Waveform inversion and rock physics methods for quantitative 4D seismics Morten Jakobsen, University of Bergen and IRIS
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Waveform inversion and rock physics methods for quantitative 4D seismics
Morten Jakobsen, University of Bergen and IRIS
Introduction
Fahimuddin (2010):
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
The scalar wave equation
Formal solution
Scattering integral equation
Scattering integral equation
Operator notation
Operator notation
The transition operator
The transition operator
The forward seismic modelling problem
R
V
S
The forward seismic modelling problem
R
V
S
T-matrix perspective
T-matrix perspective
T-matrix vs finite difference
Distorted Born iterative (DBIT) T-matrix inversion method
Distorted Born iterative (DBIT) T-matrix inversion method
Distorted Born iterative (DBIT) T-matrix inversion method
Distorted Born iterative (DBIT) T-matrix inversion method
Marmousi model
21
22
SEG/EAGE salt model
23
24
Inversion of time-lapse seismic waveform data
Muhumuhza (2015).
The Norne field
26
2D Norne baseline model
27
2D Norne monitor model
28
2D Norne time-lapse model
29
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
Frequency domain seismic waveform data at 20 Hz
31
Inverted monitor model at 1 HZ
32
Inverted monitor model at 3 Hz
33
Inverted monitor model at 5 Hz
34
Inverted monitor model at 7.5 Hz
35
Inverted monitor model at 12 Hz
36
Inverted monitor model at 15 Hz
37
Inverted monitor model at 18 Hz
38
Inverted monitor model at 20 Hz
39
2D Norne monitor model
40
Inverted time-lapse model
41
2D Norne time-lapse model
42
Effects of random noise
43
The true model
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)
Elastic wave equation
Actual and reference media
Scattering integral equation
Born approximation
D
x
x’
Inversion friendly form
Isotropic media
Frechet-derivatives
Linear forward model
Linear inversion
DBIT inversion of noiseless seismic waveform data
DBIT inversion of noisy seismic waveform data
Seismic waveform inversion for rock physics parameters
Zooming in on a single grid block:
Pilskog, Lopez and Jakobsen (2014)
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.
Born approximation for the effects of stiffness perturbations
D
x
x’
Seismic wave propagation in cracked porous media
Rock physical parametrization of the reference medium and perturbation
Frechet-derivative of the scattered wavefield wrt. the fracture density
Matrix representation
Regularized linear inversion
True vs inverted fracture density models
Elastic constants of the true model
Elastic constants of the inverted model obained by ignoring the effects of pore
fluid pressure communication
Elastic constants of the inverted model obtained including the effects of pore fluid
pressure communication
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.
Unified inclusion model
Jakobsen et al. (2003)
The t-matrix of a single communicating cavity
Jakobsen and Hudson (2003)
Gassmann-consistent low-frequency limit
Predicted vs observed velocity and attenuation spectra of clayey sandstones
Predicted ultrasonic velocity and attenuation in clay-bearing sandstones
Rock physics modelling of log data from the Norne field
76
77
78
79
80
81
82
83
84
Field scale statistical analysis
85
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.
Related Documents
