**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) = Ѕ[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.