2271 extended elastic impedance

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EXTENDED ELASTIC IMPEDANCEEXTENDED ELASTIC IMPEDANCE

Im lementin Extended ElasticIm lementin Extended Elastic

Impedance in CE7Impedance in CE7 Kevin Gerlitz 2004 Kevin Gerlitz 2004


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x en e as c mpe ance s escr e n a paper en e x en e as c

Impedance for fluid and lithology prediction by Whitcombe et al., Geophysics,

2002, 67, 1, p 63-67.

from 0 to 30, theoretically we can extend this over a greater range of angles, , suchas 90 to +90.

(from Whitcombe et al, Geophysics, 2002)

e sin term in t e Zoeppritz inear approximation imits t e range at w icreflectivities can be defined.

If we re-write the Zoeppritz linear approximation as R = A + B tan and then scale it

Rs = A cos + B sin


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,from the P-wave, S-wave and density logs for each angle from the scaled reflectivity

equation using the following equation:

an generate a spectrum o ogs.

(from Whitcombe et al, Geophysics, 2002)


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ere are wo me o s or e erm n ng w a ang e o use n or er o es e nea e

the reservoir parameter reflectivity section.

1. By generating the EEI log spectrum and cross-correlating the log reflectivities

with the desired reservoir arameter reflectivit .

2. By generating the scaled reflectivity seismic spectrum at each well location andcross-correlating with the desired reservoir parameter reflectivity.

The second method is preferable for practical purposes since noise in the seismic

section, anisotropy, velocity errors, etc, may yield an optimum angle that is

different than that achieved by the cross-correlating the EEI logs.

When we have determined , we can then create the equivalent seismic

reflectivity section from the combination of intercept and gradient stacks using

the R = A + B tan equation.

- ,we can implement both methods of the Extended Elastic Impedance method and

generate the desired reflectivity section.


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To start, you need a well with a P-wave, Density, S-wave, and the log that you wish tocreate the reflectivity section (i.e., Vp/Vs, Sw, , , , , AI, SI, etc)


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Now open the CE7 AVO version and build a 3D depth model using the Advanced Setup


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and build the geometry.

The first trick to making this process work is to have something in the

header that can be related to angle. In this example, I have built a model

with 181 traces that start from X = -90 to X = 90. The X value will now

correspond to the angle


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Select the logs for the

model: P-wave, Density,

S-wave. The second trick

is to also include the

other logs that you wish

to correlate with


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Make a note of the sample

rate that you are using. In

this case, my volume is

sam led ever 0.20 m


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ap e we o e oca on correspon ng o .e., e cous c mpe ance oca on


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Now apply a Trace Maths script to the P-wave, Density

and S-wave log volumes to create the EEI log spectrum.

** Rename the volume variables to P_wave,Density and S_wave as shown


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ou may wan o ca eoutput something useful

like EEI_logs


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Load the EEI.prs file from the

Trace Maths directory into the

parser window.

If you made your Xs equal to

your angles and if you

renamed the volume variables,

then ou do not have to

change anything in this

script

value for you. If you want to

hard-code your K, edit this

part here.


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The result is the spectrum of Elastic Impedance logs ranging form 90 to +90. I have

changed the Inserted Curve to the P-Impedance log for a comparison.


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Change the EEI logs volume variable name to refand the other log volume to input and

ow use ano er race a s scr p o cross-corre a e one o e o er ogs n edepth model against the EEI log suite. In my example, I will first cross-correlate the

EEI logs with the Porosity log volume.

se e sage o o o use . ange e ou pu name o some ng use u e

xcor_por to indicate that it is the cross-correlation of the porosity logs with the EEI logs...


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The Trace Maths script,crossCorrelateReflectivity, is

referenced to the depths.

This is where you set your

. ,

my sample rate, s_int, is 0.20

m. I am starting the

correlation window at

the window ends at

inputEndDepth = 710 m. The

cross-correlation coefficients

outputStartDepth = 160 m

depth in the output volume.

Ive set the delay (maxDelay)

- -

correlation


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e ou pu pro a y won oo o n eres ng. ou ave o c ange some o e v ewparameters like the zoom, Mean and Std, turn off fill trace and color interpolation, etc


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o ge some ng a oo s a e er


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- . ,cross-plot against a lithology indicator log like the Gamma Ray


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e gamma ray re ec v y og cross-corre a e w e re ec v y ogs.


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- - .both cross-correlation results into the cross-plot window


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> -X-axis and the cross-correlation results on the Y-axis.


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-

zoomed in view shows the maximum

negative correlation at 45


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EXTENDED ELASTIC IMPEDANCEEXTENDED ELASTIC IMPEDANCEThe cross-correlation of the Gamma Ray reflectivity log with the EEI reflectivity log

spectrum

A zoomed in view shows the

maximum correlation at 65


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- -,spectrum. As expected, we get a perfect correlation at 0


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EXTENDED ELASTIC IMPEDANCEEXTENDED ELASTIC IMPEDANCEWe can now compute the associated elastic parameter reflectivity volumes using Trace

Maths applied to the A & B AVO attribute volumes


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o compu e e poros y re ec v y, ve rename e n ercep an ra envolume variables to A & B


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n ype n e equa on: -1*( A + B*tan(45 * pi /180)). In this case, the

maximum correlation was a

nega ve va ue so ave

negated the results


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The porosity

reflectivity

volume


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,


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The

lithology

reflectivity


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In Strata we can invert these volumes to yield


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- .


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u -we mo e s can a so ecreated. In this example, Ive

placed each well at the end of

separate cross-lines


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- .

wells at X = -91 and used the Triangulation interpolation scheme. Ill do all

subsequent processing starting at Inline 2 (I.e., X = -90)


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EXTENDED ELASTIC IMPEDANCEEXTENDED ELASTIC IMPEDANCEHeres the cross-correlation of the porosity reflectivity for 12 wells against the EEI

reflectivity log spectrum. Its up to you to determine which cross-line corresponds towhich Well. The Well in blue does not have a porosity log.

T TT T


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volume from the AVO A & B attributes and cross-correlating them with the logs.

To test this method, Ive created a synthetic gather and extracted the AVO attributes.



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Convert both the AVO A and B

attributes to the Depth domain using

Process > Utility > Time to Depth



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ow u e ep mo e us ng a e ogs. vecreated a model with 182 traces starting from X =

-91 to X = 90



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Now we have to make the AVO A & B volumes the same size as the Depth Model. Use

Process > Utility > Concatenate and copy the trace 181 times



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Heres the new AVO A & B traces in depth copied 181 times.



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ow use race a s o crea e e sca e re ec v yvolume from the A & B AVO attribute volumes.



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Call the output something useful like

scaled_reflectivity

rA = rad( inline - 91 );

output = A * cos( rA ) + B * sin( rA );

.

In this case, I refer the angle to

the inline values

output;



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e sca e _re ec v y vo ume s ou c ange rom one s e o e o er suc atroughs become peaks and vice versa



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Another test to determine if the scaled_reflectivity was calculated correctly is to open theAVO A volume and view the difference between the two traces. The two should cancel

each other out at 0 degrees



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ow use race a s o cross-corre a ethe scaled reflectivity with the target log.

In my case, I will test this with the P-

Impedance log curve

For this particular script to

,

scaled reflectivity volumeseismic and the target log

volume should be called logs



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Call the output something

useful

and load in the followin scri t:

crossCorrelateLogReflectivityWSeismic



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This scri t is similar to the

other cross-correlation tracemaths script but it

calculates the reflectivity of

the logs volume and cross-

corre a es w e se sm c

volume make sure that the

logs volume is renamed aslogs and that the scaled

reflectivity volume is renamed

as seismic.

Again, only edit the values in

the USER-DEFINED

PARAMETERS section.



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Cross-plot the resulting cross-correlation volume against itself and

adjust the plot parameters to plot the

X-Coord on the X-axis. As expected,

we see the greatest positive correlation

at nearly 0 degrees.



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This approach can probably be applied to multiple wells in a seismic volume. I will notdemonstrate this whole process because I dont have an appropriate data set.

First extract an arbitrary line on the AVO attribute volume that goes through all the



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ecause e ar rary ne s as n ne x ne n orma on e o e or g na se sm ccube, you will have to read it in again from the SEGY file and overwrite the

Inline/Xline information

Ive set the ori in to 100 0 with a

spacing of 10 m and with the wells

oriented along the Y-axis



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Next, Ill use the

concatenation process to

repeat the inline 181

s from 91 to +90



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remap e we s o e rs n ne a = -



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-. .


ACKNOWLEDGEMENTSACKNOWLEDGEMENTS


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Thanks to

Dan Hampson (HRS) for suggesting cross-correlating the log reflectivities.

Richard Kruger (BP, Calgary) for suggesting creating the scaled reflectivity

volume and cross-correlating with the logs.

Brian Russell (HRS) and John Logel (Anadarko, Calgary) for their comments

.

2271 extended elastic impedance

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