Deriving the Poisson Impedance in Hampson-Russell Software · The “Poisson Impedance” is an attribute that is derived from a combination of the P- and S-impedance values and is

Deriving the Poisson Impedance in Hampson-Russell Software

Kevin GerlitzGeophysicist, VHR JakartaApril 2006

The “Poisson Impedance” is an attribute that is derived from a combination 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

POISSON IMPEDANCEThe idea of the Poisson Impedance is illustrated in the figure on the left.

In the Acoustic Impedance / Shear Impedance cross-plot, it is difficult to discriminate the litho-fluid distributions on the horizontal and vertical axes. But rotating the axis to be parallel with the trends would ensure a distinct discrimination of the 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)

POISSON IMPEDANCERecall that the Poisson’s Ratio can be written as:

)2()(2

2)(2

22222

22

VsVpVVVV

VVVV

SP

SP

SP

SP −−

+=

−−

=σ

If we rewrite the PI=AI – cSI in terms of velocities and density, then we can define the so-called “Poisson Velocity”

σρρρρ VcVVcVVPI SPSP =−=−= )(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 scaling factor, D, then

σσ DV=

(1)

(2)

(3)

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.

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-Impedance logs.

Click on the Math… button

POISSON IMPEDANCE

Select the Log Mathsoption and select the P-and S-impedance logs for the input. Make the Output Log Type of type “Poisson Impedance”…

POISSON IMPEDANCEType in the equation for the Poisson Impedance.

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

POISSON IMPEDANCE

Similarly, we can derive the c term from the cross-plot of the P-and S-Impedance logs for 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.

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.

POISSON IMPEDANCEThe same process can be applied to the P-and S-impedance volumes derived from the seismic using Simultaneous Inversion. In this case, use Process > Utility > Trace Mathsand follow the same workflow…

POISSON IMPEDANCEHere is the output Poisson Impedance volume with the low blue values indicating the gas zone. The PI log is spliced into the section.

POISSON IMPEDANCE The Poisson Impedance has a very close relationship with the “Fluid Factor” 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 clasticsilicate 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 wet trend are more likely to have hydrocarbons.

From Smith and Gidlow (1987)

POISSON IMPEDANCEWe can derive the following relationship between Vp/Vs and Poisson’s Ratio as follows:

2/1

2/11

⎟⎠⎞

⎜⎝⎛

−−

=σσ

S

P

VV

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

SP

SP

VV

VV

VVVV Δ

−Δ

=Δ

/)/(

σρρ VcVVPI SP =−= )(

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

(4)

(5)

POISSON IMPEDANCEThe Fluid Factor was defined as the difference between the actual Vp reflectivity and the reflectivity calculated from the mudrock line, i.e.,

S

S

P

S

VV

VVc

VpVpF 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

RR

VVc

RpRpF 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 Impedancehas been additionally scaled so that amplitudes are close to 0.

REFERENCESCastagna, 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.