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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