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Stratigraphic modelling of turbidite prospects to reduce exploration risk

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This article presents an integrated workflow to model the evolution of ancient turbidity currents on a 3D structurally reconstructed palaeo-seafloor, allowing ancient turbidite sediment distributions to be estimated. Effective use of such approaches requires efficient model-inversion procedures so that model parameters (e.g. flow dimensions, densities etc.) can be estimated from any available data. It is shown that a directed Monte Carlo approach (i.e. a simple genetic search algorithm) is very effective. A case study of a Mesozoic prospect in the UK North Sea shows the power of these methods to discriminate between potentially attractive sediment-source locations. The main power of this approach lies in its ability to exclude many, otherwise attractive, sedimentation scenarios.
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Stratigraphic modelling of turbidite prospects to reduce exploration risk
Dave Waltham
1
, Noah Jaey
2,3
, Stuart MacLean
2
and Valentina Zampetti
2,3
1
Department of Geology, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK
(e-mail: d.waltham@gl.rhul.ac.uk)
2
Midland Valley Exploration Ltd, 144 West George Street, Glasgow G2 2HG, UK
3
Present address: Shell International Exploration and Production B.V., Kessler Park 1, 2288 GS Rijswijk,
The Netherlands
ABSTRACT: This article presents an integrated workflow to model the evolution of
ancient turbidity currents on a 3D structurally reconstructed palaeo-seafloor,
allowing ancient turbidite sediment distributions to be estimated. Effective use of
such approaches requires efficient model-inversion procedures so that model
parameters (e.g. flow dimensions, densities etc.) can be estimated from any available
data. It is shown that a directed Monte Carlo approach (i.e. a simple genetic search
algorithm) is very effective. A case study of a Mesozoic prospect in the UK North
Sea shows the power of these methods to discriminate between potentially attractive
sediment-source locations. The main power of this approach lies in its ability to
exclude many, otherwise attractive, sedimentation scenarios.
KEYWORDS: turbidity currents, forward modelling, inverse modelling, 3D reconstruction
INTRODUCTION
The increasing importance of turbidite reservoirs over the last
30 years (Weimer et al. 2000) has resulted in the development of
seismic-based techniques for the evaluation of sand distribution
in turbidity current deposits. Seismic attribute maps have
proved to be particularly effective, as have isopach maps
formed between closely spaced horizons (see Fonessu (2003)
for excellent examples of both these techniques). This paper
proposes an alternative approach which does not require
the exceptionally high data quality necessary for attribute/
isopach-based techniques. In outline, the workflow involves:
+3D seismic interpretation of major horizons and faults;
+structural reconstruction of the palaeo-seafloor at the time
of turbidite deposition;
+modelling of turbidity current flow across the palaeo-
seafloor to determine areas of sand deposition;
+re-imposition of the structural deformation to move the
predicted turbidite deposits back to their present-day
locations.
This paper will describe this methodology in more detail and
demonstrate its application to a specific North Sea prospect.
Three-dimensional structural reconstruction of palaeo-
surfaces is now a well-established technique (Barr 1985; Buddin
et al. 1997; Williams et al. 1997; Rouby et al. 2000; Yin &
Groshong 2006), which has been developed from 2D ‘section
balancing’ (see Buchanan (1996) for a review). The objective is
to reconstruct the palaeogeometry of a volume by successively
stripping off each top layer and removing the effects of faulting,
folding and compaction on all remaining horizons.
Forward modelling of particulate gravity currents is equally
well established in the geological literature, where it has been
used for modelling pyroclastic flows and debris flows as well as
for turbidity currents (Parker et al. 1986; Dade & Huppert 1995;
Mulder et al. 1997; Huppert 1998; Iverson & Denlinger 2001;
Pratson et al. 2001; Waltham & Davison 2001; Bursik et al. 2005;
Sheridan et al. 2005). However, stratigraphic modelling in
general has not yet established itself as a widely used technique
in hydrocarbon exploration. It should be noted that in forward
modelling the distribution of deposits is predicted from sup-
plied parameters, such as flow volume and density. In inverse
modelling, on the other hand, parameters are determined from
knowledge of the sediment distribution. In practice, both
forward and inverse modelling are needed since modelling
parameters are first estimated from any limited data that may be
available and then forward modelling allows the consequences
of these parameters to be determined for areas lacking data.
The aim of this paper is to present a general methodology
for using stratigraphic models to reduce risk. This paper
concentrates upon an inverse modelling strategy which is quite
general and could be adapted for use with many other forward
models. The details of this particular stratigraphic model are
therefore not central to the argument but, for completeness, are
outlined in the Appendices. The next section describes a
specific Moray Firth (UK North Sea) exploration problem and
outlines the structural reconstruction used as input for subse-
quent stratigraphic modelling. The paper then discusses the
inverse modelling approach and shows how it resolves Moray
Firth exploration issues.
STRUCTURAL RECONSTRUCTION AND THE
EXPLORATION PROBLEM
Client confidentiality prevents specification of the precise
location and age of the dataset, which covers a Mesozoic
prospect lying near the Moray Firth region of the North Sea off
northeast Scotland. The 3D seismic data cover an area of
c.2025 km, within which ten key reflectors were picked and
depth-converted by the client company.
Structural reconstruction was undertaken by removing the
top interval and decompacting the remaining beds (Sclater &
Petroleum Geoscience, Vol. 14 2008, pp. 273–280 1354-0793/08/$15.00 2008 EAGE/Geological Society of London
Christie 1980). The effect of thermal subsidence and isostasy
was removed by bulk rotation of the entire model. The
deformation at every new upper surface was restored using
vertical shear and fault block translation and rotation. This
sequence of operations was repeated for each successive upper
surface until the formation of interest reached the seafloor.
Figure 1 shows the resulting accommodation space estimate.
Note that this represents the maximum bathymetric variation
that could have existed at this point in time assuming that space
had been created rapidly and slowly filled in. Figure 1 also
shows the locations of five wells for which there are net-to-
gross (NTG) estimates (defined as fractional thickness of clean
sand) in the overlying formation, based upon interpretation of
wireline logs. The NTG values themselves are given in Table 1.
Note that wells C and D have good sand content but that the
remaining wells contain no clean sand at all. The exploration
issue was to determine a sediment transport path to the high
NTG wells (C, D) that did not place sand in the remaining wells
(A, B, E). The ultimate objective was to improve understanding
of the exploration risk associated with further drilling in the
area.
The key features of the resulting surface are a general
deepening towards the north and the existence of a possible
north–south channel supplying sand to wells C and D. A flow
starting at the south-entry point in Figure 1 and moving along
this channel towards wells C and D could result in high-quality
sand deposits within this channel and so it is important to
investigate whether such a scenario is plausible. Figure 2 shows
a forward model of such a flow. However, note that there are
no significant barriers to this flow reaching wells A, B and E.
Hence, the question becomes: does the absence of sand in wells
A, B and E preclude the possibility that sediment was supplied
to wells C and D by a flow along the channel? If this sediment
path is not viable then an alternate sediment supply for
locations C and D is needed. The stratigraphic modelling
therefore needs to investigate two alternatives: (1) sediment
supply is from the south and deposits good quality sand in the
channel; (2) sediment supply is from close to the sand-rich wells
and never enters the channel. Flow-entry points for both
scenarios are indicated in Figure 1.
Fig. 1. Reconstructed palaeo-seafloor used for modelling turbidity currents. Large arrows indicate the flow-entry locations for the two flows
modelled in this paper. Note the narrow channel used by the south-entry flow.
Table 1. Net-to-gross at the well locations shown in Figure 1, together with the calculated
coarse fractions for the best-fit numerical model
Location Well Best model
NTG coarse fraction
A00
B00
C 0.64 0.642
D 0.39 0.379
E00
rms.error 0.005
NTG, net-to-gross
D. Waltham et al.274
INVERSE MODELLING OF TURBIDITY
CURRENTS
The forward model is controlled by the seafloor bathymetry
together with the 14 parameters described in Table 2. If these
parameters are given, then the forward model can be used to
predict the coarse-fraction distribution across the modelled area
for comparison with the known NTG in the wells. Note that
this comparison is valid only if coarse-deposits are predomi-
nantly clean (i.e. not contaminated by simultaneous fine depo-
sition) and if the multiple, successive flows responsible for a
particular turbidite unit are fairly similar to one another (i.e. the
properties of a single deposit are reasonably representative of
the bulk properties of stacked multiple deposits). The first
assumption could be avoided by using a more sophisticated
measure of forward-model NTG but the second assumption is
fundamental since modelling of (possibly) hundreds of very
different flows would require the specification of thousands of
parameters (i.e. 14 for each flow).
For the specific case of the Moray Firth problem investigated
in this paper, it might be thought that finding 14 parameters
given five constraints (i.e. the NTG values at the well locations)
is a severely under-constrained problem. However, all 14
parameters are constrained to a greater or lesser extent by
physical reasonableness. For example, a flow with an initial
thickness of 10 km would not be plausible. Given loose
constraints, it is perfectly possible for a nonlinear problem to
have no solutions at all (e.g. the parabola y=x
2
has no solution
for real xgiven the loose constraint that ymust be negative).
Fig. 2. Example flow 800 seconds after entry into the modelled area. Note relatively thick flow along channel but that a thin overbank flow is
also spreading out from the entry point.
Table 2. Parameters used in the forward model
Parameter Comments
Inflow location Easting (m)
Inflow location Northing (m)
Inflow direction (EofN)
Inflow width (m)
Inflow thickness (m) Also controls inflow velocity
(assumes Froude Number1.0)
Deposit volume (km
3
)
Flow concentration (%) Flow volume=Deposit
volume/concentration
Grain density (kg m
3
) Fixed at 2500 kg m
3
Sea-water density (kg m
3
) Fixed at 1030 kg m
3
Inflow grain distribution modal
diameter (µm)
Inflow assumed to have a
log-normal distribution
Inflow grain distribution sorting
index (ϕ)
Defined as standard deviation of ϕ
Seafloor roughness (m) Controls relation between basal
shear stress and flow speed
Sand diameter (µm) Defines coarse-fine transition. Fixed
at 250 µm
Pelagic thickness (m) Thickness of fine sediment
deposited between flows
Inverse modelling attempts to determine these parameters by finding values
that minimize the root mean square error between the NTG in the wells and
the coarse-fractions produced by the model.
Stratigraphic modelling of turbidite prospects 275
On the other hand, if a solution does exist it is likely to be
highly non-unique (e.g. consider the foregoing parabola
example but with the constraint that ybe positive). Hence, the
objective with modelling is not to determine the precise set of
parameters that produced a given deposit but, rather, to
establish whether any set of parameters could produce the
observed deposit given a specified sediment-input location.
Inverse modelling starts by defining an objective function,
i.e. a measure of misfit between model and data. In the Moray
Firth example the constraints were in the form of NTG
estimates and so an objective function given by the root mean
square (rms.) error (rmse) was defined with
rmse2=i=1
Nwi
mi2(1)
where w
i
is the NTG at the ith well and m
i
is the modelled
coarse-fraction at the same location. This, in turn, was calcu-
lated using
mi=Ci
Ci+Fi+P(2)
where C
i
is the thickness of coarse sediment modelled at the
location of the ith well, F
i
is the corresponding fine thickness
and Pis the thickness of pelagic background sediment
deposited between flows. Note that pelagic sedimentation is
therefore assumed to have a spatially uniform thickness and to
be entirely fine grained. The grain diameter defining the
threshold between coarse and fine sediments is user defined
(see Table 2) and is assumed to be known.
Hence, given a particular model output (controlled by all the
parameters in Table 2 except P), the value for Pwhich
minimizes the rms. error can be found and this is the rms. error
for that model run. In practice, equations (1) and (2) can be
evaluated very rapidly for a large number of different values for
Pand so a simple exhaustive search approach is viable. This has
the advantages of being very robust, being unaffected by local
minima and being easy to constrain within geologically plausible
limits (e.g. 0–10 m thick pelagic deposits).
This leaves the problem of minimizing rms. error with
respect to the remaining 13 parameters in Table 2 (i.e. excluding
pelagic thickness). Of these, three are assumed to be known
(the sand cut-off, the grain density and the ambient water
density) and so this leaves ten parameters to be found.
Exhaustive search is not feasible since, even searching over just
five values for each parameter, would require 5
10
10 million
simulations. A typical forward-model simulation takes the order
of one minute (on a mid-range PC) and so searching would take
approximately 20 years even at this very crude parameter-
resolution. Gradient-descent techniques (Press et al. 2002) are
likely to become trapped in shallow, local minima given the
highly nonlinear nature of the problem and so more robust
approaches are needed. Here, a Monte Carlo approach was
modified.
Starting with a user-defined range for all parameters, the
forward model was run repeatedly using sets of parameters
obtained by randomly choosing values within the allowed
range. The power of this approach was increased greatly by
making a modification that changes the Monte Carlo approach
into a very simple genetic search algorithm. The search range
within which parameters were chosen was decreased, as the
simulations proceeded, with the reduced range centred upon
the best set of parameters found so far. Hence, an initially large
parameter search-volume was gradually collapsed onto a good
solution.
The upper curve in Figure 3 illustrates this process for the
case of the sorting index, which controls the width of the
grain-size distribution for the suspended sediments in the flow
as they enter the model. This shows the progress of inversion
for an inflow location in the northwest of the model (see
Fig. 1). In the early part of the search, the sorting index
fluctuates over the entire user-supplied range. However, as the
simulations proceed, the fluctuations become smaller and
slowly converge. The lower curve in Figure 3 shows how the
rms. error changes during the same set of simulations. The rms.
error is initially relatively large but, as improved solutions are
found, all model parameters are adjusted to concentrate search-
ing in regions of good solutions and there is overall a very
gentle decrease in the lowermost rms. error values. After
simulation of 200 flows (taking typically1–10 hours on a laptop
PC, depending upon the exact parameters ranges chosen) an
excellent match between model and wells is found, as can be
seen from the very small rms. error (0.005) and also by direct
comparison of the modelled sand fractions to the well values
(Table 1). Note that Figure 3 shows the rms. error for each of
the 200 simulations but that the final model chosen is the single
simulation that happens to have the smallest rms. error. This
will not generally be the final iteration (i.e. iteration 200 here)
but, because of the gradually narrowing search-range, will
tend be one of the later simulations (in fact, the minimum
does occur for the very last simulation here but that is a
coincidence).
The excellent match of model to data is emphasized by
Figure 4, which shows the coarse-fraction distribution across
the entire modelled area. The superimposed wells are colour-
coded using the same scheme as the underlying map and so any
data/model discrepancies would show up very clearly. Figure 5
shows a similar map but for the case where parameter-
searching was carried out for an inflow assumed to be from the
south and along the channel. Note that the match between
model and wells is very much poorer, a point emphasized by
the much higher final rms. error (0.29). Observation of the 200
individual flows that were tested during the production of
Figure 5 shows that the key problem is in getting sand into well
C without also supplying sand to well E. Flows large enough to
reach C invariably also reach E and, in fact, many of them also
flood wells A and B. Moreover, even when sand does get to
well C, well D always has the higher coarse-fraction and this
contrasts sharply with the true situation in the wells. However,
Fig. 3. The upper curve shows an example inversion run in which
the sorting index was initially allowed to vary between 0.5 and 0.9 but
with this range gradually decreasing. The lower curve shows the
evolution of the root mean square error (rmse; as a result of
progressively modifying all parameters, not just the sorting index).
Note that there are occasional good solutions (below dotted line at
0.05) throughout the inversion but that the algorithm converges onto
excellent solutions (rmsem0.01) towards the end.
D. Waltham et al.276
when the inflow comes from the north (i.e. Fig. 4) it is very easy
to supply sand to wells C and D without the flows reaching
wells A, B or E and, provided the inflow location is chosen
appropriately, it is also quite easy to obtain a higher coarse-
fraction in well C than in well D. Indeed, Figure 3 shows that
there are several different northerly-sourced solutions that
produce very low rms. errors (e.g. iteration 182 has
rmse=0.0056).
DISCUSSION
The foregoing modelling confirms the expectation that, for
some parameter constraints (e.g. a flow from the south), there
are no parameter sets which produce a good match of model to
data whilst, for others (e.g. a flow from the north), there are
multiple possible solutions. This suggests that a good way to
apply such models is to use them to exclude possibilities. In
addition, even although no single good solution can be
extracted, the modelling can be used to draw conclusions about
the likely properties of the true solution by looking at features
that all good solutions have in common. The unknown, correct
solution is likely to share those common properties. Finding
properties common to all solutions is a powerful method that
has been applied to the modelling of shallow-marine clastic
sequence stratigraphy (Waltham et al. 2003) and to the very
different problem of unravelling the causes of oceanic stron-
tium isotope fluctuations (Waltham & Grocke 2006). Applying
this methodology to turbidite deposition is a much more
complex problem, however, and remains the topic of ongoing
research.
The specific problem addressed in this paper was unusually
poorly constrained. However, the software has been used in a
similar fashion for investigating datasets containing more than
thirty wells and still produced useful outputs that matched most
wells extremely closely. It should be noted that adjacent wells
tend to have similar NTG values and so it is not correct to state
that 30 wells give 30 independent constraints. As a result, the
foregoing analysis holds and parameter searches still separate
into those having multiple solutions and those having none.
Hence, it is not believed that the algorithm discussed above is
useful only in very under-constrained problems.
The algorithm presented here for parameter searching has
therefore proved to be extremely robust. It also has the
significant advantages of being easy to program (and hence
more likely to be error-free) and of being ideal for distributed
processing. This search algorithm has been run simultaneously
on 20 different PCs and produced excellent results in a small
fraction of the time needed by a single PC. Hence, using a PC
cluster, it is quite possible to produce good fits of model to data
within a few minutes. The search algorithm also appears to be
very efficient in that it can find reasonable solutions (when they
exist) in as few as 20 iterations. However, this may be a
consequence of the high degeneracy in solutions and remains
the subject of further research.
In conclusion, a novel combination of structural reconstruc-
tion and turbidity current simulation has been presented,
Fig. 4. Modelled coarse-fraction for the best-fit run with the north-entry point. Circles show the well NTG values using the same colour code
as used for the model coarse-fraction.
Stratigraphic modelling of turbidite prospects 277
together with an effective inversion procedure. It has been
demonstrated that these tools can be used to eliminate potential
sediment-path scenarios and hence reduce the risk associated
with possible further drilling.
Noble Energy (Europe) Ltd is acknowledged for generously allowing
publication of the data used in this paper.
APPENDIX A: GENERAL GRAVITY FLOW
EQUATIONS
The starting equations are (Acheson 1990):
Conservation of mass for an incompressible fluid
i=1
3)ui
)xi
= 0 (A1)
where u
i
is velocity in the x
i
-direction.
Conservation of momentum (Cauchy’s equations of motion)
)uj
)t+
i=1
3
ui
)uj
)xi
=Tj
+gj(A2)
where jis1,2or3;tis time; g
i
is gravity and
Tj
=1
i=1
3)Tij
)xi
(A3)
where T
ij
is stress in the i-direction on the plane perpendicular
to the j-direction.
With depth-averaged equations, the study is interested only
in j=1 or 2 assuming j=3 corresponds to the vertical direction.
This removes the gravity term from the right-hand side of
equation (A2). Integrating equations (A1) and (A2) over the
flow depth, H, and using Leibniz’s theorem (Abramowitz &
Stegun 1965) then produces
i=1
2
)
)xi
Hu
¯i+)H
)t= 0 (A4)
and
)
)tHu¯j+
i=1
2
)
)xi
Hu¯iu¯j=HT j
(A5)
where an overbar indicates a depth-averaged quantity. Finally,
combining equations (A4) and (A5) gives
)
)tu
¯j+
i=1
2
u¯i
)
)xi
u¯j=Tj
(A6)
which is simply a 2D version of equation (A2). Equations (A4)
and (A6) are used to model the evolution of flow thickness and
flow velocity, respectively. These expressions are quite general
as they make no assumptions concerning rheological properties
Fig. 5. Modelled coarse-fraction for a run with a south-entry point. Circles show the well NTG values using the same colour code as used for
the model coarse-fraction.
D. Waltham et al.278
(e.g. non-zero viscosity or yield strength), flow style (e.g.
laminar, turbulent or granular) or about how flow density varies
in time and space. These factors enter only via the stress term
on the right-hand side of equation (A6).
APPENDIX B: STRESSES IN A TURBULENT
NEWTONIAN FLOW
A Newtonian fluid is defined by the stress relationship
(Acheson 1990)
Tij =pij +
)uj
)xi
+
)ui
)xj
(B1)
where pis pressure and µis viscosity. For the turbulent flow
case considered in this paper, velocities should be understood
as being ensemble averages (i.e. averages over a large numbers
of identical flows) whilst µis the eddy viscosity. For the
low-concentration turbidity current case the flow density is
nearly constant (i.e. equal to water density,
w
) so that equations
(A3) and (B1) yield
Tj
1
w
)p
)xj
+2uj+jHj0
(B2)
where 2)2
)x1
2+)2
)x2
2and j=)uj
)x3
is horizontal shear stress in
the jdirection.
For a thin flow, in which characteristic horizontal scales are
generally much greater than flow thickness, a hydrostatic
approximation is appropriate for calculation of the pressure
gradient in equation (B2). In addition, for simplicity, it is
assumed that flow concentration is constant so that
)p
)xj
=)p
)xj
=g)h
)xj
(B3)
where  is the density contrast between the flow and the
ambient fluid and his the height of the flow top.
The eddy-viscosity term in equation (B2) is formally equiva-
lent to a velocity-diffusion equation and this therefore simply
smoothes the resulting velocity field. The diffusion coefficient is
given by µ/
w
which depends upon the flow speed and could
be anisotropic. However, for simplicity, this is treated as a
constant modelling parameter chosen to ensure numerical
stability.
The horizontal shear stress terms in equation (B2) can be
estimated using mixing-length theories (Duncan et al. 1960).
Full details are given in Waltham (2008) where it is shown that
the basal shear stress is given by
=w
ku
¯
blnHf/z0
2
(B4)
where kis von Kármán’s constant (note: the clear-water value
of 0.4 is unlikely to be greatly in error for the low-
concentration flows considered in this paper); bis a constant of
order one; fis the turbulent boundary-layer fractional-thickness
and is around 0.05 (Kneller et al. 1999); and z
0
is the laminar
sub-layer thickness which can be related directly to the ob-
served roughness of the channel floor since the size of the
elements generating channel floor roughness is approximately
30z
0
(Raudkivi 1998). For the 2D (after depth-averaging) flows
used here, equation (B4) may be generalized to
j=wu¯jV
k
blnHf/z0
2
(B5)
where Vis the depth-averaged speed (i.e. V2=u¯ 1
2+u¯ 2
2). Thus,
the basal friction is controlled by two constants; bwhich is
assumed to be unity and z
0
/f2r/3 where ris the scale of the
seafloor roughness. Note that this approach to calculating basal
shear stress is formally equivalent to using a Chezy-type friction
law except that the resulting Chezy-coefficient has a weak
dependency on flow thickness and, more importantly, it is
related directly to a quantifiable parameter (i.e. the seafloor
roughness).
APPENDIX C: PARTICULATE CURRENT
MODIFICATIONS
The preceding algorithm applies to any turbulent, thin, gravity
underflow and so, to complete the description, one needs to
add processes specifically related to sediment suspension and
deposition. The modelling is concerned with deposition from
the distal parts of the flow, thus it is assumed that the flow is
fully developed in terms of sediment and ambient-fluid entrain-
ment so that sediment deposition is the dominant process.
For sediment suspension, the turbulence-generated rms.
fluctuations in vertical velocity should exceed the fall velocity,
v
k
(where kruns over all grain diameters), (Raudkivi (1998), but
see Leeder et al. (2005) for a critique) and laboratory studies
(e.g. Bagnold 1966; Kneller et al. 1999) show that the rms.
fluctuations are of similar magnitude to the shearing velocity,
u*, given by
=wu*
2(C1)
An entirely equivalent suspension criterion is that the Rouse
number should be less than 2.5 (Rouse 1937; Allen 1997) since
this also leads to the expectation of a suspension threshold
when fall-velocity approximately equals the shear velocity. The
sedimentation rate, s
k
, is therefore zero for u*>v
k
but equal to
c
k
v
k
when the flow is stationary (where c
k
is the volumetric
concentration of grain-size k). The simplest mathematical
model consistent with these end-members is
sk=ckvk
u*u*#vk(C2)
s=0 u*>vk(C3)
The still-water fall velocity can be calculated using a large
number of different formulae but, for the first-order model
described in this paper, Stokes’s Law is adequate. Each grain
diameter is independently modelled using a modified form of
equation (A4) which incorporates sediment loss:
i=1
2
)
)xi
Lku¯i+
)Lk
)t=sk(C4)
where L
k
is the sediment load associated with grain-size k, i.e.
Lk=ckH(C5)
Flow thickness is then recalculated using
H=c
k
Lk(C6)
where the overall flow concentration, c, is assumed to be fixed
for consistency with earlier model assumptions.
Stratigraphic modelling of turbidite prospects 279
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Received 1 May 2007; revised typescript accepted 7 April 2008.
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... The study of these sediments gained relevance with the discovery of large offshore oil deposits [19]. Research has been done regarding the modeling of maritime turbidites [7], [11], [14], including simulations of the evolution of sedimentation [16]. ...
... Stratigraphy has been used to model stream fluvial reservoirs through rotation and translation methods [15]. Monte Carlo genetic algorithms have been used in the reproduction of 3-D turbidite currents [16]. Further along, the filling of turbidite reservoirs and the categorization of their channel margins have been studied with randomized models [14]. ...
Article
Turbidite deposits are known to be potential oil reservoirs. The techniques used to detect these deposits are usually indirect measurement methods, normally, using sound waves emission. From several studies, it is known that these data have uncertainties. With the development of new technologies and the relevance of the oil exploration area, this theme has been gaining importance. However, this issue remains a major challenge for the scientific community. This work aims to develop a method based on geostatistics to generate possible scenarios (ensembles) that allow to quantify the uncertainties of the data used to identify turbidite deposits. For this, a set of coordinates extracted from the F3 field was used as study area. The results obtained showed that the methodology proposed in this study is appropriate to quantify the uncertainties in the detection of turbidite deposits.
... .com/), which is based on turbidity-flow physics (Waltham et al., 2008). Such modeling, used for hydrocarbon exploration of turbidite-filled basins, is easily adaptable for qualitatively exploring how large-volume flows evolve in this paleodrainage system. ...
... Such modeling, used for hydrocarbon exploration of turbidite-filled basins, is easily adaptable for qualitatively exploring how large-volume flows evolve in this paleodrainage system. Waltham et al. (2008) reported that turbidity-current modeling can be approached using forward modeling. In a forward model, flow-distribution patterns can be predicted from input of flow parameters and particle information. ...
... .com/), which is based on turbidity-flow physics (Waltham et al., 2008). Such modeling, used for hydrocarbon exploration of turbidite-filled basins, is easily adaptable for qualitatively exploring how large-volume flows evolve in this paleodrainage system. ...
... Such modeling, used for hydrocarbon exploration of turbidite-filled basins, is easily adaptable for qualitatively exploring how large-volume flows evolve in this paleodrainage system. Waltham et al. (2008) reported that turbidity-current modeling can be approached using forward modeling. In a forward model, flow-distribution patterns can be predicted from input of flow parameters and particle information. ...
Article
We identify and describe submarine channels, submarine landslides, and three unusual erosional features on the toe of the Cascadia accretionary wedge near Willapa Canyon, offshore Washington, USA. We use new high-resolution multibeam bathymetric data and chirp sub-bottom and multichannel seismic-reflection profiles. Composite data sets were generated from the Cascadia Open-Access Seismic Transects (COAST) cruise and from the site survey cruise for the Cascadia Initiative. This high-resolution data set has illuminated geomorphic features that suggest that this section of the margin underwent largescale erosion event(s) which likely occurred during the latest Pleistocene. Three unusual features imaged superficially resemble slope failures of the landward-vergent frontal thrust ridge but are distinguished from such failures by (1) complete or near-complete incision of the crest of the frontal thrust, anticlinal ridge, and piggyback basin; (2) the lack of semi-coherent blocky landslide debris; (3) asymmetrical incision of feature floors to levels well below the abyssal plain; and (4) connections to the main Willapa Deep-Sea Channel by likely co-genetic but now barely active paleochannels. We conclude that the unusual geomorphic features were likely created by massive turbidity currents created by the Missoula glacial-lake outburst flood events. The floods directed massive sediment volumes through the Willapa Submarine Canyon System, eroding a broad swath of the accretionary wedge and either cutting through or causing slope failure of the frontal thrust. Turbidity- current modeling on a bathymetric reconstruction supports our hypothesis that a large-volume flow like the Missoula floods could have inundated the paleodrainage system and created the unique features we imaged.
... Process-based modelling aims to model the stratigraphic record from the properties and dynamics of individual flows; identifying input points at the basin margin and predicting where sediment will be deposited and what calibre of sediment will be deposited in different positions along the transport paths ; (Teles, et al., 2016). Construction of process-based models requires the user to define the values of parameters for which there may be limited constraint from real world data, such as the precise point of sediment input, average flow concentration, flow thickness, and geometry of the seafloor slope at time of deposition (Paola, 2000); (Waltham, et al., 2008); these controlling factors are likely to be different for each flow event. ...
Thesis
Deep-water depositional systems in different tectonic regimes display markedly different tectonostratigraphic evolution. The objective of this PhD was to develop a stratigraphic forward modelling program which deconvolves the controlling factors on basin fill architecture, in order to understand the dynamic interaction between structural deformation and sediment supply, using real, mapped structural geometries and stratigraphic package thicknesses. Understanding the interaction between structural deformation and sediment supply is important on active continental slopes. This interaction controls the vertical and lateral distribution of reservoir and seal lithologies, and their relation to growing structures. Subsurface prediction of trap and seal effectiveness is a vital component of CO2 sequestration or hydrocarbon exploration projects. Onlapse-2D is a geometric-based stratigraphic forward modelling program that simulates the tectonostratigraphic evolution of mini-basins using only commonly available reflection seismic, age-dated horizon interpretations and well data, if available (not required). The resulting models efficiently simulate the stratal architecture and palaeobathymetry of the mini-basin through time. Onlapse-2D produces geologically realistic cross-sections of a range of idealized mini-basins and simulates the evolution of a mini-basin using real data in the Gulf of Mexico. Through the modelling, I show that the development of offlap and onlap stratal terminations in structurally active mini-basins may be linked to sediment supply in some cases. However, in others the link between onlap and offlap may be weak or non-existent. Therefore, there is no requirement for the development of onlap or offlap to have a hard-wired link to extrinsic processes, such as relative sea-level change. Simulating the tectonostratigraphic evolution of the Late Miocene within three mini-basins in the Sureste Basin of Mexico allowed me to test and develop the capacity of Onlapse-2D. This case study integrated high resolution age-dated horizons and well data with 3D-seismic horizon interpretations, and the model results revealed three phases of structural activity, which controlled the stratigraphic development in the Late Miocene. These comprise two distinct pulses of contraction-related folding, and the long-term effects of salt-withdrawal and diapirism. This case study highlights the capacity of Onlapse-2D to aid in hydrocarbon exploration, by predicting reservoir presence away from well control and by identifying candidate stratigraphic traps.
... Turbidity currents were modeled to predict depositional patterns of typical Holocene and in some cases Pleistocene turbidity currents using the sediment modeling code in the Midland Valley Exploration Ltd. Modeling package Move 2015. The algorithm is described in detail in Waltham et al. (2008). Using this method, turbidity current pathways and turbidite sedimentation may be modeled using modern or paleobathymetry using forward and inverse/search methods. ...
Article
The Washington continental margin presents both a classic test of submarine paleoseismology, and an opportunity to explore advancement of the field through analysis of sediment dispersal in a heterogeneous system.New and archive core, bathymetric, backscatter and seismic reflection data from the Washington Cascadia margin show that during high-stand conditions, the northernmost canyons, Barkley, Nitinat, JDF, and to some extent Quillayute are relict systems, with little Holocene recharge. The remaining canyons, Quinault, Grays, Guide, and Willapa, are recharged to a varying degrees by northward transport of Columbia River derived sediment.All systems are nonetheless active conduits for turbidity currents during the Holocene, which are weaker and more restricted than Pleistocene counterparts.Sedimentologic and CT analysis, supported by radiocarbon ages, micropaleontology, and the Mazama ash datum show that the Holocene sedimentary sequence consists of a series of sand to mud turbidites in the active portions of all systems, interbedded with hemipelagic sediment.However, the Pleistocene Astoria and Nitinat fans, are largely inactive in the Holocene, with turbidity current activity limited to the proximal parts of the main channels.Within active systems, the turbidite record is modulated by local landsliding and growth of active folds and faults.
Preprint
Full-text available
This study proposes a new method of inverse analysis from ancient turbidites to the non-steady turbidity currents with consideration of multiple grain-size classes. The forward model employed in this study is based on the shallow water equation, and the initial condition of flows are assumed to be the lock-exchange type condition. To obtain a solution of the inverse problem, this study employed the genetic algorithm for finding the optimized initial conditions. The present method successfully estimated the true given initial conditions of the turbidity currents from the artificial data sets of deposits created by the calculation of the forward model. The author also applied the method to the turbidite bed in the Kiyosumi Formation. As a result of inverse analysis, the obtained solution fits well to the observed data of the individual turbidite, providing estimates of the flow velocity, the flow thickness and the sediment concentration of the turbidity current. The flow thickness and velocity when the turbidity current reached at the downstream end of the study area were reconstructed to be 334.6 m, 0.98 m/s respectively at the location of the downstream end. Result of our analysis is the first example of reconstructing a reasonable conditions of the turbidity current from an ancient turbidite observed in the field, and the method is expected to be applied in various regions in the future.
Chapter
The potentially large volume of oceanic natural gas hydrate (NGH) resources, combined with new understanding of the NGH petroleum system and demonstrated exploration techniques, suggests that near-term extraction of natural gas from the resource is feasible. Sandy marine turbidite sediments in the Nankai (Japan) and Walker Ridge (US—Northern Gulf of Mexico) localities have been proven to host high concentrations of NGH. NGH is a stratigraphic play insofar as the present primary exploration targets are marine turbidite sands. Sediments of this type, deposited on deep continental shelves and slopes, are a primary target for NGH extraction potential. Similar, more deeply-buried turbidites are prominent first-order hosts for conventional gas and oil deposits. Concentrations of NGH cluster along the base of the GHSZ although NGH is more stable toward its top. These are proven hydrocarbon resources and amenable to extraction of gas and oil. We infer that conversion of NGH to its constituent gas and water will allow the natural gas to be recovered. Exploration tools are sufficient to identify and value NGH concentrations.
Chapter
The potentially large volume of oceanic natural gas hydrate (NGH) resources, combined with new understanding of the NGH petroleum system and demonstrated exploration techniques, suggests that near-term extraction of natural gas from the resource is feasible. Sandy marine turbidite sediments in the Nankai (Japan) and Walker Ridge (US—Northern Gulf of Mexico) localities have been proven to host high concentrations of NGH. Sediments of this type, deposited on deep continental shelves and slopes, are a primary target for NGH extraction potential. Similar, more deeply-buried turbidites in marine sediments are prominent first-order hosts for conventional gas and oil deposits. Concentrations of NGH cluster along the base of the GHSZ although NGH is more stable toward its top. These are proven hydrocarbon resources and amenable to extraction of gas and oil. We infer that conversion of NGH to its constituent gas and water will allow the natural gas to be recovered. Exploration tools are sufficient to identify and value NGH concentrations.
Article
Sedimentary forward modeling is an effective and economical approach for exploration of sandstone reservoirs, especially in deepwater settings. Computational fluid dynamics brought innovation to modeling and simulating the behaviors of sediment gravity flows (turbidity currents in most cases) along with the prediction of turbidite distribution pattern. Furthermore, establishment of structural and isostatic balancing technique contributed to quantitative reconstruction of paleo-basin structure and paleo-bathymetry. Recent dramatic improvements of computer operating speed and software performance have allowed us to apply such numerical methods to a three-dimensional (3-D), several ten to hundred kilometer wide dataset. The integration of these sedimentary and structural approaches has finally produced an advanced forward sedimentary model that numerically predicts a turbidite distribution on the reconstructed 3-D paleo-bathymetry. Such an integrated model is powerful and useful for better understanding of lobate turbidite distribution and of turbidite deposition in topographically complicated basins, or confined basins, and also for stochastic determination on input parameters of turbidity current (s) based on a limited number of available well-log data. Combination with seismic geomorphology and seismic attribute analysis can improve the quality and accuracy of geological evaluation in deepwater turbidite play.
Article
The ability to extract the history of motions associated with geologic structures is a key element in understanding fundamental deformation processes, for example, the growth of folds or faults in three dimensions, the interactions between faults, and the spatial relationships between deformation and sedimentation. Here, we show how to extract these motions for complexly faulted and folded structures using a new method of three-dimensional (3-D) restoration. We perform the restoration on sets of stratigraphic horizons defined in three dimensions as irregular triangular networks (triangulated surfaces), with the unfaulting and unfolding as separate steps. The unfolding is achieved by a best-fit packing of the triangular surface elements, implementing several restoration mechanisms, including (1) flexural slip, (2) homogeneous inclined shear, and (3) 3-D inclined shear oriented in the azimuth of the local surface dip. After unfolding, we restore the displacement on the faults in map view by a best-fit rigid-body packing of fault blocks in a way that allows for complex systems of faults. By performing the combined unfolding and unfaulting with multiple orientations of the unfolding vectors, we determine the optimum combination of unfolding plus unfaulting, which yields a best estimate of the surface-strain fields, the particle-displacement field, and the fault-slip vectors in three dimensions. We illustrate the restoration method with synthetic examples and a complexly faulted structure from the western Niger Delta that is imaged in 3-D seismic data. We include the results of tests to quantify some potential sources of error in the restorations.
Book
Given the diverse and extensive literature available on the subject of loose boundary hydraulics, this book attempts to bring together and condense present knowledge on the subject into a mangeable introductory text. The book is divided into 12 cahpters, covering, along with an introduction; sediment and fluid properties; thresholds of particle movement; sand transport by air; geometry of fluvial channels; resistance to flow; sediment transport; stable channel design; erosion and deposition; cohesive sediments; coastal zones; and transport in pipelines. Assuming that the reader has a working knowledge of fluid mechanics and open channel hydraulics, this book has a bias towards the engineering aspects of the field.
Article
Gravity currents are of considerable environmental and industrial importance as hazards and as agents of sediment transport, and the deposits of ancient turbidity currents form some significantly large hydrocarbon reservoirs. Prediction of the behavior of these currents and the nature and distribution of their deposits require an understanding of their turbulent structure. To this end, a series of experiments was conducted with turbulent, subcritical, brine underflows in a rectangular lock-exchange tank. Laser-Doppler anemometry was used to construct a two-dimensional picture of the velocity structure. The velocity maximum within the gravity current occurs at y/d ≈ 0.2. The shape of the velocity profile is governed by the differing and interfering effects of the lower (rigid) and upper (diffuse) boundaries and can be approximated with the law of the wall up to the velocity maximum and a cumulative Gaussian distribution from the velocity maximum to the ambient interface. Mean motion within the head consists of a single large vortex and an overall motion of fluid away from the bed, and this largely undiluted fluid becomes rapidly mixed with ambient fluid in the wake region. The distribution of turbulence within the current is heterogeneous and controlled by the location of large eddies that dominate the turbulent energy spectrum and scale with flow thickness. Turbulent kinetic energy reaches a maximum in the shear layer at the upper boundary of the flow where the large eddies are generated and is at a minimum near the velocity maximum where fluid shear is low.
Article
This paper summarizes the results of a joint EAGE/AAPG research conference that was convened in Almeria, Spain in October 1998. The theme of the conference was how to better produce deep-water reservoirs based on lessons learned from the past 25 years. A repeated message at the conference was that there is more complexity than anticipated in turbidite reservoirs, contrary to the expectations of many geoscientists. Such complexity may go unnoticed during initial depletion, and only be observed during,secondary injection of fluids. Early recognition of shale occurrences and geometries, bed continuity, and stratigraphic variations in net-to-gross ratios appear to be the main issues related to maximizing well performance.
Book
Earth Surface Processes is an introductory text for those studying the dynamics of fluid and sediment transport in the environments, in the context of both present-day patterns as well as the environmental changes decipherable in the geological record. The book is divided into two parts. The first deals with the global-scale aspects of the earth's surface system. The second part focuses on the physical underpinnings for fluid and sediment transport in a number of settings, found at the earth's surface and in its oceans. Earth Surface Processes fits into the literature of the broad holistic discipline of 'Earth System Science.' The author illustrates the physical principles of earth's surface processes and explains the relevant theories by quantitative practical exercises. The pioneering textbook on the "new sedimentology" One of the first textbooks to adopt the Earth Systems approach to geology, developed at Penn State and Stanford. Should reinvigorate more traditional courses in physical sedimentology and dynamical sedimentology. Successfully marries the innovative holistic approach to Earth Systems with the traditional reductionist approach to sedimentary processes. Explains both the global-scale Earth Surface System and the fluid dynamics and sedimentary transport processes that underlie this. Quantitative approach is reinforced with worked examples and solutions. Richly illustrated with original diagrams and a colour plate section
Article
BANG1D simulates the mechanics of a subaqueous, turbid surge, a seafloor-failure-induced turbidity current that behaves like a snow avalanche or a pyroclastic burst. BANG1D uses the one-dimensional, layer-averaged equations for the conservation of fluid, sediment, momentum and turbulent kinetic energy in a turbidity current. The Lagrangian forms of these equations are solved explicitly at nodes within the turbid surge as they are tracked moving at discrete time steps across a bathymetric profile. BANG1D simulations compare well with experimental data of turbid flows and with simulations produced by other numerical models. Intermodel comparisons demonstrate the importance of frictional drag at the base of a turbid flow and entrainment across its surface in retarding accelerations induced by fluid pressures and gravity. Sensitivity tests also show that a constraint must be placed on the erosive power of the flow. This is accomplished in BANG1D by coupling the shear velocity at the base of the flow to its turbulent kinetic energy. Use of this coupling results in successful simulations of experimental sediment-laden turbid flows, but not experimental saline flows, which do not carry sediment. This latter finding suggests that additional research is needed into the linkage between frictional drag along a sedimentary boundary and the turbulent kinetic energy in turbid flows.
Article
A broad review is presented of the flow of particulate suspensions. The fundamental concepts are discussed and the governin equations described. Simplified horizontally uniform, box–model solutions are obtained and numerical integrations of the nonlinea shallow–water equations are presented, along with a brief description of an approach using the full power of the technique of computational fluid dynamics. Extra situations, such as the influence of a mean external flow, interstitial fluid whic is less dense than the ambient, plumes, entrainment of the ambient, and polydispersivity are reviewed. Applications from engineerin and the Earth sciences are described.