10 attribute inversion

8/11/2019 10 Attribute Inversion

1/104


2/104


3/104


4/104

10-4

Seismic Lithology Estimation

Gathers Stack

InversionAVO Analysis

Attribute 1 Attribute 2

Estimate VP, VS, and

Estimate

Z= VP

The AVO method allows us to simultaneously estimate

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


5/104

10-5

Possible Attributes

But which two attributes will give us the best estimate of

these parameters? Various authors have proposed a number of options:

Range-limited stacking

Elastic Impedance

Intercept/Gradient analysis RP/RSextraction followed by inversion.

/analysis.

Lets look at the theory of these methods, and then at

some examples. As we will see, these methods combine all of the ideas

that we have considered in the course so far, starting withrock physics and progressing through AVO and post-stack inversion.


6/104


7/104

10-7

(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 thebright-spot event at

about 630 ms is

stronger on the far-

angle stack than it is

on the near-anglestack. As we saw

earlier, this is a gas-

sand induced bright-

spot.

Range limited stacking over gas sand


8/104


9/104

10-9

The zones are mapped back to the seismic. A pitfall in this method relates to

amplitude changes unassociated with fluid change.

Top Gas

Base GAS

Coal

Cross-plotting angle range stacks


10/104

10-10

Cross-plotting angle range stacks.

A solution

would be todefine more

detailedzones.



11/104

10-11

Cross-plotting angle range stacks.

Top GASBase GAS

Coal



12/104

10-12

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.


(a) (b)


13/104

10-13

Range Limited Stacking

Gathers

AVO Analysis

Near Stack Far Stack

Fluid/Lithology Interpretation

Range-limited stacking, using constant offsets or

constant angles, is very robust, and avoids misaligned

event problems. But what does it mean?


14/104

10-14

Elastic Impedancenear-offset form

Using the Aki-Richards eq., Connolly(1998) proposed

the Elastic Impedance (EI) concept to physically explainrange-limited stacks, where:

)sinK41()sinK8(

S

)tan1(

P

222

VV)(EI

2

P

2

S

V

VKwhere

Note that if =0

o

, EI reduces to Acoustic Impedance(AI), where:

PVAI


15/104

10-15

Elastic Impedancefar-offset form

Connolly(1998) proposed proposed a second form of the

Elastic Impedance (EI) concept for far offsets, wheresinreplaces tanin the first equation:

)sinK41()sinK8(

S

)sin1(

P

222

VV)(EI

2

P

2

S

V

VKwhere

Note that if =0o

, far offset EI also reduces to AcousticImpedance (AI):

PVAI


16/104

10-16

Exercise 5-1

Let us use a simple example where VP

= 1000 m/s,

VS_wet= 500 m/s, VS_gas= 667 m/s, and = 2.0 g/cc.

Work out the values for elastic impedance at = 0o and

=30ofor the wet and gas cases:


17/104

10-17

Exercise 5-1 Answers

For the wet case:

423VV)30(EI 75.05.0S25.1

P

o

20001000*2AI)0(EI o

For the gas case:

53.25VV)30(EI 56.089.0S25.1

P

o

20001000*2AI)0(EI o


18/104

10-18

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 Impedanceeffect of oil saturation


19/104

10-19

Elastic Impedancedata example

The following figure, from Connolly (1999) shows the

computed curves for AI and EI at 30 degrees:


20/104


21/104


22/104


23/104

10-23

We will now illustrate the procedure with the shallow gas sand case

study considered in the AVO section. The well logs are shown

above.

Gas sand case study


24/104

10-24

The figure above shows the previous logs after fluid substitution in the gas zone. The

EI_Nearlog on in blue was created at 7.5oand the EI_Farlog in red was created at

22.5o. Note that the NearNearinside the sand.

Gas sand case study


25/104

10-25

The figure above shows the (a) crossplot between the near and far EI logs, and

(b) the logs themselves.

Gas sand case study

(a) (b)

EI_Near EI_Far


26/104

10-26

The figure above now shows the (a) interpreted crossplot between the near and

far EI logs, and (b) the zones marked on the logs themselves. Notice the clear

indication of the gas sand zone.

Gas sand case study

(a) (b)

EI_Near EI_Far


27/104

10-27

Gas sand case study

(a)

(b)

Here are the (a) near

and (b) far anglestacks from the

seismic dataset.

Notice that the

amplitude of the

bright-spot event atabout 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.


28/104

10-28

Gas sand case study

Above is shown the inversion of the near-angle stack using an

elastic impedance model. The angle range in the stack is from 0oto

15o, so an average value of 7.5

owas used for the model.


29/104

10-29

Gas sand case study

Above is shown the inversion of the far-angle stack using an elastic

impedance model. The angle range in the stack is from 15oto 30

o,

so an average value of 22.5owas used for the model.


30/104

10-30

Gas sand case study

(a)

(b)

Here is the

comparison between

the inversions of the

(a) near-angle stack

and (b) far-angle

stack, using the

elastic impedance

concept. Notice the

decrease in the

elastic impedance

value on the far-angle stack.


31/104


32/104


33/104

10-33

Gulf coast case study

In the following set of slides, we will consider

a Gulf coast case study (we do not have

permission to tell you where, however).

This is a 3D example which presents adifferent set of problems than the 2D case

study considered last.

Note that we will be able to find the

anomalous zone using crossplot analysis, and

look for similar anomalies throughout the 3D

volume.


34/104


35/104



36/104

10-36

Near angle

stack (5- 35)

Far angle stack

(35- 65)



37/104

10-37

Initial guess acoustic impedance model




38/104

10-38

Comparing the Acoustic impedance and the Elastic impedance

logs clearly highlights the hydrocarbon zone.



39/104



40/104

10-40

Near (left) and far (right) wavelets used in inversions. Note

the decrease in frequency content with offset.



41/104


42/104

10-42

Elastic impedance inversion result.




43/104

10-43

The cross plot

shows the near

inversion on thex-axis and the far

inversion on the

y-axis.

Using the cross

plot technique

overcomes the

normalisation

issue.




44/104

10-44

The cross plot

zones are

plotted in map

view.This is a time

slice at 1200ms

and shows the

track of the

anomalous zone



45/104

10-45

RP/RSInversion

Gathers

AVO Analysis

RP Estimate RSEstimate

RP/RSinversion is a powerful method, but is dependent

on the quality of the data and the approximations used.

Invert to ZP Invert to ZS


46/104


47/104


48/104


49/104

10-49

Applying P and S inversion to seismic data

We will now look at an application of thepreceding inversion method using the Colony

sand example that we have considered in many

of our examples.

The first slide will show the full stack and the

extracted RPand RSstacks.

The second slide will show the inversions of all

three stacks.


50/104

Colony Sand Example - Gathers


51/104

10-51

Colony Sand Example - Gathers

Here are the gathers, with the correlated sonic log displayed at its

proper location.


52/104


53/104

10-53

Inversion Procedure

The inversion procedure used here involves thefollowing steps:

Insert the appropriate logs at the correct locations,

which has already been done.

Correlate the logs, which has also been done.

Pick the major seismic horizons.

Find an optimum wavelet.

Build the starting model for inversion.

Invert the data.

We will now apply this procedure to the RPandRSsections.


54/104


55/104

C l S d E l P M d l


56/104

10-56

Colony Sand Example - P-wave Model

Here is the model result, using a single well and the picked

horizons. The model is scaled to P-Impedance.

C l S d E l P I i


57/104

10-57

Colony Sand Example - P-wave Inversion

Here is the final P-wave inversion result. The low impedance just below

Horizon 2 represents the gas sand.


58/104

Colony Sand Example -S-Impedance Model


59/104

10-59

Colony Sand Example S Impedance Model

We now have the created S-Impedance model, as shown above.

Note that the new colour key represents S-wave impedance

values.


60/104

10-60

Colony Sand Example - S-wave Inversion

The result of the S-wave inversion is shown above. Notice that thegas sand below Horizon 2 is now associated with an increase inimpedance.

Th LMR A h


61/104

10-61

The LMRApproach

Goodway et al (1998) proposed a new approach to AVO

inversion based on the ,,parameters, called LMR

. Thetheory is shown below:

2

S

2

P

2

P

2

P

2

S

2

S

SP

Z2Zso

)2()V(Zand

)V(Zthen

Vand

2

VSince

PanCanadian Petroleum


62/104


63/104

10-63

From Goodway et al 1999

Original Zp vs Zs Observations


64/104


65/104

10-65

Interpreting Lambda-Rho and Mu-Rho

The original paper by Goodway et al, gives the

following physical interpretation of the lambda()

and mu()attributes: The term, or

incompressibility, is sensitive to pore fluid,

whereas the term, or rigidity, is sensitive to therock matrix.

As we saw in the theory, it is impossible to de-

couple the effects of density from and when

extracting this information from seismic data. It is therefore most beneficial to cross-plot vs

to minimize the effects of density.


66/104

Biot theory for porous rocks


67/104

10-67

Biot theory for porous rocks

Biot (1941) linked the saturated and dry frame to

the Lame coefficients in the following way:

M2drysat

sat= the Lame coefficient for the saturated rock,

dry= the Lame coefficient for the dry frame,

= the Biot coefficient, or the ratio of the volume

change in the fluid to the volume change in the

formation when hydraulic pressure is constant,

M= the modulus, or the pressure needed to force

water into the formation without changing the

volume.

G f


68/104

10-68

Gassmann theory for porous rocks

Gassmann (1951) linked the saturated and dry

frame to the Bulk modulus in the following way:

MKK 2drysat

modulus.theMt,coefficienBiotthe

,framedrytheofmodulusbulktheK

,rocksaturatedtheofmodulusbulktheK

dry

sat


69/104

Biot-Gassmann summary


70/104

10-70

Biot Gassmann summary

In summary, we can rewrite the velocity equations inthe following way using the Biot-Gassmann equations:

sat

satP

2V

sat

satP

34KV

.M

,MKK,:where

2

drysat

2

drysat

satdry

sat

SV


71/104


72/104

The constant term c and s


73/104

10-73

The constant term c and s

Note that the constant term cis simply the square of

the ratio between the dry rock P-wave velocity andthe dry rock S-wave velocity:

3

4K

2V

V

c

drydry

2

dryS

P

The key question is: how do we find the value of c?

Note that the term sis simply given by c(VS)2.


74/104


75/104


76/104


77/104

Extended LMR Analysis


78/104

10-78

Gathers

AVO Analysis

RP Estimate RSEstimate

Crossplot

Invert to ZP Invert to ZS

Transform to fand s


79/104

10-79

Whiterose example

The next five slides show and example from a well

log in the Whiterose field from offshore eastern

Canada, courtesy of Ken Hedlin and Husky Oil.

As will be seen, we will experiment with fourvalues of c: 1.333, 2, 2.333, and 2.5.

We are expecting a vertical separation between

gas and non-gas sections of the reservoir. There

is no perfect result, but a c value of 2.333 appears

to give the best separation.

S wave, P wave, Density and Porosity for

Whiterose L 08 Cretaceous Shale and Sands


80/104

10-80

Whiterose L-08 Cretaceous Shale and Sands

Cretaceous

Shale

Gas sand

Oil sand

Wet sand

Limestone

Vs Vp Den Porosity

85m

97m

95m

Courtesy, Ken Hedlin and Husky Oil

f vs s with c = 1.33 for Whiterose L-08


81/104

10-81

rho*f vs rho*s for c = 1.333

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.00 2.00 4.00 6.00 8.00

rho*f

rho*s

Shale Gas Oil Wet


82/104

f vs s with c = 2.333 for Whiterose L-08


83/104

10-83

rho*f vs rho*s for c = 2.333

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.00 1.00 2.00 3.00 4.00

rho*f

rho

*s

Shale Gas Oil Wet


84/104


85/104

10-85

Colony example

Next, we will apply the generalized LMR method tothe Colony seismic example that we were evaluatingearlier.

We will use c values of 2 (which corresponds to

LMR) and 2.333, which corresponds to a dry rockPoissons ratio of 0.125.

For the Kporevs mu result, a value of c = 2.233 wasused.

Colony Sand f with c = 2.0


86/104

10-86

Colony Sand f with c 2.0

The extraction of the

f section using a cvalue of 2.0 and the ZPand ZSinverted sections shown earlier.

Colony Sands with c = 2.0


87/104

10-87

y


s section using a cvalue of 2.0 and the ZSinverted section shown earlier.

Colony Sands vs f with c = 2.0


88/104

10-88

A cross plot of the the extractedf ands sections using a cvalue of

2.0. Two zones are shown, where red=gas and blue=non-gas.

C = 2.0Gas Zone in Red


89/104

10-89

The interpreted zones from the previous cross-plot, shown now onthe seismic section. Note the continuity of the gas sand in red.


90/104


91/104

10-91

c = 2.0

c = 2.333

Colony Sands with c = 2.333


92/104

10-92

y


s section using a cvalue of 2.333 and theZSinverted section shown earlier.

Colony Sands vs f with c = 2.333


93/104

10-93

A cross plot of the the extracted

f and

s sections using a cvalue of2.333. Two zones are shown, where red=gas and blue=non-gas.

C = 2.333Gas Zone in Red


94/104

10-94

The interpreted zones from the previous cross-plot, shown now onthe seismic section. Note the slightly improved continuity of thegas sand in red.

Blackfoot Case Study


95/104

10-95

Now, let us return to the Blackfoot case study considered earlier in thecourse. The figure above shows the AVO responses of the various events.Note that the Upper Valley porous sandstone shows a class 2 response.

(Dufour et al.)



96/104

10-96

y

The figure above shows the zero offset P-wave reflectivity, Rp, on line 95.Notice the troughs at the upper and lower valleys. (Dufour et al.)



97/104

10-97

The figure above shows the zero offset S-wave reflectivity, Rs, on line 95.Notice the different response at the upper and lower valleys than that ofthe Rp section. (Dufour et al.)



98/104

10-98

The figure above shows the fluid factor (F) on line 95. This wascomputed using the formula F = Rp g (t)Rs. Note the anomalousresponse at the Upper Valley. (Dufour et al.)


99/104


100/104


101/104



102/104

10-102

The figure above shows (b) the annotation of the potential hydrocarbon zone

on the

extracted amplitude map, and (b) the annotation of the potential

hydrocarbon zone on the

extracted amplitude map. (Dufour et al.)

(a) (b)

Conclusions


103/104

10-103

This has been a brief overview of the ElasticImpedance, R

P

/RS

inversion and LMR approaches, aswell as the general theory behind LMR from a Biot-Gassmann perspective.

The AVO method allows us to estimate two (or more)independent parameters from our prestack data.

Poststack inversion techniques can then be applied tothese extracted attributes.

The crossplot of the inverted attributes allows us toseparate the fluid and matrix effects of the reservoirrock.

In each area, the pair of attributes best suited for theparticular play needs to be evaluated using both welllog and seismic data.

Exercise 5-1 Answers


104/104

Recall that VP= 1000 m/sand VS= 500 m/s(therefore K

= 0.25), and = 2.0 g/cc. At =0o

, we have:

480VV)30(EI94.05.0

S

25.1

P

o

At = 30owe have sin= 0.5, and we get:

20001000*2AI)0(EI o

10 attribute inversion

Documents