimation of absolute impedance
values, cannot be obtained from the seismic data, but have to be added from
elsewhere. Usually from a model based on well data and geological knowledge.

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Figure 11.3: Seismic Inversion
3.1.2.2. Extending the bandwidth
To get more information into a seismic section than is actually present in the
seismic traces, extra data have to be obtained from elsewhere; different algorithms
differ in detail, but they all have the following general features
(1) Begin with a model that describes the subsurface explicitly or implicitly,
this will contain a number of layers of different acoustic impedance.
(2) Calculate the seismic response from this model using the wavelet
representing the seismic dataset.
(3) Compare the calculated seismic response with the real data.

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(4) Modify the models to reduce the misfit between the calculated and real
seismic, perhaps iteratively and perhaps incorporating constraints on the impedance
values that may be assigned to particular layers on the complexity of the model and
on the variation of layer parameter from one seismic trace to the next along a seismic
line.
(5) Perhaps add low-frequency information obtained from a model based on
geological data. The additional information that has been taken into account is thus:
(a) The wavelet removal of its effects is equivalent to a de convolution
extending bandwidth at the high-frequency end
(b) The model the geological input extends bandwidth at the low-frequency
end.
To make all this more concrete it is helpful to work through an actual
processing flow. A common approach to building a subsurface model is to split it up
into macro layers, probably several hundred so Fms thick, bounded by the main
semi-regional seismic markers and consisting of a single broad lithology .This makes
it easier to construct a geological model to constrain impedance variation within a
macro layer Inside the macro layer the subsurface is represented by means of a series
of reflectivity spikes. These spikes when convolved with the wavelet should
reproduce the observed seismic Trace and integration of the reflectivity will give the
impedance variation within the Macro layer To prevent the software from trying to
reproduce all the noise presenting the seismic section it is usual to impose a
requirement that the reflectivity spike series is as simple as possible either in the
sense of using a small total number of spikes or using spikes of small total absolute
amplitude; the algorithm will trade off the misfit between real and calculated seismic
section against the complexity of the spike model, usually under user control of the

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Figure 12.3: Synthetic trace and wavelet extraction Buiting,J . J.
M. & Bacon,M . (1999)
acceptable degree of misfit. The result is usually called a 'sparse spike' representation
of the subsurface. It is obviously critical to the success of this process that we know
the wavelet accurately. This is usually obtained from a well-tie study. Well synthetic
or VSP information will tell us how zero-phase seismic ought to look across the
well; comparison with the real data tells us that wavelet is present shows an example
display from such a study. To the left, in red is the candidate wavelet, which in this
case is close to being symmetrical zero-phase to; the right is a panel of six
(identical)traces showing the result of convolving this wavelet with the well
reflectivity
Sequence derived from log data .They should be compared with the panel of
traces in the middle of the figure, which are the real seismic traces around the well
location. Various geologically significant markers are also shown. There is clearly a
very good match between the real and synthetic data so far as the principal
reflections are concerned, so it is possible to have confidence that the wavelet shown
is indeed that presenting the data. The real so some differences in detail which will
limit the accuracy of an inversion result. These may arise from imperfections in the
seismic processing perhaps the presence of residual multiples or minor imaging
problems With luck, the inversion process will leave some of this low-energy noise
out of the inverted image because of the sparseness of the spike reflectivity series.

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3.2. Post-stack Inversion Methods
The post-stack time-migrated data is input for the inversion algorithm. It is
important to have clean seismic data as input and that proper data conditioning is
done (Da Silva et al. 2004). This entails CDP Gather cleaning, preserved amplitude
processing, amplitude balancing with sophisticated gain control, multiple
suppression and 3D noise attenuation. Comparative analysis of seismic processing
(CASP, Ajlani 2003) is a multi-disciplinary approach to secure the QC of the seismic
processing results, whereby quality, turnaround and cost are taken into account.
Usually the seismic is processed with a certain target zone in mind. All the
processing parameters have been tuned to this objective. The target in the inversion
may be somewhat different. Therefore careful examination of all processing steps is
needed before embarking on the exercise to transform amplitude into acoustic
impedance.
3.2.1. Colored inversion
The colored inversion method is basically a trace integration, achieved by
applying a special filtering technique in the frequency domain. The amplitude
spectrum of the well log is compared with that of the seismic data and that is where
the word ‘colored’ comes from. An inversion operator is designed that brings the
seismic amplitudes of the frequencies in correspondence with that seen in the well.
This operator is then applied to the whole seismic cube (Lancaster and Whitcombe
2000).
A cross plot is made between the amplitude and the logarithm of the frequency
to compute the operator. A linear fit is performed to calculate an exponential
function and this serves as a shaping filter (cf Walden and Hosken 1985, Velzeboer
1981). This filter transforms the seismic trace into an assumed acoustic impedance

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Figure 13.3: Colored inversion vs Seismic data (Lancaster and Whitcombe 2000)
equivalent. The assumption is made that the seismic cube is zero phase, which is
hardly the case. In individual cases (Giroldi et al. 2005) the results can be spectacular
with a flat spot DHI suddenly appearing in the inverted dataset (Figure 13.3). Again
this type of Colored inversion for land data from the Chaco Basin in Bolivia. The
reflectivity section on the left does not show the same break at the gas–water contact
as seen by the relative AI volume. It illustrates the benefit of extracting the relative
AI attribute in these Cretaceous reservoirs.
3.2.2. Sparse spike inversion
The seismic trace is simulated by a minimum amount of AI spikes. The spikes
are placed in such a way that they explain best the seismic response. Amplitude, time
position and number of the AI spikes is not always realistic, i.e. not conform the
geological constraints. To be more specific: if a starting model is not available, the
spikes might be placed in unrealistic positions and still the model generates a
synthetic that highly resembles the seismic trace. The recursive method uses a
feedback mechanism to obtain more satisfactory results. A low frequency AI

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variation trend can be imported to generate more appropriate results with a better
convergence of the found solution. The inversion algorithm was initially working on
a trace by trace basis, but now a multi-trace approach is implemented.
The inversion solution may vary considerably from trace to trace, making the
reliability of the output weaker. The constrained option uses a low frequency model
as a guide. The low frequency variation is estimated from blocked well logs and this
gives much better results (e.g. Ronghe and Surarat, 2002). QC tests are normally
necessary, based on the match between the up scaled well log impedance and the
inverted traces, because little well info is required in the construction of the a-priori
impedance model (Klefstad et al. 2005). It provides a consistency check of the
inversion results. The inversion replaces the seismic trace by a pseudo acoustic
impedance trace at each CDP position (Pendrel and Van Riel 2000). The sparse spike
hypothesis implies, however, that a thin bed geometry will not always be mimicked
in the most optimal way.
The zero phase requirement can be circumvented by choosing a compound
wavelet for the inversion, thus compensating the non-zero phase characteristics of
the input data. A multi-trace approach results in better stability of the generated
inversion solution. Sophisticated model-driven sparse spike inversion gives more
realistic output. In some cases the interpreter gets away with the approximation, but
in the majority of the cases yet a better job is needed.

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3.2.3. Model-based inversion
A simple initial AI model is perturbed, a synthetic computed using the seismic
wavelet and the difference with the seismic trace is established (Cook and Sneider
1983, Fabre et al. 1989, Gluck et al. 1997). The AI model with a very small
difference is retained as solution (Figure 6.22). A simulated annealing technique
using a Monte Carlo procedure is applied (Goffe et al. 1994, Duboz et al. 1998). This
technique shows an analogue to the growth of crystals in a cooling volcanic melt
(Ma 2003). It starts with a reflectivity model M0 and computes the difference with
the seismic input data after convolution with a wavelet. The model is now perturbed
and a new model Mn is simulated, where for the same difference is established. The
two differences are compared and if the misfit for f(Mn) is smaller than that for M0,
Figure 14.3: Sparse spike inversion (modified after Ronghe and Surarat 2002).

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than the Mn model is unconditionally accepted. If not, than the Mn model is accepted
but with a probability:
P = e(−f(Mn)−f(M0))/T , (6.22)
Whereby T is a control parameter (acceptance temperature). This acceptance
rule is known as the Metropolis criterion (Metropolis et al. 1953). The process is
repeated a large number of times until a very small residual difference is found
(threshold value) that is stable. Computation of Cost functions permit to determine
a real regional minimum for the difference. The initial AI model is made up of
macro-layers defined by the shape of the seismic mapped horizons. Micro-layers are
automatically introduced in this macro model. It provides a stratigraphic grid cell
volume together with the inline and crossline subdivision for storing constant AI
values. The use of micro-layers makes sure that an adequate number of spikes (i.e.
vertical change in AI) is utilized in the modelling (Figure 6.23). This model-driven
inversion method is much more robust and often a real 3D inversion algorithm is
applied to stabilize the solution (Duboz et al. 1998, Coulon. et al. 2000, Veeken et
al. 2002b; Figure 6.24). A bulk phase rotation can be applied to zero phase a seismic
sub cube. Normally this procedure is valid for a small time window (<1.5 sec TWT),
where a stable wavelet is derived (Figure 6.25). The results are evaluated at the well
control points in so-called composite well plots (Figure 6.26). The seismic and the
AI cubes are compared (Figure 6.27). Layer maps are quite useful to delineate the
extent of AI anomalies (Figure 6.28). The method can give satisfactory results even
when well control is limited and the seismic quality is rather poor (Veeken et al.
2002a; Figures 6.29 and 6.30). It is also possible to derive a wavelet straight from
the seismic dataset. The model-driven inversion does not always honour the well
control completely, but a great advantage is that the seismic data is the guide for the
inversion. Errors in the well logs do not propagate in the inversion.

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This is an advantage when the old well database is unreliable. The averaging
effect, introduced by the 3D approach, results in small discrepancies at the well
locations that are in fact quite acceptable.
Also in carbonates good inversion results are possible. The relative velocity
and density changes induced by the pore fill are decisive for creating AI anomalies.
Figure 15.3: Model based inversion (Goffe et al.1994, Duboz et al. 1998)
Figure 16.3: Correlation between check shots and impedance log veeken 2006

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Figure 17.3: Seismic vs Impedance, Veeken 2006

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3.2.4. Stochastic inversion
Geostatistics are used to build a complete subsurface model and constrain the
inversion solutions (Dubrule 2003). Simulation is done on local level as well as
globally, on the totality of the generated model (Haas and Dubrule 1994, Dubrule
2003). All models honour the well data, otherwise they are rejected. The architecture
of reservoirs is classified in various ways (Weber and Van Geuns 1990) and this
helps in selecting the simulation approach. Probability density functions (PDF’s) are
established for each grid point and these are used to perform a random simulation
(Van der Laan and Pendrel 2001). The input for the PDF comes from well logs,
spatial properties (variograms) and lithological distributions.
The stochastic algorithm calculates for each simulation a synthetic trace,
compares it with the real seismic trace and accepts or rejects it. A simulated
annealing process is utilized. The number of solutions is reduced in this way and
probability maps are produced to assess the risk. The retained simulations are
examined on their variance. If they closely resemble, then the prediction is rather
good and the confidence level of the output is increased
A probability volume is generated for grid points with porosities above 10%,
using the simulation histograms. Subsequently bodies are outlined where the
probability is above 70% for the porosity to be higher than 10%. As more wells are
drilled in the same petroleum system, the best matched simulations are retained to
further refine the predictions (Sylta and Krokstad 2003). Drawback of the
probabilistic method is that the interpreter has to quantify the uncertainties in a
realistic way. This is a tedious and precarious task (cf Klefstad et al. 2005). Areas
without proper well control are still difficult to predict and assumptions have to be
made. There is a cumulative increase in prediction error as various reservoir
parameters have to be estimated at the same time.

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Figure 18.3: Stochastic inversion (modified after TorresVerdin et al. 1999).

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CHAPTER 4:
4. SEISMIC INVERSION USING HAMPSON-RUSSELL
SOFTWARE
4.1. Introduction
Inversion is the process of extracting, from seismic data, the underlying
geology which gave rise to that seismic. Traditionally, inversion has been applied to
post-stack seismic data, with the aim of extracting acoustic impedance volumes
(Strata).Recently, inversion has been extended to pre-stack seismic data, with the
aim of extracting both acoustic and shear impedance volumes. This allows the
calculation of pore fluids (Strata + AVO).
Hampson-Russell has been providing innovative geophysical software since
1987. The Hampson-Russell software suite encompasses all aspects of seismic
exploration and reservoir characterization, from AVO analysis and inversion to 4D
and multicomponent interpretation.
There are several types of seismic inversion can be done using STRATA-HR:
Post-stack:
-Recursive: Traditional band-limited inversion.
-Model Based: Iteratively updates a layered initial model.
-Sparse Spike: Constrained to produce few events.
-Colored: Modern derivative of Recursive Inversion.
Pre-stack:
-Elastic Impedance: Enhancement for pre-stack data.

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-Independent Inversion: Enhancement for pre-stack data.
-Lambda-mu-rho (LMR): Enhancement for pre-stack data.
-Simultaneous Inversion: Enhancement for pre-stack data.
4.2. Available Data
Netherlands F3 Block with coordinates N 54°52′0.86″ / E 4°48′47.07 this project
was held in 1987 and that by making 3d seismic survey and drilling of 4 wells in
different area to cover our cube which has 24*16 km square our target is at late
Jurassic early cretaceous for very rich gas prospect.
The available data is:
Seismic Data:
• A 3D seismic cube that consists of 740 in lines and 949 xlines and it is
post stack cube
Horizons
• Demo0 (FS4)
• Demo1 (MFS4)
• Demo2 (FS6)
• Demo3 (Top_Foresets)
• Demo4 (Truncation)
• Demo5 (FS7)
• Demo6 (FS8)

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Figure 19.4: combination between the geology and
seismic data in inversion
• Demo7 (Shallow)
Wells and available logs
4.3. Inversion Concepts
All inversion algorithms suffer from “non-uniqueness”. There is more than
one possible geological model consistent with the seismic data. The only way to
decide between the possibilities is to use other information, not present in the seismic
data. Figure (4.1) represents the combination between the geology and seismic data
in inversion. This other information is usually provided in two ways:
• The initial guess model
• Constraints on how far the final result may deviate from the initial
guess.
The final result always depends on the “other information” as well as the seismic

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Figure 20.4: Seismic Inversion Components
Model Based Inversion starts with the equation for the convolutional model:
Assume that the seismic trace, S, and the wavelet, W, are known. Assume that
the Noise is random and uncorrelated with the signal. Solve for the reflectivity, R,
which satisfies this equation. This is actually a non-linear problem, so the solution
is done iteratively:
Step 1: The initial background model for Model Based Inversion is formed by
blocking an impedance log from a well (Figure 21.4).
Step 2: Using the blocked model, and the known wavelet, a synthetic trace is
calculated. This is compared with the actual seismic trace. By analyzing the errors
or “misfit” between synthetic and real trace, each of the layers is modified in

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Figure 21.4: Step 1Figure 22.4: Step 2
thickness and amplitude to reduce the error. This is repeated through a series of
iterations (Figure 22.4).
Model Based Inversion produces a broad-band, high frequency result a
potential problem is that the high frequency detail may be coming from the initial
guess model, and not from the seismic data. This problem is minimized by using a
smooth initial model.
Issues in Model Based Inversion:
(1)Because the wavelet is known, its effects are removed from the seismic
during the calculation. For example, the seismic does not have to be zero-phase, as
long as the wavelet has the same phase as the seismic.
(2)Errors in the estimated wavelet will cause errors in the inversion result.
(3)The effective resolution of the seismic is enhanced.
(4)The result can be dependent on the initial guess model. This can be
alleviated by filtering the model.

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Figure 23.4: Comparison between Input Seismic and Model Based Inversion
(5)There is a non-uniqueness problem, as with all inversion.
4.4. Model-Based Inversion Workflow on F3-Block Seismic Cube
4.4.1. Data Importing
Start with creating new well database "Inv.wdb"
Figure 24.4: Opened Database List
Figure 25.4: HR Opened Database List

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Figure 27.4: Well Explorer Window
Figure 28.4: Importing Logs
HR Software interface appear as shown (Figure 25.4)
Figure 26.4: Hampson-Russell Interface
Well Explorer is used to import well information (Logs,Tops or Geometry)
Import LAS files and use default settings till the shown window in (Figure 27.4)

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Figure 29.4: Identifying unknown logs
Figure 30.4: STRATA Project Selection Mode
Sometimes unknown logs problem happen in this case identifying logs again is
required (Figure 28.4)
Check Shots and well tops can be imported with the same steps.
STRAT is the responsible part from HR for running inversion. Thus, after
creating well database start new project from STRATA as shown (Figure 29.4)

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Figure 31.4: Importing Data
Importing F3-Block Seismic Cube (Figure 30.4)
Identifying seismic parameters and byte location is a critical step in importing
seismic data, In F3-Block the following information was used (Figure 31.4):
Inline byte location= 189
Xline byte location= 193
Data Sample Format: IBM
NOTE: In Post-Stack Inversion we can ignore Receiver X & Y Coordinates but we
cannot in Pre-stack Inversion.

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Figure 32.4: SEG-Y Seismic File Open
Figure 33.4: Geometry Grid Page
In Geometry Grid page, we can see number of inline and xlines, no. of traces and
other parameters shown in (Figure 32.4)

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Figure 34.4: Well to Seismic Map Menu
Then each well location is determined in the cube by inserting their xline and inline
in Well to Seismic Map Menu where the CDPs are calculated automatically (Figure
33.4)
4.4.2. Identifying Target Reservoir in F3-Block Cube
The target reservoir is known in this area but the available geologic information told
enough to identify the reservoir. Geology told that to look for deltaic package
consists of sand and shale, with an overall high porosity (20–33%) for Gas sand.
Cross plot tool in HR eLog is used to make a cross plot between GR values and
Porosity. (Figure 34.4). The plot shows two zones (Grey and Blue) with low GR
values (Sand) and porosity values 20-40 % what matches the reservoir conditions
told by Geology. By creating cross-section on log for this zones the possible
reservoir zones could be seen. Blue zone at depth range 720-800m and Grey zone at
depth range 1050-1100m at well F02 (Figure 35.4).

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Figure 35.4: GR-Porosity Cross plot
Figure 36.4: Well F020-1 Cross Section

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Figure 37.4: GR-Impedance Cross Plot
To make sure about reservoir another cross plot between GR Values and P-
Impedance Values (Figure 36.4). found that at the same GR Values of Blue and Grey
zones in the GR-Porosity cross plot P-Impedance are mostly high between 4200-
5600 ((m/s)*(g/cc)) which is quite near to Gas Sand impedance values that
confirmed by Lithology Prediction using Seismic Inversion Attributes, Dan
Hampson, 2010.
Using cross-section for well F02 for Blue Zone we could identify reservoir zone
clearly at depth 720-800m besides small adjacent zones (Figure 37.4)
From well tops data target reservoir is FS8 (Figure 38.4).

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Figure 38.4: F02-2 Cross section for GR-Impedance cross plot
Figure 39.4: FS8 the target reservoir

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Figure 40.4: Picking Horizon FS8
Figure 41.4: Actual Picks of FS8
Then FS8 Horizon is picked as target reservoir on seismic in addition to FS11 as a
good marker in region. Import Horizons file in STRATA as shown in (Figure 39.4)

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Figure 42.4: Difference between Time logs and Depth logs
4.4.3. Depth-Time Conversion and Check Shot Correction
The initial guess model for each trace consists of an impedance log, usually derived
by multiplying a real sonic log by a real density log. The impedance log model must
be measured in 2-way travel time. The original logs are measured in depth. A critical
step is depth-to-time conversion. (Figure 41.4)
The depth-to-time conversion is made using a depth-time table which maps each
depth to the two-way travel time from the datum (surface) to that depth and back
(Figure 42.4).
The depth-time table is usually calculated from the sonic log velocities using this
equation:

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Figure 43.4: Depth time table
The time to an event depends on all the velocities above that layer, including the first
velocity to the surface, V1. That velocity is unknown and is usually approximated
by extrapolating the first measured velocity back to the surface.
The depth-time table calculated from the sonic log is rarely sufficient to produce
model impedance which ties the seismic data properly because:
-The seismic datum and log datum may be different.
-The average first layer velocity is not known.
-Errors in the sonic log velocities produce cumulative errors in the calculated travel-
times.
-The events on the seismic data may be mis-positioned due to migration errors.
-The seismic data may be subject to time stretch caused by frequency-dependent
absorption and short-period multiples.

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Figure 44.4: Check Shot Correction
Check Shot Correction:
Check shot table is a series of measurements of actual 2-way time for a set of depths.
The depth-time table calculated from the sonic log must be modified to reflect the
desired check shot times. (Figure 43.4)
4.4.4. Wavelet Extraction and Synesthetic Trace
After check shot correction, Correlation between seismic data and synthetic trace is
made to extract the appropriate wavelet and get the highest correlation value.

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Figure 45.4: Wavelet with different phases (0, 90,180 and 270)
We used statistical method to extract wavelet with different phases (0, 90,180 and
270) and compare its correlation percentage to get the best wavelet parameters in
each well. (Figure 44.4)
In well F02-1 Wavelet-270 gives the best correlation about 30% at time range 500-
1100 ms and the percentage increases at the reservoir zone 750-900 ms to 75.5 %(
Figure 45.4). While in well F03-4 main phases gives low correlation so we used scan
tool to get the best phase with highest possible correlation which is 38 deg. with
correlation about 45.5%. (Figure 46.4).

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Figure 46.4: Wavelet 270 correlation in well F02-1
Figure 47.4: Wavelet zero correlation in well F03-4

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Figure 48.4: Initial Model Building
4.4.5. Initial Model Building
Now, we have two synthetic traces in both wells (F02-1 and F03-4) with good
correlation with seismic data besides two picked horizons (FS8 and FS11). All of
them enables me to start building initial model for inversion process.
In STRATA, Choose Model  Build/Rebuild a Model as shown (Figure 47.4)
Insert correlated wells only (F02-1 and F03-4) (Figure 48.4)
Figure 49.4
In each well we used Corrected P-wave log resulted from correlation and computed
Impedance resulted from multiplying p-wave log by Density log (Figure 49.4)
Figure 50.4

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Use default settings for Modeled Trace Filtering Options (Figure 50.4)
Figure 51.4
Resulted Initial Model (Figure 51.4)
Figure 52.4: Initial Model for F3-Block Seismic Cube

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4.4.6. Quality Control (QC)
Before running inversion we carried out some QC analysis which is very important
to make sure that inversion results would be effective and the whole work is not in
vain.
In STRATA, Analysis tool provide good QC functions (Figure 52.4):
Red curve represents Inverted result and Blue one represents original log. This
window shows us the matching between them with error = 238 which is good error
value and the correlation between Synthetic traces (in Red) and Seismic (in Black)
with value 0.93 which is good but we can get higher by modifying some parameters
such as number of iteration.
Figure 53.4: Inversion Analysis for Post-stack Data

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In the same window, Invert enables us to run virtual Inversion before real process to
get the appropriate parameters and avoid run time consumption. Number of Iteration
is one of this critical parameters as if it exceeds certain limit would lead to high error.
It found that iteration value between 10-20 gives best results in most cases we used
20. (Figure 53.4)
Figure 54.4: Number of Iteration

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Figure 56.4: Inversion Analysis Cross plot
Error plot enables us to get the error value at each well (Figure 54.4)
Figure 55.4: Error Plot
Inversion Analysis Cross plot create plot between computed impedance and original
one in log. The heaviest the cloud of dots the better inversion results (Figure 55.4).

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4.4.7. Running Inversion
Once running inversion process program calculate P-Impedance at each well and
interpolate between them to extend all over the cube.
Figure 57.4: Inverted Inline
Figure 58.4: Inverted Xline

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Figure 59.4: Inverted Arbitrary Line
4.4.8. Results
Model based inversion shows high impedance zones at reservoir zone with values
between 4500-6500 which is the same for Gas Sand.
By taking time slices from inverted model based cube and comparing it with same
slices from reflectivity cube (Figure 59.4)(Figure60.4), more features appear
showing what may could be channels matching with described geology.

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Figure 60.4: Reflectivity (Right) Impedance (Left) Slice-750 (upper) Slice-780 (lower)

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Figure 61.4: Reflectivity (Right) Impedance (Left) Slice-950 (upper) Slice-1600 (Lower)

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Summary
The project is held in The North Sea is a marginal, shallow sea on the
European continental shelf. It is more than 970 kilometers from north to south and
580 kilometers from east to west, with an area of around 750,000 square kilometers.
The North Sea RAC area is larger, because it includes the Skagerrak and Kattegat
which connect the North Sea proper to the Baltic. The North Sea is bordered by
England, Scotland, Norway, Denmark, Germany, the Netherlands, Belgium and
France. In the southwest, beyond the Straits of Dover, the North Sea becomes the
English Channel which connects to the Atlantic Ocean. The North Sea is a fairly
shallow coastal sea and depths in the southern basin do not exceed 50m. The northern
areas are deeper but are still generally less than 200m except in the Norwegian
Trough, in the north-east, which is the only region of very deep water.
The Dutch part of the North Sea (NCP) occupies an area of 57,000 km2 which
is larger than the mainland of The Netherlands. In addition to traditional activities,
like fishery and shipping, since the 1960s there have been new activities such as oil
and gas exploration and exploitation, and extraction of sand from the seabed. New
plans for installation of wind turbines and coastal extensions are in progress. In
addition the area forms part of a valuable marine ecosystem. Knowledge of the
morphology of the seafloor and the sediment properties is important, both to
understand the ecosystem as well as for developing infrastructural activities.
The available data is a 3D seismic cube in Dutch sector with 24*16 km square
consists of 740 in lines and 949 xlines and it is post stack cube there were four
drilled wells in the area in the logs that is measured are

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Our target is at late Jurassic to early cretaceous and the trap is shallow full of
biogas and the formation name is fs8 which is gas sand
Then use Hampson Russell to convert reflectivity cube to impedance cube so
the bright spot appear on the section could be an indication of gas presence
Conclusion
The reason that we use seismic inversion that it allow to make interpolation
between wells in the area so that the view of impedance extended from only under
the wells to the whole cube and in opposite to reflectivity cube the inverted do not
deal with layer interfaces but deal with zones of layer give the advantage of
interpreting the area and gives push in reservoir characterization as we can use
impedance in the prediction of porosity so evaluation of hydrocarbon in reservoir is
enhanced by inversion and using this porosity in permeability computation and shale
volume and effective porosity

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