![Page 1: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/1.jpg)
Waveform inversion and rock physics methods for quantitative 4D seismics
Morten Jakobsen, University of Bergen and IRIS
![Page 2: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/2.jpg)
Introduction
Fahimuddin (2010):
![Page 3: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/3.jpg)
Outline• Acoustic waveform inversion
• for Vp
• for changes in Vp
• Elastic waveform inversion
• for elastic parameters
• for rock physics parameters
• Uncertainties in the rock physics model
![Page 4: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/4.jpg)
The scalar wave equation
![Page 5: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/5.jpg)
Formal solution
![Page 6: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/6.jpg)
Scattering integral equation
![Page 7: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/7.jpg)
Scattering integral equation
![Page 8: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/8.jpg)
Operator notation
![Page 9: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/9.jpg)
Operator notation
![Page 10: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/10.jpg)
The transition operator
![Page 11: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/11.jpg)
The transition operator
![Page 12: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/12.jpg)
The forward seismic modelling problem
R
V
S
![Page 13: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/13.jpg)
The forward seismic modelling problem
R
V
S
![Page 14: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/14.jpg)
T-matrix perspective
![Page 15: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/15.jpg)
T-matrix perspective
![Page 16: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/16.jpg)
T-matrix vs finite difference
![Page 17: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/17.jpg)
Distorted Born iterative (DBIT) T-matrix inversion method
![Page 18: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/18.jpg)
Distorted Born iterative (DBIT) T-matrix inversion method
![Page 19: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/19.jpg)
Distorted Born iterative (DBIT) T-matrix inversion method
![Page 20: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/20.jpg)
Distorted Born iterative (DBIT) T-matrix inversion method
![Page 21: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/21.jpg)
Marmousi model
21
![Page 22: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/22.jpg)
22
![Page 23: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/23.jpg)
SEG/EAGE salt model
23
![Page 24: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/24.jpg)
24
![Page 25: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/25.jpg)
Inversion of time-lapse seismic waveform data
Muhumuhza (2015).
![Page 26: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/26.jpg)
The Norne field
26
![Page 27: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/27.jpg)
2D Norne baseline model
27
![Page 28: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/28.jpg)
2D Norne monitor model
28
![Page 29: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/29.jpg)
2D Norne time-lapse model
29
![Page 30: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/30.jpg)
Numerical experiment
• The DBIT inversion method in differential time-lapse mode will be used in an attempt to reconstruct the monitor model and the corresponding time-lapse changes, with the baseline model as the initial model.
• The grid sizes for modelling and inversion is (25m x 5m) and (100m x 5m), respectively.
• Local minima are avoided by using a multi-scale regularization technique with the following selected frequencies: (1, 3, 5, 7.5, 12, 15, 18, 20) Hz. 30
![Page 31: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/31.jpg)
Frequency domain seismic waveform data at 20 Hz
31
![Page 32: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/32.jpg)
Inverted monitor model at 1 HZ
32
![Page 33: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/33.jpg)
Inverted monitor model at 3 Hz
33
![Page 34: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/34.jpg)
Inverted monitor model at 5 Hz
34
![Page 35: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/35.jpg)
Inverted monitor model at 7.5 Hz
35
![Page 36: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/36.jpg)
Inverted monitor model at 12 Hz
36
![Page 37: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/37.jpg)
Inverted monitor model at 15 Hz
37
![Page 38: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/38.jpg)
Inverted monitor model at 18 Hz
38
![Page 39: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/39.jpg)
Inverted monitor model at 20 Hz
39
![Page 40: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/40.jpg)
2D Norne monitor model
40
![Page 41: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/41.jpg)
Inverted time-lapse model
41
![Page 42: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/42.jpg)
2D Norne time-lapse model
42
![Page 43: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/43.jpg)
Effects of random noise
43
![Page 44: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/44.jpg)
The true model
![Page 45: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/45.jpg)
Inverted model at 40 Hz40 Hz
Velocity model inverted from noiseless seismic waveform data (DBIT)
Velocity model inverted from noisy seismic waveform data (DBIT, SN = 20 dB)
![Page 46: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/46.jpg)
Elastic wave equation
![Page 47: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/47.jpg)
Actual and reference media
![Page 48: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/48.jpg)
Scattering integral equation
![Page 49: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/49.jpg)
Born approximation
D
x
x’
![Page 50: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/50.jpg)
Inversion friendly form
![Page 51: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/51.jpg)
Isotropic media
![Page 52: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/52.jpg)
Frechet-derivatives
![Page 53: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/53.jpg)
Linear forward model
![Page 54: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/54.jpg)
Linear inversion
![Page 55: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/55.jpg)
DBIT inversion of noiseless seismic waveform data
![Page 56: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/56.jpg)
DBIT inversion of noisy seismic waveform data
![Page 57: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/57.jpg)
Seismic waveform inversion for rock physics parameters
Zooming in on a single grid block:
Pilskog, Lopez and Jakobsen (2014)
![Page 58: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/58.jpg)
References• Pilskog, I., Lopez, M. and Jakobsen, M., 2015.
Linearized waveform inversion for fracture density. Extended abstract, 16th International Workshop on Seismic Anisotropy, Brazil.
• Jakobsen, M. and Pilskog, I., 2016. Gassmann-consistent Born inversion for fracture density. Extended abstract, 78th EAGE annual meeting, Vienna.
![Page 59: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/59.jpg)
Born approximation for the effects of stiffness perturbations
D
x
x’
![Page 60: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/60.jpg)
Seismic wave propagation in cracked porous media
![Page 61: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/61.jpg)
Rock physical parametrization of the reference medium and perturbation
![Page 62: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/62.jpg)
Frechet-derivative of the scattered wavefield wrt. the fracture density
![Page 63: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/63.jpg)
Matrix representation
![Page 64: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/64.jpg)
Regularized linear inversion
![Page 65: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/65.jpg)
True vs inverted fracture density models
![Page 66: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/66.jpg)
Elastic constants of the true model
![Page 67: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/67.jpg)
Elastic constants of the inverted model obained by ignoring the effects of pore
fluid pressure communication
![Page 68: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/68.jpg)
Elastic constants of the inverted model obtained including the effects of pore fluid
pressure communication
![Page 69: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/69.jpg)
Uncertainties in the rock physics model
• Are Gassmann’s formulae always valid?
• How do we model pressure effects?
• How about clay content and other parameters.
• Contact theory vs inclusion models.
![Page 70: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/70.jpg)
Unified inclusion model
Jakobsen et al. (2003)
![Page 71: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/71.jpg)
The t-matrix of a single communicating cavity
Jakobsen and Hudson (2003)
![Page 72: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/72.jpg)
Gassmann-consistent low-frequency limit
![Page 73: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/73.jpg)
Predicted vs observed velocity and attenuation spectra of clayey sandstones
![Page 74: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/74.jpg)
Predicted ultrasonic velocity and attenuation in clay-bearing sandstones
![Page 75: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/75.jpg)
![Page 76: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/76.jpg)
Rock physics modelling of log data from the Norne field
76
![Page 77: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/77.jpg)
77
![Page 78: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/78.jpg)
78
![Page 79: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/79.jpg)
79
![Page 80: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/80.jpg)
80
![Page 81: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/81.jpg)
81
![Page 82: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/82.jpg)
82
![Page 83: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/83.jpg)
83
![Page 84: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/84.jpg)
84
![Page 85: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/85.jpg)
Field scale statistical analysis
85
![Page 86: Waveform inversion and rock physics methods for ... · Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS](https://reader030.vdocuments.net/reader030/viewer/2022040212/5e8174004913d6182f6eeb13/html5/thumbnails/86.jpg)
Concluding remarks• The DBIT method of Jakobsen and Ursin (2015) =
a powerful tool for seismic FWI in time-lapse mode, suitable for uncertainty analysis (Eikrem et al., 2015).
• An elastic version of the DBIT method is currently under development.
• Rock physics can help FWI in anisotropic media.
• Uncertainties in the rock physics model can be dealt with in a systematic manner.