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8/19/2019 2274 Poisson Impedance

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Deriving the Poisson Impedance in

Hampson Russell Software

Kevin Gerli tz

Geophysicist, VHR Jakarta

April 2006


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The “Poisson Impedance” is an attribute that is derived from acombination of the P- and S-impedance values and is a good

hydrocarbon indicator. This method was described in a paper

called “Poisson Impedance” by Quakenbush, Shang and Tuttle in

The Leading Edge, February 2006.

This document illustrates a method of deriving the “Poisson

Impedance” logs from either P- and S-Impedance well logs or

seismic attribute volumes created from Simultaneous Inversion.

The relationship between the Poisson Impedance and the Fluid

Factor attribute will also be illustrated.

POISSON IMPEDANCE


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POISSON IMPEDANCE

The idea of the Poisson Impedance isillustrated in the figure on the left.

In the Acoustic Impedance / Shear

Impedance cross-plot, it is difficult

to discriminate the litho-fluiddistributions on the horizontal and

vertical axes. But rotating the axis

to be parallel with the trends would

ensure a distinct discrimination ofthe litho-fluid distributions.

The method for defining the Poisson

Impedance can be written as:

PI = AI – cSI

Where c is the term that optimizes

the rotation.From Quakenbush et al. (2006)


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POISSON IMPEDANCE

Recall that the Poisson’s Ratio can be written as:

)2(

)(2

2

)(2

22222

22

VsVp

V V

V V

V V

V V

S P

S P

S P

S P −

−

+=

−

−=σ

If we rewrite the PI=AI – cSI in terms of velocities and density,

then we can define the so-called “Poisson Velocity”

σ ρ ρ ρ ρ V cV V cV V PI S PS P =−=−= )(

Notice that we can now relate the Poisson’s Ratio (1) with the

Poisson Velocity (2) and if we define c=sqrt(2) and a scalingfactor, D, then

σ σ DV =

(1)

(2)

(3)


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POISSON IMPEDANCE

The significance of the c term is that it is the inverse of the slope

of the litho-fluid trends. For example, the Greenberg-Castagna Vp-

Vs equation is Vs = 0.77 Vp – 869 m/s. The inverse of the slope is

1/0.77 = 1.3 which is an approximation to the square root of 2 (i.e.,

1.41).

Implementing this relationship within Hampson-Russell Software

is quite easy to do and involves some simple Trace Maths scripts.


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POISSON IMPEDANCE

In order to create the

Poisson Impedance logs,

you first need to be in eLog

with a well that has both

the P- and S-Impedancelogs.

Click on the Math… button


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POISSON IMPEDANCE

Select the Log Maths

option and select the P-and S-impedance logs for

the input. Make the

Output Log Type of type

“Poisson Impedance”…


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POISSON IMPEDANCE

Type in the equation for

the Poisson Impedance.

If we use c=sqrt(2), thenthe equation is as shown…


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POISSON IMPEDANCE

Similarly, we can

derive the c term from

the cross-plot of the P-

and S-Impedance logsfor the wet trend and

calculate a regression

line. The inverse of

the slope could be

used as the c value, in

this case, 1/.746561 =

1.339.


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POISSON IMPEDANCE

The far right track shows

the computed Poisson

Impedance logs for the two

c values (red: c = 1.41, blue:

c=1.339). The Computed

Poisson Ratio curve is

shown beside it for

comparison.


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POISSON IMPEDANCE

The same

process can be

applied to the P-

and S-impedance

volumes derivedfrom the seismic

using

Simultaneous

Inversion. In thiscase, use

Process > Utility

> Trace Maths

and follow the

same workflow…


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POISSON IMPEDANCE

Here is the output Poisson Impedance volume with the low blue valuesindicating the gas zone. The PI log is spliced into the section.


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POISSON IMPEDANCE

The Poisson Impedance has a very close relationship with the “FluidFactor” attribute. The “Fluid Factor” concept was first introduced in

a paper by Smith and Gidlow in a paper called “Weighted stacking

for rock property estimation and detection of gas”, 1987,

Geophysical Prospecting.The basic idea of the Fluid Factor is that brine-saturated clastic

silicate rocks define a “mudrock line” trend on the Vp-Vs cross-plot

space (Castagna et al., 1985). The mudrock line equation is given

as : Vp = 1.16 Vs + 1360 m/s

The simple idea of the “Fluid

Factor” is that points that lie

further away from the brine wettrend are more likely to have

hydrocarbons.

From Smith and Gidlow (1987)


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POISSON IMPEDANCE

We can derive the following relationship between Vp/Vs andPoisson’s Ratio as follows:

2/1

2/1

1⎟ ⎠

⎞⎜⎝

⎛

−

−=

σ

σ

S

P

V

V

This is a direct linear relationship with Vp/Vs increasing with

increasing σ. The “pseudo-Poisson’s Ratio reflectivity” can thus

be defined as:

S

S

P

P

S P

S P

V

V

V

V

V V

V V Δ−

Δ=

Δ

/

)/(

σ ρ ρ V cV V PI S P =−= )(

Note that reflectivity equation above would be the same as thereflectivity of the previously derived Poisson Velocity.

(4)

(5)


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POISSON IMPEDANCE

The Fluid Factor was defined as the difference between the actualVp reflectivity and the reflectivity calculated from the mudrock line,

i.e.,

S

S

P

S

V

V

V

V c

Vp

VpF

Δ−

Δ=Δ

This was modified by Fatti et al. (1994) to include the density term

and write it in terms of acoustic and shear impedance reflectivities:

S

S

P

S

R

R

V

V c

Rp

RpF Δ−Δ=Δ (7)

(6)

Where c represents the slope of the wet clastic reservoir trend.

Using the mudrock line, c was defined as 1.16 in both the Smith

(1987) and Fatti (1994) papers. The Fluid Factor is thus the

reflectivity of the Poisson Impedance, where the Shear Impedance

has been additionally scaled so that amplitudes are close

to 0.


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REFERENCES

Castagna, J.P., Batzle, M.L., and Eastwood, R. L., 1985.Relationships between compressional and shear-wave velocities

in elastic silicate rocks: Geophysics, 50, p. 571 – 581.

Fatti, J.L., Smith, G.C., Vail, P.J., Strauss, P.J. and Levitt, P.R.,

1994. Detection of gas in sandstone reservoirs using AVO

analysis: a 3-D seismic case history using the Geostack

technique: Geophysics, 59, 1362 – 1376.

Quakenbush, M., Shang, B., and Tuttle, C, 2006. Poisson

Impedance: The Leading Edge, 25, 128 – 138.

Smith, G.C., and Gidlow, P.M., 1987. Weighted stacking for rock

property estimation and detection of gas: Geophysical

Prospecting, 35, 993 – 1014.

2274 poisson impedance

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