Seismic Inversion4 2k3671

Seismic inversion

Seismic inversion course, UPPA, 2008

Course Outline General aspects of seismic inversion ƒ Concept and purpose ƒ Petrophysical basis ƒ Data requirements ƒ Overview of methods and basic inversion process

Poststack inversion – practical workflow ƒ Data QC ƒ Wavelet extraction ƒ A priori model building ƒ Inversion parameterization and QC of results

Prestack inversion – practical workflow ƒ Data QC ƒ Wavelet extraction ƒ A priori model building ƒ Inversion parameterization and QC of results

Advanced inversion techniques ƒ Geostatistical inversion ƒ t PP/PS inversion ƒ 4D inversion

2 - Seismic inversion course, UPPA, 2008

Geostatistical inversion

3 - Seismic inversion course, UPPA, 2008

Geostatistical inversion concept Generate impedance models that satisfy the statistics of the input data: mean, variance, variogram

Impedance models are geologically constrained:

• stratigraphic framework • 3D a priori information • variograms Wavelet

Vertical covariance on Well log 1 0

Amplitude 0

time

Horizontal variogram on seismic

γ (h)

AI

1

20ms 0

4 - Seismic inversion course, UPPA, 2008

Statistical LF a priori model

800 m h

time Mean Mean +/- 2*s.d.

Variogram analysis Variogram: Mean squared difference between pairs of points as a function of distance

Horizontal variogram (seismic amplitude)

Semi-variogram Model Data variance

Lag Distance (feet)

Horizontal variograms (2D) are calculated parallel to stratigraphy

Vertical variogram (AI well logs)

Semi-variogram Data variance Combined Model Model Structure 1 Model Structure 2

Vertical (1D) variograms along the vertical direction (Courtesy O. Dubrule)

5 - Seismic inversion course, UPPA, 2008

Lag Distance (feet)

2-22

Geostatistical inversion algorithm For each global realization Define a random path through all nodes (x,y) to be simulated

Trace location to be simulated

For each node (x,y) perform a local optimization ƒ

generation of a large number of local realizations of acoustic impedance traces, such that input data statistics are honoured

ƒ

convolution with the wavelet

ƒ

comparison with the actual seismic

ƒ

retain the best trace which becomes conditioning data

(x,y)

Go to next node

Actual seismic trace 6 - Seismic inversion course, UPPA, 2008

Local realizations

(Courtesy O. Dubrule)

Dozens of realizations… Real. 7

Real. 27

All honour the well and seismic data Real. 13

7 - Seismic inversion course, UPPA, 2008

Real. 31

Main features of geostatistical inversions One realisation

4

AI (km/s . g/cc)

9

Mean

Impedance realizations honour - seismic data - well data Great number of AI realisations => uncertainty on impedance results High vertical frequency of impedance realizations controlled by vertical variogram model

SD

Impedance results are at high resolution related to the stratigraphic grid definition (~ 2 - 8m ; ~ 0.5 - 2ms) 0

8 - Seismic inversion course, UPPA, 2008

σAI (km/s . g/cc)

0.7

Frequency bandwidth in a geostatistical inversion Statistical layer constraints control low frequencies Seismic amplitudes control medium frequencies Variogram model controls high frequencies

Seismic bandwidth

(Courtesy E. Robein & L. Barens)

9 - Seismic inversion course, UPPA, 2008

5-9

How to summarise geostatistical inversion results? Threshold impedance probability without seismic

1

P (AI > 6.6)

Threshold impedance probability with seismic

0

N

10 - Seismic inversion course, UPPA, 2008

(Courtesy O. Dubrule)

From impedance to petrophysical properties 50 Impedance realizations 50 Porosity realizations

Impedance vs. Porosity

11 - Seismic inversion course, UPPA, 2008

Collocated cokriging

Deterministic versus Stochastic inversion The mean of all stochastic realizations looks like the deterministic, but it is different in details Ra-10 w

Ra-7 w

Ra-1 w

Ra-10 w

Ra-1 w

Ra-7 w

0.25ms sampling rate

4ms sampling rate

Reservoir Top

15ms

Reservoir Top

Reservoir Base

Reservoir Base

STOCHASTIC REALIZATION

DETERMINISTIC Red color indicates low AI

& porosity development

Ra-10 w

Ra-1 w

Ra-7 w

Litho 3 ∅ > 15% Litho 2 10<∅ < 15%

W -10

Reservoir Top

Litho 1 ∅ < 10%

W -1 W -7

Reservoir Base 4 km

CO-SIMULATED LITHOTYPE Depth Map

12 - Seismic inversion course, UPPA, 2008

t PP/PS inversion

13 - Seismic inversion course, UPPA, 2008

t PP/PS inversion Simultaneous inversion of PP and PS seismic volumes PS data need to be transformed into PP time and reflections need to be correlated Calibration of PS data with shear-wave logs is necessary t PP/PS inversion often constrains IS better than single PP inversion

14 - Seismic inversion course, UPPA, 2008

PP prestack gather

PS prestack gather (From Margrave & Stewart, 2001)

t inversion results ΔIP

ΔIS ΔIP-ΔIS (From Margrave & Stewart, 2001) 15 - Seismic inversion course, UPPA, 2008

t inversion case study: Impedance crossplots PP-PS t inversion

ΔIp/Ip

ΔIp/Ip

PP single inversion

ΔIs/Is

ΔIs/Is LOG DATA

ΔIs/Is from single PP inversion: ƒ Wrong polarity at top reservoir ƒ Appears to be simply a scaled version of ΔIp/Ip

ƒ Correct polarity at top reservoir ƒ Independent parameter

Oil sands Is

ΔIs/Is from t PP-PS inversion:

Ip

Shales Vclay

16 - Seismic inversion course, UPPA, 2008

t inversion case study: 3D results ΔF, t inversion

ΔF is the fluid factor, the product of ΔIp/Ip and ΔIs/Is, which highlights zones of gas

17 - Seismic inversion course, UPPA, 2008

4D inversion

18 - Seismic inversion course, UPPA, 2008

3D Simultaneous Elastic Inversion in a Stratigraphic Framework Macro Stratigraphic Grid Framework

19 interpreted horizons in an interval of 400 ms

Micro Stratigraphic Grid Framework 173 layers (5ms/5m)

Vp,Vs and ρ: 3D kriging of low- filtered log data

Model optimization: Simulated Annealing Perturbations: Vp, Vs, ρ and time Case study: ƒ Δρ linked with ΔVp through Gardner’s relation 19 - Seismic inversion course, UPPA, 2008

4D Coupled Inversion Workflow Monitor a priori model building Base a priori model building

• Base inversion interpretation • Base/Monitor time shift estimation • Rock Physics Model

3D simultaneous inversion Base acquisition

3D simultaneous inversion Monitor acquisition

(P,S Impedance)

(P,S Impedance)

Δ Ip, Δ Is Base/Monitor QC and interpretation 20 - Seismic inversion course, UPPA, 2008

Layer 42 - P Impedance - Base Inversion gr/cm3 x m/s

6500

10 ms

100 m

Well B

Well D

4000

42

Well C Well E

Well A

21 - Seismic inversion course, UPPA, 2008

Layer 42 - P Impedance - Monitor Inversion 6500

10 ms

gr/cm3 x m/s

100 m

Well B

Well D

4000

42

Well C Well E

Monitor inversion performed with the same a priori constraints as Base inversion

22 - Seismic inversion course, UPPA, 2008

Well A

10 ms

Layer 42 - Delta P Impedance: Base-Monitor gr/cm3 x m/s

Base

+600

Well B

- 600

Well D

42

10 ms

100 m Well C

Monitor

Well E

42 Monitor inversion performed with the same a priori constraints as Base inversion 23 - Seismic inversion course, UPPA, 2008

Well A