elastic impedance (ei) inversion

1

Elastic Impedance (EI)

Inversion

2

Gathers Stack

Inversion

Estimate

Z= VP

Seismic Lithology Estimation

Traditional methods of seismic lithology estimation involve stack followed by

inversion. This allows for only the estimation of acoustic impedance, which is not

sufficient for inferring fluid content.

3

Gathers Stack

Inversion AVO Analysis

Attribute 1 Attribute 2

Estimate VP, VS, and

Estimate

Z= VP

The AVO method allows us to use multiple attributes to simultaneously

estimate VP, VS, and , thus inferring fluid and/or lithology.

Seismic Lithology

Estimation

4

CDP Gather Data (example)

5

Range Limited Stacking

Gathers

AVO Analysis

Near Stack Far Stack

Above, we see a simple flowchart for range-limited stacking. Range-limited

stacking, using constant offsets or constant angles, is very robust. But how

do we interpret the results?

6

(a)

(b)

Here are the (a) near angle

(0o-15o) and (b) far angle

(15o-30o) stacks from the

Colony seismic dataset.

Notice that the amplitude

of the “bright-spot” event

at about 630 ms is

stronger on the far-angle

stack than it is on the

near-angle stack. As we

saw earlier, this is a gas-

sand induced “bright-

spot”.

Range Limited Stacking Over Gas Sand

7

Here is a crossplot

of the near and far

offset, with

several high

amplitude zones

highlighted.

Cross-plotting Angle Range Stacks

[0 – 15 deg] stack [1

5 –

30

de

g]

sta

ck

8

Here are the highlighted zones from the crossplot shown back on

the seismic section. Note that the gas sand zone has been well

delineated.

Top GAS

Base GAS

Coal

9

The above plot shows the (a) near-angle stack (0-15o), and (b) far- angle stack (15-30o)

over a 3D channel sand. To enhance the amplitude display, the amplitude envelope has

been averaged over a 10 ms window and the Z-score transform has been applied.

Again, note the excellent delineation of the anomaly.

Angle Range Stacks

(a) (b)

10

GXT 3D preSDM showing AVO anomalies over producing fields

Average absolute amplitude Top Balder +50 - +200

Near stack (0º-25º) Far stack (25º-50º)

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Near stack Far stack

GXT 3D preSDM showing AVO anomalies over producing fields

12

From Range Limited Stacking to Elastic Impedance

Range-limited stacking, using constant offsets or constant angles, is very

robust, and avoids misaligned event problems. But what does it mean?

Patrick Connolly, from BP, came up with a novel approach to the

interpretation of range limited stacks, called Elastic Impedance.

Elastic Impedance is based on the Aki-Richards equation, and the next few

slides will develop the concept.

13

Elastic Impedance Theory

Recall that the Aki-Richards Equation can be written:

222 tansinsin CBAR

,2

1:

P

P

V

VAwhere

22

242

1

P

S

S

S

P

S

P

P

V

V

V

V

V

V

V

VB

.2

1:

P

P

V

VCand

Connolly (1999) proposed that, analogously to acoustic impedance, we could define

elastic impedance (EI) as:

EIEI

EIR ln

2

1

2

1

14

If we let

2

P

S

V

VK and note that ,sintantansin 2222

we can re-arrange the Aki-Richards equation to get:

222 sin41sin8tan1

2

1ln KK

V

V

V

VEI

S

S

P

P

If we let K be a constant, we can write:

222sin41sin8tan1

lnlnlnln kk

SP VVEI

222sin41sin8)tan1(

ln kk

SP VV

15

If we then integrate and exponentiate, we get the following form for EI:

)sinK1()sinK8(

S

)tan1(

P

222

VV)(EI

2

P

2

S

V

VKwhere

Note that if = 0o, EI reduces to Acoustic Impedance (AI), where:

PVAIEI 0

16

The preceding equation used all three terms in the Aki-Richards equation. For angles

greater than 300, this equation does not give a straight line fit. For a higher angle

(larger offsets), we use only the first two terms, which leads to:

)sin1()sin8()sin1( 222

)( KK

SP VVEI

2

P

S

V

VKwhere

Again note that where = 0o, we get:

PVAIEI 0

17

The transformation of an AI log from 0° to 30° results in a generally similar

log but with lower absolute values. The apparent acoustic impedance

decreases with an increase in angle. The percentage decrease is greater for

an oil sand than for shale.

Connolly 1999

Elastic Impedance – Effect of Oil Saturation

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Elastic Impedance – Data Example

The following figure, from Connolly (1999) shows the computed curves for AI and EI at 30 degrees:

19

The following figure, also from Connolly (1999) shows

that when we scale the curves shown on the previous slide, we get a better

separation for the oil sands using EI over AI:

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EI Inversion Steps

Gathers

AVO Analysis

Near angle

stack at 1

Far angle

stack at 2

Invert to EI(1) Invert to EI(2)

22

After Mavko, 2007

23

After Mavko, 2007

24

After Mavko, 2007

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Angle Stack at 15 degree

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Elastic Impedance at 15 degree

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Elastic Impedance of 20 degree

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Elastic Impedance of 24 degree

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32

Thank You

38

Lithofacies Classification based on linear discriminant analysis

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End of Slide

elastic impedance (ei) inversion

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