Saya Boleh minta juga Pak ??
----- Original Message -----
From: "Leonard Lisapaly" <[EMAIL PROTECTED]>
To: <fogri@iagi.or.id>
Sent: Monday, February 13, 2006 7:33 AM
Subject: RE: [fogri] "Seismic Inversion – Still the Best Tool for Reservoir
Characterization"
Vick,
Ada attachmentnya ?
LL
-----Original Message-----
From: Rovicky Dwi Putrohari [mailto:[EMAIL PROTECTED]
Sent: Sunday, February 12, 2006 4:25 PM
To: fogri@iagi.or.id
Subject: [fogri] "Seismic Inversion – Still the Best Tool for Reservoir
Characterization"
Lunch talk di Calgary yg diadakan 2 minggu lalu, "masih percaya"
dengan seismic inversion utk reservoir characterisation.
RDP
===
"Seismic Inversion – Still the Best Tool for Reservoir Characterization"
John Pendrel
Telus Convention Centre 8th Ave SE, Calgary
Date/Time: Jan. 23, 2006 - 11:30am
ABSTRACT
Introduction
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 drilled and logged wells at all 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. In
addition, inversions make possible the formal estimation of uncertainty and
risk.
In various forms, seismic inversion has been around as a viable exploration
tool for about 30 years. It was in common use in 1977 when the writer joined
Gulf Oil Company's research lab in Pittsburgh.
During this time, it has suffered through a severe identity crisis, having
been alternately praised and vilified. Is it just coloured seismic with a 90
deg phase rotation or a unique window into the reservoir? Should we use well
logs as a priori information in the inversion process or would that be
telling us the answer? When should we use inversion and when should we not?
And what type: blocky, model-based, sparse spike? In the following, I will
briefly discuss the most common methods in a somewhat qualitative manner,
keeping the equations to a minimum.
The Post-Stack Inversion Method
The modern era of seismic inversion started in the early 80's when
algorithms
which accounted for both wavelet amplitude and phase spectra started to
appear. Previously, it had been assumed that each and every sample in a
seismic trace represented a unique reflection coefficient, unrelated to any
other. This was the so-called recursive method. The trace integration method
was a popular approximation. At the heart of any of the newer generation
algorithms is some sort of mathematics - usually in the form of an objective
function to be minimized. Here, I will write that objective function, in
words, rather than symbols and claim that it is valid for all modern
inversion algorithms - blocky, model-based or whatever.
Obj = Keep it Simple + Match the Seismic + Match the Logs (1)
Let's look at each of these terms, starting with the seismic. It says that
synthetics computed from the inversion impedances should match the input
seismic. This is usually (but not always) done in a least squares sense.
Invoking this term also implies knowledge of the seismic wavelet. Otherwise,
synthetics could not be made. At this point, life would be good except for
one thing. The wavelet is band-limited and any broadband impedances that
would be obtained using the seismic term only, would be non-unique. Said
another way, there is more than one inversion impedance solution which, when
converted to reflection coefficients and convolved with the wavelet would
match the seismic. In fact, there are an unlimited number of such
inversions.
Worse, such one-term objective functions could even become unstable as the
algorithm relentlessly crunches on, its sole mission in life being to match
the seismic, noise and all, to the last decimal place.
Enter the simple term. Every algorithm has one. It could not care less about
matching the seismic data, preferring instead to create an inversion
impedance log with as few reflection coefficients as possible. Different
algorithms invoke simplicity in different ways.
Some do it entirely outside of the objective function by an a priori
"blocky"
assumption. It can also be placed inside the objective function in the form
of an L-1 norm (sum of absolute values) on the reflection coefficients
themselves. This is advantageous since it locates all the important terms
together where their interactions can easily be controlled. How much
simplicity is best? The answer is project-dependent and will be different
for
example, for hard-contrast carbonates and soft-contrast sands and shales.
Control can be exercised by multiplying the seismic term by a constant. When
the constant is high, complexity rules. When it becomes smaller, the
inversion becomes simpler with a sparser set of reflection coefficients. We
refer to these as mixed-norm types of inversions. The term, sparse-spike is
used to describe algorithms wherein the simplicity term is outside the
objective function.
What about the "Match the Logs" term? When turned on, it makes the inversion
somewhat model-based. Sounds reasonable - the inversion impedances should
agree or a least be consistent with an impedance model constructed from the
well logs. And it is reasonable, as long as it is not overdone. The primary
use of the model term should be to help control those frequencies below the
seismic band. When it is used to add high frequency information above the
seismic band, great care should be exercised. High frequencies from a model
will be unaddressed and unchanged by the input seismic when they are above
the seismic band. They can then appear in the output inversion, even though
they are completely model driven.
You might now be saying that all inversions must, to some degree, be
model-based. The writer would not dispute this assertion. The important
point
though, is that the band in which the model has influence.
The Details - Constraints, QC, Annealing, Global and Colored Inversion There
are other strategies in seismic inversion which control the way in which the
output impedances are obtained. It is common to define high and low limits
on
the output impedances. These are supposed to keep the inversions physical
and
consistent with known analogues and theories. Some implementations offer a
non-fixed percentage of the log impedances, freely defined at each horizon
and variable with time. The constraints are interpolated along the horizons
throughout the project, riding them like a roller coaster. Could the
inversions be then critically dependent upon inaccurate horizons interpreted
from seismic data? This potential problem can be addressed in two ways. In
the first pass of inversion, the constraints are relaxed to allow for
inaccuracies. The horizons are then re-evaluated against the initial
inversion, before a final pass with tighter constraints. Second, the
re-evaluation can be done on an inversion without the model-based low
frequencies added in at all. We call this the relative inversion and it is
by
definition, free from any inaccuracies in the input model.
The relative inversion can play a vital role in quality control if the
algorithm is constructed such that the impedance logs are not made available
to the algorithm. Only the user constraints and the objective function
settings control the output, leaving it free to disagree with the logs. It
then follows that comparing the relative inversion and the band-limited
impedance logs is a very powerful quality control tool. The corollary is
that
the addition of more logs to the inversion project increases confidence in
the result rather than copying the answer into it.
Another inversion strategy is the imprint of stratigraphy - should it
influence the result and in which band? Including it in the low frequency
mode is easy and does not affect the computation adversely.
Algorithms which opt to constrain the seismic band to assumed stratigraphy
require special solution techniques. This is because the solution space
becomes more complex with many local minima beside the one representing the
optimum result. Stochastic strategies such as simulated annealing are used
to
avoid local trapping.
Global is another term which has recently been used in conjunction with
inversion. In Global mode, more than one trace is inverted at the same time
within a common objective function. The idea is that seismic noise induced
variations that are not consistent over a user-specified number of traces
will tend to be suppressed in the output impedances.
The result is a smoother looking inversion, which, if one has been careful,
does not compromise resolution.
Another technique introduced recently is the so-called Colored Inversion. It
trades computation speed for resolution. Phase is first assumed to be known.
Then the spectrum of the reservoir impedances is assumed to be a straight
line on a log frequency cross-plot. The slope of the line is determined from
available logs. Then, an operator is designed which transforms the seismic
spectrum to the desired log spectrum. This matching operator can be very
ringy and some stabilization is usually required. However, once obtained,
the
inversion can be produced by a simple convolution of the operator with the
input data.
Putting it all together, seismic inversion can play the central role in an
improved understanding of the reservoir. In Figure 1, upper panel, is a
Southeast Asia clastic example from Latimer et al., 1999.
The facies are an alternating sequence of sands and shales.
Interpretation is problematic due to the close vertical positioning of
contrasting layers within half of a wavelet length. The result is severe
interference (tuning) and a general complication of the seismic section. The
interpretation of the yellow reservoir event is particularly difficult.
Figure 1, lower panel, shows the inversion result. It is generally simpler
and the interpretation of the yellow event is obvious. It is now interpreted
as a sequence boundary which is overlain by an incised valley sand.
The value of the inversion process is illustrated again in Figure 2 from
Caulfield et al., 2005. The facies of interest are McLaren sandstones as
indicated. The figure shows the original seismic, the inversion in colour
with smoothed P Impedance logs overlain. Well cross-plot analyses showed
that
the best sandstones should be resolvable by P Impedance alone. The inversion
method used here was blind to the logs in the seismic band, making the good
agreement between the logs and the inversion a strong QC. As shown in the
figure, there is a strong change in the inversion at well 121-16 which is
indicative of a shale member. Shale had not been encountered at the nearby
141-16. The seismic reflection in the zone of interest (partially hidden by
the overlying logs) does not suggest this change of reservoir property. At
well 121-12, resolution also appears to be improved as there seems to be two
separate levels of sandstone deposition. These are revealed upon converting
to depth and preparing impedance slices (Figure 3). The probability of
sandstone deposition can also be formalized for any inversion (post-stack or
AVO), as demonstrated in Figure 4. In 3D probability space, is the
likelihood
of occurrence of a single McLaren sandstone. Figure 5 is a comparison of
interpretations from the seismic and the inversion. There is better
definition of channeling in the inversion and the authors judge that the
accuracy of net pay estimates were improved by a factor of at least two.
AVO Inversion
It should come as no surprise that all of the above ideas transfer readily
to
the AVO World (see, for example, Pendrel et al., 2000).
Instead of a single full-stack, we have a set of partial offset or angle
stacks, each with their own wavelets. In addition to a P Impedance model for
the low frequencies, we now need two more – S Impedance and Density. We also
want to include two more "keep it simple" terms for S Impedance and Density.
After that, it is pretty much the same. The Zoeppritz equations dictate the
range of allowable solutions. Alternate parameterizations are possible, P
Impedance, Vp/Vs and Density being popular. Other modes can be inverted too,
although PP is the most common. It is important, however, to ensure that the
NMO is correct to sub-sample accuracy. Failure to observe this criterion
will
result in an S measure which will have too much dynamic range – too many
strong lows and highs. Commonly, the S Impedance and any other reservoir
parameter derived from it will exhibit a narrower bandwidth compared to the
P
Impedance inversion.
This is natural and a consequence of the loss of frequency with offset.
The example in Figure 6 from the CREWES / EnCana Blackfoot data set
illustrates the classic problem of separating sandstones from shales when
discrimination is not possible from P Impedance alone. In Figure
6 are slices of P Impedance and Vp/Vs from a Simultaneous AVO Inversion. The
two reservoir properties are indeed different. Regional and valley shales
dominate the P Impedance slice. The major feature of the Vp/Vs slice is the
sandstone valley itself, brighter in the south due to the presence of gas.
Figure 7 is a 3D perspective of the Vp/Vs volume where it can bee seen that
the valley development is essentially defined by Vp/Vs. The LambdaRho-MuRho
(LMR) technology popularized by Goodway et al., 1997) can offer advantages
to
interpretation by optimally separating fluid and rock effects. LMR volumes
are easily computed from any AVO Inversion.
Density has its own particular problems. The density contribution to AVO is
many dB down from the Shear contribution in normal field acquisition. It
only
begins to become important at angles greater than 50 deg. In addition,
Anisotropy is also a significant contributor at these large angles and must
be accounted for in any attempt to invert for density. When large angles are
not recorded, density needs to be softly constrained to something like the
Gardner relation or perhaps, the relationship observed in logs between it
and
P Impedance.
The so called Joint inversions are variants of this technology. The theory
readily accommodates PP-PS or any other possible combination.
We have already noted the importance of accurate alignment and the correct
alignment of PS modes to PP takes these challenges to a new level.
Nevertheless, this technique contains the potential for density estimation
at
low angles, as illustrated by the heavy oil synthetic example in Figure 8.
The figure shows PP and PS gathers and their simultaneous inversion to P
Impedance, Vp/Vs and Density. The maximum angle used to make the synthetic
gathers shown was only 35 deg. The band of the PP gather was 10-60 Hz while
that of the PS was restricted to 10-35 Hz. Comparing the overlain logs to
the
inversion results shows that density information can be extracted.
Curiously, Joint Inversions find application to 4D projects. When the low
frequencies below the seismic band are believed to be constant, then a Joint
PP inversion of all vintages will provide the most stable baseline, against
which to measure differences. The method also works for 4D AVO.
Geostatistical Inversion
Geostatistical simulation differs from all of the other methods in one
respect. There is no objective function and hence no need for a simplicity
term to stabilize it. Rather, property solutions (impedance, porosity, etc)
are drawn from a probability density function (pdf) of possible outcomes.
The
pdf is defined at each grid point in space and time. A priori information
comes from well logs and spatial statistical property and lithology
distributions. As in the other model-based methods, the logs are assumed to
represent the correct solution at the well locations. It is useful to run a
mixed-norm inversion first, to establish this. Historically, away from
wells,
geostatistics has had problems. It is the inversion aspect of geostatistics
which has finally guaranteed its use as a modern inversion tool. The
geostatistical inversion algorithm simply accepts or discards simulations at
individual grid points depending upon whether they imply synthetics which
agree with the input seismic. The decision to accept or reject simulations
can optionally be controlled by a simulated annealing strategy. The
inversion
option results in a tighter set of simulations, the variation of which, can
be used to estimate risk or make probability maps. The simulations can be
done at arbitrary sample intervals. Close to wells, resolution beyond the
seismic band can reasonably be inferred. Away from wells, the absence of a
simplicity term in the simulation and the statistical conditioning hold the
possibility of resolution beyond that of traditional inversion methods.
Important end results of 3D Geostatistical modelling are property
probability
volumes. A set of volume simulations of porosity, for example, can be
modelled as a Normal probability density function at each grid point in time
and space. From these, volumes can be constructed giving the probability
that
the porosity lies within a specified range. Figure 9 shows an example of
this
for simulations of porosity over a Western Canadian Devonian reef. Twenty
simulations were used to generate a probability volume for the occurrence of
porosity above 10%. This volume was then viewed in 3D perspective and
probabilities less than 80% were set to be transparent. The tops and bottoms
of the viewable remainders were picked automatically. It is the thickness of
one of these high-probability bodies which is mapped in Figure 9. The
colours
represent the thickness, within which, the probability of 10% or greater
porosity exceeds 80%. In this way, uncertainty can be formally measured and
input directly into risk management analyses.
In geostatistical modelling, property and indicator (facies) simulations can
be combined to produce both property (eg impedance) and facies volumes. This
is illustrated in Figure 10 from Torres-Verdin et al., 1999, which shows
such
an estimate from Argentinean data. The green patches are sand bodies from a
single simulation. Favourable locations for new wells were determined by
integrating the sand volume at each CMP for a set of simulations. The
results
of this development programme showed a definite improvement in sand
detection. Accumulated production has been up to three times the field
average in some instances, more than justifying the effort and expense of
the
inversion.
Merging Technologies – The New Inversions Concatenating seismic inversion
with other technologies, such as neural nets, seismic attributes or pattern
recognition has been a strategy employed by some explorationists over the
years. The idea has been to try and extract every last bit of information
from the input data sets. We are now seeing disparate technologies beginning
to be combined within the same algorithm. Figure 11 is such an example from
Blackfoot. It brings together aspects of pattern recognition and post-stack
and AVO Inversion. The top is a traditional Simultaneous AVO Inversion for
Vp/Vs while the bottom is the new high resolution technology. It was run in
a
"blind-to-the-wells" mode, so the agreement to the logs is not perfect. As
resolution is pushed to its limits, we must understand that there can be no
single answer, only a collection of probable answers. The new technologies
recognize this and in fact, the bottom panel in Figure 11 is an average of
six such realizations. The variability between the realizations could have
been used to compute a probability of occurrence for the low Vp/Vs
sandstones. All of this sounds very geostatistical, although upon closer
examination, there are differences.
Summary
I hope that I have been able to convey the wide range of possibilities in
modern seismic inversions. Careful consideration should be given in
selecting
the best tool. Interpreters need to consider seismic inversion whenever
interpretation is complicated by interference from nearby reflectors or when
the end result is to be a quantitative reservoir property such as porosity.
Outputs in the format of geologic cross-sections of rock properties (as
opposed to seismic reflection
amplitudes) are putting geologists, geophysicists, petrophysicists and
engineers "on the same page".
The days of viewing seismic inversion as an extra processing step or subject
of an isolated special study are long gone. Modern inversions are intimately
connected to detailed and quantitative reservoir characterization and
enhanced interpretation productivity. The process requires and integrates
input from all members of the asset team.
Horizons should be re-assessed, models re-built, log processing reviewed and
inversion steps iterated toward the best result. After drilling, new
information should be used to create a living volume, always up-to-date with
all available information. It is this partnership directed to the solution
of
real reservoir characterization problems which leads to success.
References
Caulfield, C., Feroci, M., Yakiwchuk, K., Seismic Inversion for Horizontal
Well Planning in Western Saskatchewan, CSEG Ann. Mtg., 2005
Goodway, B., Chen, J., Downton, J., 1997, AVO and Prestack Inversion, CSEG
Ann. Mtg. Abs. p.148
Latimer, R.B., Davison, R., Van Riel, P., 2000, An Interpreter's Guide to
Understanding and Working with Seismic-Derived Acoustic Impedance Data, The
Leading Edge, 19 #3, p.242
Pendrel, J., Debeye, H. Pedersen-Tatalovic, R., Goodway, B., Dufour, J.,
Bogaards, M., Stewart, R., 2000, Estimation and Interpretation of P and S
Impedance Volumes from the Simultaneous Inversion of P-Wave Offset Data,
CSEG
Ann. Mtg. Abs. paper AVO 2.5
Torres-Verdin, C., Victoria, M., Merletti, G., Pendrel, J., 1999,
Trace-Based
and Geostatistical Inversion of 3-D Seismic Data for Thin Sand Delineation:
An Application to San Jorge Basin, Argentina, The Leading Edge, 18, #9,
p.1070
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