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Seismic Petrophysics: A
Technology to Extract Lithology, Porosity and Hydrocarbon
Content from Conventional Seismic
Data
Young, Roger A., eSeis, Inc.
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ABSTRACT
The quantification of lithology, fluids, and structure are
the definitive goals of seismic exploration. Exploitation of
amplitude information only, although sufficient for many
structural interpretations, fails in the ability to adequately
define lithology. Conventional post-stack inversion
technology, while quantifying rock property information in the
form of acoustic impedance, velocity, or density, conveys
little in the way of definitive mineral or fluid information.
For example, a low velocity interval from an inversion may be
interpreted as either a porous sand reservoir or a slow shale,
with obviously different drilling results.
AVO technology exploits the loss or gain in reflected
P-wave energy due to shear wave conversion at interfaces.
Although AVO measurements from pre-stack seismic data contain
fluid and lithology information, conventional AVO gradient
products fail to provide quantification of lithology or
fluids.
We present a technology for extracting detailed lithology,
porosity and hydrocarbon content sections from conventional
seismic data through a unique combination of AVO and seismic
inversion technologies. The method has been in use for several
years and successfully decomposes sand, shale, and carbonate
lithologies including gas/oil fluid content and effective
reservoir porosity. Current research is successfully extending
the technique to quantify salts and
coals.
Introduction
Decomposing seismic data into the influences of lithology
porosity and fluids starts with understanding how the rocks
directly influence the seismic signal. This is seismic
petrophysics. Therefore, this paper starts with some model
examples that directly relate the rocks (lithology, porosity
and fluids) to seismic. The forward modeling problem (rocks to
seismic) must first be understood before the inverse problem
(seismic to rocks) can be attacked. The proposed approach to
solving the inverse problem takes advantage of petrophysical
techniques. After the explanation of the approach, the
technology will be applied to a model and subsequently to two
data examples. An example of combining this technology
together with seismic coherency will also be
presented.
Seismic response to
rocks
Conventionally seismic models are created from logs such as
a sonic, density and a shear sonic. For the purposes of this
investigation, dealing directly with logs is one step removed
from what is really needed. Rocks can be forward modeled to
logs and logs can be forward modeled to seismic. Therefore
logs are an intermediary step that can easily be computerized
allowing a transformation from rocks directly to seismic. With
this tool created, many what-if situations can be explored.
In this first example, rock conditions where selected that
represent “end points”. Figure 1 illustrates the rock
conditions and the resulting seismic response. Four different
events can be seen in this model. On the left the rocks are
defined and on the right is the resulting full offset stack
and the AVO gradient response. The first column defines the
rock’s lithology; shales are in green, sands in yellow and if
the sand contains gas it is colored red. The second column
represents the rock’s porosity as labeled in the figure. The
fourth event on the stack is a result of a change in lithology
but no change in porosity. The third event is the result of a
porosity change but no lithology change. The top two events
are sands with different porosities with the top half of the
sands being filled with gas. Note that the low porosity sand
when filled with gas results in a dim spot, while the high
porosity sand when gas filled causes a bright spot. Notice
that all of the above-described conditions cause an event on
the stack and AVO gradient.
This simple example points out a pitfall in trying to
relate seismic full stack amplitude to porosity. However there
is a solution to this problem. The stacked amplitude, as well
as the AVO gradient, are both functions of lithology, porosity
and fluids. This is the problem that log analysis routinely
solves. That being that most logs are themselves functions of
lithology, porosity and fluids. By solving the logs
simultaneously, lithology, porosity and fluid volumes can be
extracted.
Seismic petrophysics, the
application.
Solving equations simultaneously requires at least two
independent equations. Getting two independent equations out
of seismic data means making use of AVO and inversion.
Inversion transforms the seismic trace into a log like form
and AVO to provides two traces. There are many ways to combine
the traces within a CDP gather. Among them is the full stack,
range limited stacks, angle stacks, normal incidence (P)
sections, AVO gradient (G), P – G which is ~ S (shear
impedance reflectivity), and P + G which is ~ Poisson’s ratio
reflectivity (PR). Since we are going to assume the Shuey two
term approximation, only two of these mentioned products can
be considered independent pairs.
From a petrophysical point of view the full stack or any
common offset stacks are not even worth considering. Stacks
are influenced by acquisition geometry as each CDP contains a
different distribution of offsets making them spatially
variant. Stacks are also time variant as the average incidence
angle is influenced by the mute zone as well as by depth. With
today’s computing power it is surprising that the full stack
is still the product of choice for inversion over the zero
offset section.
The two products to choose from must be understood from a
petrophysical point of view. This makes angle gathers a less
desirable choice. This leaves the P, G, S, and PR. The
simplest pair to choose is felt to be P and S.
The utilization of AVO and inversion together will now be
demonstrated. The AVO gradient (G) and the theoretical P-wave
stack (P) are derived with a least squares line fit to the
trace amplitudes versus incident angle at each time sample
(after Shuey):
A(?,t) = P(t) + G(t) sin2 [?(x,t)]
where x is trace
offset.
Using these we can derive pseudo-shear wave reflectivity
(S) (after Gelfand and Larner):
S(t) = ½[P(t) - G(t)]
We now have two independent reflectivity sections. Each of
these sections can be inverted, with low frequency constraints
the initial rock model.
Petrophysical well log analysis, based on volume averaging,
allows inversion of the inverse P and S impedance (IIP and
IIS) to yield mineral volumes.
IIP = IIPfl*? + IIPss*Vss + IIPcl*Vsh
IIS = IISfl*? +
IISss*Vss + IIScl*Vsh
where, Vss and Vclay are the fraction of sand and clay
(respectively) in the matrix, and ? is the porosity of the
matrix. The remaining factors (IIPfl, IISfl, IIPss, IISss,
IIPcl, IISsh) are the physical properties corresponding to the
impedances of pure water, sandstone and shale. The constants
for water and sandstone remain relatively constant while the
impedances of shale may vary slightly with the geologic
setting and are usually adjusted as part of the calibration.
The same analysis technique can be applied to the compressible
hydrocarbon quadrant of the cross-plot resulting in
hydrocarbon volume.
Figure 2 shows the flow from gathers to lithology porosity
and fluids.
Figure 3 shows the crossplot used for calibration of
pre-stack inversion. Note the cluster of points falling in the
gas quadrant of the plot corresponding to a known gas charged
reservoir.
This inversion is applied to the entire prestack seismic
data set (after careful pre-processing and migration to
preserve AVO effects) resulting in sand, shale, and fluid
volumes for the entire seismic
section.
Seismic petrophysics applied to a
model
The technology will now be applied to two models. The first
example will be on the model that was displayed in Figure 1.
This is a good example as it contains extreme conditions of
rocks within the same model.
Prestack petrophysical
inversion was applied to the model in Figure 1 resulting in
the successful decomposition of the seismic data into the
three key components; Lithology, porosity and fluids. The
results are displayed in Figure 4. Key things to notice are:
- Event 1 and 2 see the gas water contact at the correct
position and the porosities associated with the gas invert
to be the input porosities, not values influenced by the gas
effect.
- Event 3 is only due to a porosity change, the inversion
reflects exactly that.
- Event 4 is only caused by a lithology change and the
prestack petrophysical inversion shows that.
Rock-Based Integration
Since the technology exists to relate logs and seismic to
rocks and rocks directly to logs and seismic we can integrate
our data sets with what they have in common, the rocks. This
example shows how this full circle can be made.
Figure 5 shows the relationship between
the logs and the rocks. This is simply log analysis. Next this
1D rock model can be extrapolated following a seismic horizon
into a 2D rock model. This extrapolation is shown as two
seismic sections in Figure 6. The top one represents the
relative sand to shale volume, the greens are dominated by
shale while the browns are half shale and half sand and the
yellows are clean sands. If the sand contains gas it is
colored red. The bottom section represents the porosity. This
figure also contains the 2D CDP gathers generated from the
given rock model.
Inverting this rock model would represent the upper limit
of what can be expected to get out of a seismic decomposition
of the actual data. Figure 7 shows the
results of such an inversion. The conclusion here is that the
existing rock conditions along with the frequency content of
the seismic, are favorable to the seismic decomposition
process. The next step is to apply seismic decomposition to
the actual seismic data.
The process was run and the results are displayed in
Figure 8. The full offset stack is displayed
with the lithology/fluids and porosity results in 2D then the
1D display of the inversion at the well location is shown. The
theory demonstrated on model and predicted to work with the
given rock conditions turned out to do an excellent job of
“seeing” the reservoir and the wet sands.
Figure 9 is the 2D comparison of the rock
models created from the extrapolated log analysis results, the
inverted model, and then finally to the inverted seismic. It
is sometimes easier to visualize the results of the inversion
in 1D. Figure 10 shows such a comparison. In
this type of presentation porosity and fluids can be displayed
in one graphic. Also the gas shown is only a few samples thick
so the inversion graphic looks blocky. Notice how close the
inversion came to the theoretical upper
limit.
Lithology coherency
Seismic coherency is a method of detecting the edges,
whether from a fault or the edges of a channel. If the seismic
stack is a composition of the variations in lithology,
porosity and fluids, then the coherency result on a full
offset stack should be somewhat confusing. The situation
should be cleared up if coherency where to be run on the
decomposed data.
Figure 11 shows time slices of coherency
results courtesy of Coherence Technology Company and data with
the courtesy of Pan Canadian. The first slice is the coherency
of the conventional prestack-migrated stack. Notice the
channel running through the center. The display on the top
right is the coherency cube of the decomposed lithology
section with the porosity section below it. Notice how both of
the decomposed sections show the boundaries sharper than the
conventional migrated stack. This result is to be expected as
the stack is a combination of porosity and fluid effects and
therefore its coherency will result in blurred images. Notice
that the boundaries of the two decomposed sections are clear
but distinctly different from each other. Although beyond the
scope of the paper, there is a lot to be had from the
interpretation of these two products concerning their
depositional environments.
Also in aide to understanding depositional environments is
the ability to visualize the data quickly and in 3D. The Pan
Canadian data set was loaded into Texaco’s visualization
center. Figure 12 shows the decomposed
porosity of the sand filled channel. It is speculated that the
variations in the porosity are consistent with of the geometry
of the channel.
Seismic decomposition
discovery
The time slices shown in the previous example where wet and
predicted so by the described seismic decomposition method. A
higher zone was predicted to contain gas and drilling results
proved the prediction correct. Figure 13
shows the time slice of the discovered sand bar that contains
gas while Figure 14 shows the porosity
results.
Conclusion
Seismic petrophysics is sure to be an important force in
maximizing the rock and fluid information that is locked up in
the seismic data. With today’s computing power and price of
oil, we simply must be smarter than trying to relate rock
properties to stacked
data.
Acknowledgements
References cited
Shuey, R.T., 1985. A simplification of the Zoeppritz
equations: Geophysics, V. 50, p. 609-614.
Gelfand, V., et al, 1986: “Seismic Lithologic Modeling of
Amplitude-versus-offset Data”, Proceedings of the 56th Annual
Meeting of the SEG, Nov. 2-6, 1986, p. 334-336.
Figure captions
Figure 1. A rock model is created representing “end
points”. Each of the four events is the result of a change in
the rock or fluid properties. It is easily shown that the
stacked seismic response is ambiguous.
Figure 2. Decomposing seismic into lithology, porosity and
fluids starts with the CDP gathers. P and S (P – G)
reflectivities are extracted and inverted into compressional
and shear impedances. Impedances can be inverted into
lithology, porosity, and fluid content via a crossplot as
shown.
Figure 3. The crossplot is divided into two sections; the
upper section is the solution space for sand, shale and water.
The lower section is the model space for sand, water and gas
(compressible hydrocarbons). The lithology and fluid content
of any time/space sample is the result of where that sample
lies.
Figure 4. The rock model from Figure 1 was decomposed using
prestack petrophysical inversion. The results show that
lithology, porosity and fluid effects can be separated with
the described process.
Figure 5. Relating logs to rocks and rocks to logs is the
first step in building the relationship from rocks to seismic.
The above interpretation shows the input logs, the inverted
lithology/porosity/fluids and the forward modeled logs.
Figure 6. The lithology/porosity and fluids from the log
analysis are shown on the left. This is extrapolated using
seismic horizons into a 2D model. Two seismic sections are
used to display all the information that the lithology column
on the left shows. The upper (middle) display shows the
lithology, green is shale, brown is a dirty sand, yellow is
clean sand and red is a gas filled sand. The lower section
displays the porosity. The illustrated rock model is forward
modeled into CDP gathers shown on the right.
Figure 7. The CDP gathers from the model created in Figure
6 are inverted into lithology/porosity and fluids. The 2D
display of the results are in the middle column while a single
1D result is displayed on the right.
Figure 8. The migrated stack on the left is the structure
that was modeled in Figure 6. The CDP gathers that went into
this displayed stack where inverted into the lithology and
fluids shown in the middle and right of this figure.
Figure 9. This is a comparison of the 2D results from the
modeling and inversion. On the left is the input model, that
is the log results extrapolated using seismic derived
horizons. In the middle are the results of the model gathers
inverted. This represents the upper limit of what
lithology/porosity and fluid information can be extracted from
the seismic given the frequency content of the seismic. The
right hand side of the example shows the results from the
inversion of the actual seismic data.
Figure 10. This is the 1D display of the results displayed
in Figure 9. The result on the left is the log analysis. In
the middle is the result from the log analysis converted into
seismic and back to rocks. Therefor this represents the upper
limit of what can be expected to get out of the seismic using
this technology. On the right is the result from the actual
seismic data at the well location. Notice how close the
inverted seismic is to the upper limit from the middle
column.
Figure 11.The display on the left is the Coherency Cube
result of the migrated stack. The displays on the right and
the coherency cube run on the decomposed sections. The top
display is that of the lithology while the bottom display is
from the porosity volume. Notice that coherency is sharper in
the decomposed volumes. Also note that the coherency result on
the stack is trying to see both lithology and porosity at the
same time and therefore loses sharpness. The coherency on the
decomposed volumes is very sharp and both volumes are
different from each other, as they should be.
Figure 12. Data visualization is growing in popularity,
however it is the wiggles that are usually visualized. Here is
an example of the porosity display of a channel sand.
Figure 13. A time slice of a sand bar imaged using seismic
decomposition. Sands are displayed in degrees of yellow with
red being gas filled sand. Greens are the shales.
Figure 14. This is the same time slice as in Figure 13 only
it is the porosity display.
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