stochastic seismic inversion applied to reservoir characterization

7/30/2019 Stochastic Seismic Inversion Applied to Reservoir Characterization

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36 CSEG Recorder January, 2001

FEATURE ARTICLE

Seismic inversion has been used for several decades in thepetroleum industry, both for exploration and production purpos-

es. During this time, seismic inversion methods have progressed

from the initial recursive inversion method to the present pletho-

ra of methods and software packages available to transform

band-limited seismic traces to impedance traces. The application

of seismic impedance data has also progressed from qualitative

assessments of prospects to the quantitative description of reser-

voir properties necessary for reservoir characterization.

Reservoir characterization requires the construction of

detailed 3D petrophysical property models contained within a

geological framework. Structural interpretation of seismic data

has been and continues to be important in the generation of theframework of the reservoir model. Seismic data has been less fre-

quently involved in the generation of the petrophysical parame-

ters that populate the 3D model. There are several reasons for this

lack of application of seismic data to property modeling - lack of

a 3D dataset (only 2D data available), inability to relate seismic

data quantitatively to reservoir properties, and lack of sufficient

vertical resolution to generate detailed property models. The per-

vasive availability and acceptance of 3D data has substantially

overcome the first obstacle. Seismic impedance volumes calculat-

ed from these 3D datasets can, for many reservoirs, provide a

seismic parameter that can be directly related to a reservoir prop-

erty (porosity, for example), thereby addressing the second prob-

lem. The last problem - the lack of sufficient vertical resolutionfor characterization applications, has been a more difficult prob-

lem to solve. Stochastic seismic inversion is one method that can

provide the vertical resolution sufficient to generate detailed 3D

reservoir property models.

Seismic resolution is a function of the frequency of the record-

ed seismic wavefield and the velocity of the medium. Although

some enhanced recovery methods, such as steam floods or fire

floods, can alter the velocity of the medium by elevating the tem-

perature of the reservoir, the velocity of the medium is generally

considered to be fixed. Despite our best efforts to maximize the

frequencies emitted and recorded during seismic acquisition, we

often fall short of the resolution desired by geologists and engi-

neers for use in reservoir modeling - vertical seismic resolution is

typically one to two orders of magnitude less than log resolution

(hundreds to thousands of centimeters versus tens of centimeters

or less).

Reservoir models constructed from log data alone display an

excellent vertical resolution and a poor areal (horizontal) resolu-

tion. This is a direct reflection of the resolution characteristics of

the log data - high vertical resolution and limited depth of inves-tigation. Seismic data possess the opposite resolution characteris

tics: high areal resolution (bin size of the 3D survey) and poor

vertical resolution (function of the seismic frequency content and

velocity of the reservoir). Stochastic seismic inversion provides a

unique framework wherein the advantages of seismic and log

data can be combined. The stochastic impedance volume derive

its areal resolution from the seismic data, but derives the vertica

resolution from the log data used in the inversion procedure. The

resulting high resolution (both vertical and horizontal) 3D vol

ume is well suited for use in building detailed property models.

As outlined in Haas and Dubrule (1994), the log data (sonic

and density) are used in the simulation of pseudo-logs at eachtrace within the seismic survey (figure 1). A synthetic seismo

gram is generated from the pseudo-impedance log and is com

pared with the actual seismic trace at that location. The

simulation that produces the best match between the synthetic

seismogram and the actual seismic trace, as defined by some

quantitative measure of goodness of fit, is retained as the inver-

sion solution at that location. The vertical resolution of the simu

lated log data is determined by the selection of the vertical cel

size (determined by the user), not by the frequency content of the

seismic data (as determined by Mother Nature). The result of the

stochastic seismic inversion is a 3D volume with a seismic-like

areal resolution and a log-like vertical resolution that honors both

the log data and the seismic data.

The enhanced resolution of the stochastic inversion process is

evident from a visual examination of the seismic data cubes dis

played in figures 2-4. Figure 2 displays the input seismic volume

Figure 3 is the result of a sparse spike estimation and recursive

inversion. This inversion result displays a resolution similar to

that of the input data. That is to be expected, as the vertical reso

lution is derived from the seismic data, and is therefore subject to

the inherent limitations of seismic resolution. Figure 4 depicts the

stochastic inversion cube, which displays a much finer vertica

resolution than is observed in the input data or the recursive

inversion result (figures 2 and 3). The overall impedance trends

can be observed in both inversion results (figures 3 and 4)- layer

or regions of high (red color) and low (blue color) impedance

however, the stochastic inversion result (figure 4) has a much bet

ter vertical definition within these general impedance trends.

Continued on Page 38

STOCHASTIC SEISMIC INVERSION APPLIED TORESERVOIR CHARACTERIZATION

By Gary Robinson, (RC)2, Englewood, Colorado, USA


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FEATURE ARTICLE Contd

A typical stochastic inversion exhibits a vertical resolution of

approximately 1-2 meters. This is generally the same order ofmagnitude of resolution used in constructing the petrophysical

reservoir property models, and the impedance data may be used

along with the well log data to generate models of reservoir prop-

erties such as porosity. Figures 5 and 6 present porosity models of

the interval depicted in the previous figures. The model of figure

5 was calculated using only the log data, whereas the model of

figure 6 incorporated both the impedance and porosity informa-

tion. Again, although overall trends are generally similar, specif-

ic details can be significantly different. The influence of the

stochastic inversion impedance model (figure 4) on the porosity

model shown in figure 6 is clearly discernible, as features

observed in the impedance model (figure 4) that are not present

in the log-only porosity model (figure 5) are again present in the

porosity model derived from both the seismic and the log data

(figure 6).

In carbonate reservoirs, impedance and porosity typically

exhibit an inverse relationship (Rafavich, Kendall, and Todd,

1984); in clastic reservoirs, the relationship of porosity and

impedance may be complicated by additional factors, such as a

lack of impedance contrast between reservoir and non-reservoir

rocks or fluid effects. In the case of a clear relationship between Continued on Page 40

STOCHASTIC SEISMIC INVERSION APPLIED TO RESERVOIR CHARACTERIZATION

Continued from Page 36

Figure 1. Schematic depiction of the stochastic inversion process.

porosity and impedance, the seismic impedance volume may be

incorporated directly with well data, via geostatistics, neural net-

works, or other methods, to populate the cells of the petrophysi

cal model, as was done in constructing the porosity model o

figure 6. Where the relationship between impedance and porosi-

ty is murky, the impedance data may be combined with facies

data to derive a facies volume. Petrophysical properties can then

be distributed by facies within the overall model framework.

In summary, the impedance cube resulting from a stochasticinversion provides sufficient vertical resolution, as well as area

resolution, for use in reservoir characterization. This stochastic

inversion impedance volume can be combined with log and engi

neering data, utilizing deterministic or statistical methods, to

arrive at a reservoir model which has incorporated various data

types from different disciplines (geology, geophysics, engineer-

ing) to arrive at a final, consistent 3D property model for use in

reservoir characterization.

Figure 2. Input seismic data volume.

Figure 3. Recursive inversion result. Note that vertical resolution is similar to that of thinput data.

Figure 4. Stochastic inversion result. Note that the vertical resolution is significantlyimproved from that of the input data.


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FEATURE ARTICLE Contd

STOCHASTIC SEISMIC INVERSION APPLIED TO RESERVOIR CHARACTERIZATION

Continued from Page 38

Figure 5. Porosity model derived from kriging porosity log data.

Figure 6. Porosity model derived from collocated co-kriging of stochastic inversion andporosity log data. Compare with porosity model of figure 5 and the stochastic inversion offigure 4.

References:

Haas, A., and Dubrule, O., 1994, Geostatistical inversion - a

sequential method of stochastic reservoir modeling constrained by

seismic data: First Break, 12, 561-569.

Rafavich, F., Kendall, C. H. St. C., and Todd, T. P., 1984, The

relationship between acoustic properties and the petrographic character

of carbonate rocks: Geophysics, 49, 1622-1636.

GARY ROBINSON

Gary Robinson received a

B.S. degree in Geology from

Stanford University, and an M.S.

degree in Geophysics from the

University of Houston. He

began his career with Mobil in

1978, and has worked for CGG,

Elf Aquitaine, Eastern American

Energy, and Saudi Aramco priorto joining RC Squared in 1998.

His current interest is in the application of seismic data to

reservoir characterization and modeling.

First Canadian Open Business Forumon

Building Corporate Social and Environmental Responsibility3rd Federico Garca Lorca seminar

Calgary, Alberta Thursday 8 March 2001

Hon. David Kilgour, MP, PC, Secretary of State for Latin America and Africa *

Eric P. Newell, Chairman and Chief Executive Officer, Syncrude Canada Limited *

Tim W. Faithfull, President and CEO, Shell Canada Limited *

David Pollock, Executive Director, Pembina Institute *

Phil Prince, Phd, President and CEO, Canadian Energy Research Institute *

Henry Day, Vice-President, Peru 2021, President, Solgas, (Repsol-YPF S.A)*

Heather Scoffield,Journalist, The Globe and Mail *

Rosemarie Kuptana, Director, International Institute for Sustainable Development

Including keynote luncheon speaker:

Charles O. Holliday, Jr., Chairman and Chief Executive Officer and

Chief Safety, Health and Environmental Officer, E.I. du Pont de Nemours & Co.

Chairman, World Business Council on Sustainable Development

* confirmed

For more information, and sponsorship opportunities, please contact event organiser, David Mitrovica, P. Geoph.:

Email: [email protected] Telephone: 403-230-9031

stochastic seismic inversion applied to reservoir characterization

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