Post on 17-Jul-2020
3D high order seismic imaging salt domes in thecontext of RTM algorithm using adjoint-based
methods.
Javier Abreu, Roland Martin, Jose Darrozes
May 2020
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 1 / 23
Content
1 General context
2 Methodology
3 Preliminar results.
4 Perspectives.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 2 / 23
Salt dome basins in Mexico.
Figure 1: Mexican salt basin [Garcıa, 1983]
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 3 / 23
Characteristics of salt structures.
High impermeabilityChange shape and flow through adjacent rocks.Generally they form a trap for oil and natural gas. Many hydrocarbonreservoirs are located in a context of salt tectonics.
Figure 2: Example of a petroleum system with a salt domeJavier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 4 / 23
Characteristics of seismic images from salt domes.
Bad quality below the salt structure.
The base of the salt is not well defined.
High concentration of noise attributed to multiples.
Figure 3: Example of a seismic image of a complex geology region including salt domes. Taken from[Buehnemann et al., 2002]
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 5 / 23
Seismic imaging.
Figure 4: Forward model. Seismic data acquisition
d = g(m), (1)
where g is an operator that relates the data d recorded by the receiversand the parameters from the subsoil m.Inversion techniques:
Migration approach.
Direct inversion.
Inverse problem theory.Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 6 / 23
Elastodynamic equations.
We have to solve the elastodynamic equations, that govern the wavepropagation through the subsoil. For lack of space, I show the 2Delastodynamic equations .
ρ∂vx∂t
=∂τxx∂x
+∂τxz∂z
+ fx ,
ρ∂vz∂t
=∂τxz∂x
+∂τzz∂z
+ fz ,
∂τxx∂t
= (λ+ 2µ)∂vx∂x
+ λ∂vz∂z
,
∂τzz∂t
= (λ+ 2µ)∂vz∂z
+ λ∂vx∂x
,
∂τxz∂t
= µ(∂vx∂z
+∂vz∂x
).
* fx ,z could be point sources or moment tensors.* Finite differences: Second order, staggered grids [Virieux, 1986].* Absorbing boundary conditions (PML) [Komatitsch and Martin, 2007].
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 7 / 23
Reverse Time Migration based on adjoint theory.
Reverse Time Migration ⇒ RTMAccording to [Chang and McMechan, 1986], there are three stages in thealgorithm:
Forward modeling: Solution of the elastodynamic equation, we usedpoint sources.
Adjoint modelling: Solution of the elastodynamic equations in reversetime.*Adjoint source inversion:f †(x , t) =
∑nrr=1
(u(xr ,T − t)− d (xr ,T − t)
)*Adjoint source migration: f †(x , t) =
∑nrr=1 d (xr ,T − t)
Classical imaging condition*I (x) =
∑Nn=1 u(x ,N + 1− n)u†(x , n)
*Normalized by the forward wavefield: I (x) =∑N
n=1 u(x ,N+1−n)u†(x ,n)∑Nn=1
(u(x ,N+1−n)2
* Normalized by the adjoint wavefield: I (x) =∑N
n=1 u(x ,N+1−n)u†(x ,n)∑Nn=1
(u†(x ,N+1−n)2
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 8 / 23
Sensitivity Kernels.
Misfit function ⇒χ(m) = 12
∑nrr=1
∫ T0 ||u(xr , t,m)− d (xr , t)||2dt.
Frechet derivatives [Tromp et al., 2005], [Monteiller et al., 2015]:
δχ =nr∑r=1
∫ T
0
(u(xr , t,m)− d (xr , t)
)· δu(xr , t,m)dt
Frechet derivatives with respect to the logarithm of velocity, density andLame coeficients.
Kρ(x) = −∫ T
0ρ(x)u†(x ,T − t) · ∂2
t u(x , t)dt,
Kκ(x) = −∫ T
0(λ(x) + 2µ(x))∇ · u†(x ,T − t)∇ · u(x , t)dt,
Kµ(x) = −2
∫ T
0µ(x)∇u†(x ,T − t) : ∇u(x , t)dt,
Kβ(x) = 2(Kµ −4
3
µ
κKκ), Kα(x) = 2(
κ+ 43µ
κ)Kκ.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 9 / 23
Parameters and characteristics of the code to solvethe 3D simulation.
We use UniSolver to solve the elastodynamic equation showed previously,which is a FORTRAN, high order, finite differences-based code in 3dimension and following a parallel approach. We use supercomputers andwe also applied boundary conditions of the CPML type[Komatitsch and Martin, 2007], [Martin et al., 2010]. We use pointsources.Receptors ⇒ 500.Sources ⇒ 250.Frequency ⇒ 4[Hz]Longitude x⇒ 400(m)Longitude y⇒ 3600[m]Longitude z⇒ 9680.0[m]Total time ⇒ 3.825(s)∆x ⇒ 8.0[m], ∆y ⇒ 8.0[m], ∆z ⇒ 8.0[m], ∆t ⇒ 0.00045[s]nx⇒ 50, ny⇒ 450, nz⇒ 1210, nt⇒ 8500
Y
Z
X
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 10 / 23
Velocity and density salt dome models.
Figure 5: P velocity model [m/s] Figure 6: Density model [kg/m3].
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 11 / 23
Example of a 2D forward propagation.
Distancia Horizontal [m]
Pro
fun
did
ad
[m
]
0 2000 4000 6000 8000 10000 12000 14000 16000
0
2000
4000
6000
8000
10000
(a) t = 1.525s.
Distancia Horizontal [m]
Pro
fun
did
ad
[m
]
0 2000 4000 6000 8000 10000 12000 14000 16000
0
2000
4000
6000
8000
10000
(b) t = 2.275s.
Distancia Horizontal [m]
Pro
fun
did
ad
[m
]
0 2000 4000 6000 8000 10000 12000 14000 16000
0
2000
4000
6000
8000
10000
(c) t = 3.275s.
Distancia Horizontal [m]
Pro
fun
did
ad
[m
]
0 2000 4000 6000 8000 10000 12000 14000 16000
0
2000
4000
6000
8000
10000
(d) t = 3.775s.
Distancia Horizontal [m]
Pro
fun
did
ad
[m
]
0 2000 4000 6000 8000 10000 12000 14000 16000
0
2000
4000
6000
8000
10000
(e) t = 4.775s.
Distancia Horizontal [m]
Pro
fun
did
ad
[m
]
0 2000 4000 6000 8000 10000 12000 14000 16000
0
2000
4000
6000
8000
10000
(f) t = 5.275s.
Figure 7: Snapshots from the forward propagation.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 12 / 23
Principal methods used to attenuate multiples.
SRME methods [Verschuur and Berkhout, 1992], which use thepredictability feature of surface related multiples to predict andattenuate them.
Change of domain methods, sometimes the multiples can beseparated from the data in another domain, the most common one isthe τ - p domain, (time of intercept and slowness).
There are some approaches which use multiples as extra informationand they do not attenuate them [Liu et al., 2015].
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 13 / 23
2D Kernels using simultaneous sources.
We used a method based on CPML boundary conditions to attenuatethe multiples.SB, TS, BS, S, and B represent the Sea bottom, top of the salt, baseof the salt, sandstone and basement interfaces respectively.The kernel with multiple attenuation shows better definition ininterfaces below the salt structure.
SB
TS
BS
S
B
0 5000 10000 15000
0
2000
4000
6000
8000
10000
Horizontal Distance [m]
Depth
[m
]
-0.01
-0.005
0
0.005
0.01
(a) Kernel lambda
SB
TS
BS
S
B
0 5000 10000 15000
0
2000
4000
6000
8000
10000
Horizontal Distance [m]
Depth
[m
]
-0.04
-0.02
0
0.02
(b) Kernel lambda attenuation multiples
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 14 / 23
A priori model.
We assumed that we can know the bathymetry, below it we used agradient with the maximal and minimal value of the real model.
0 2000 4000 6000 8000
0
500
1000
1500
2000
2500
Horizontal distance [m]
Depth
[m
]
1600
1800
2000
2200
2400
2600
Figure 8: P velocity a priori model.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 15 / 23
3D seismic sections with simultaneous sources.
The 3D simulations give more information of the model because they havea higher azimuth.
100 200 300 400 500
1
1.5
2
2.5
3
3.5
Seismograms
Tim
e [
s]
-4e-11
-2e-11
0
2e-11
4e-11
(a) Horizontal x component.
100 200 300 400 500
1
1.5
2
2.5
3
3.5
Seismograms
Tim
e [
s]
-1e-09
-5e-10
0
5e-10
1e-09
(b) Horizontal y component.
100 200 300 400 500
1
1.5
2
2.5
3
3.5
Seismograms
Tim
e [
s]
-3e-10
-2e-10
-1e-10
0
1e-10
2e-10
(c) Vertical component.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 16 / 23
P velocity kernel simultaneous sources 3D.
Figure 9: P velocity model. Figure 10: P velocity kernel
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 17 / 23
P velocity kernel separated sources 3D.
With separated sources the salt dome interfaces are reproduced almost asin the original model.
0 2000 4000 6000 8000
500
1000
1500
2000
Horizontal distance [m]
De
pth
[m
]
2500
3000
3500
4000
Figure 11: P velocity model.
0 2000 4000 6000 8000
500
1000
1500
2000
Horizontal distance [m]
De
pth
[m
]
-1000
-500
0
500
1000
Figure 12: P velocity kernel obtainedwith separated sources.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 18 / 23
Perspectives.
Continue the development of the Full Waveform Inversion (FWI) inthe UniSolver code in the context of an OBC simulation in order ofattenuate the multiples in a more efective way.
Application of the FWI to synthetic data related to complex geology(salt domes) together with gravity inversion.
Application of the FWI in real hydro-geophysic data.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 19 / 23
References I
Buehnemann, J., Henke, C. H., Mueller, C., Krieger, M. H., Zerilli, A.,and Strack, K. M. (2002).Bringing complex salt structures into focus—a novel integratedapproach.In SEG Technical Program Expanded Abstracts 2002, pages 446–449.Society of Exploration Geophysicists.
Chang, W.-F. and McMechan, G. A. (1986).Reverse-time migration of offset vertical seismic profiling data usingthe excitation-time imaging condition.Geophysics, 51(1):67–84.
Garcıa, L. B. (1983).Domos salinos del sureste de mexico. origen: Exploracion: Importanciaeconomica. in spanish. salt domes of southeastern mexico. origin:Exploration. economic importance.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 20 / 23
References II
Komatitsch, D. and Martin, R. (2007).An unsplit convolutional perfectly matched layer improved at grazingincidence for the seismic wave equation.Geophysics, 72(5):SM155–SM167.
Liu, Y., Hu, H., Xie, X.-B., Zheng, Y., and Li, P. (2015).Reverse time migration of internal multiples for subsalt imaging.Geophysics, 80(5):S175–S185.
Martin, R., Komatitsch, D., Gedney, S. D., Bruthiaux, E., et al.(2010).A high-order time and space formulation of the unsplit perfectlymatched layer for the seismic wave equation using auxiliary differentialequations (ade-pml).Computer Modeling in Engineering and Sciences (CMES), 56(1):17.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 21 / 23
References III
Monteiller, V., Chevrot, S., Komatitsch, D., and Wang, Y. (2015).Three-dimensional full waveform inversion of short-period teleseismicwavefields based upon the sem–dsm hybrid method.Geophysical Journal International, 202(2):811–827.
Tromp, J., Tape, C., and Liu, Q. (2005).Seismic tomography, adjoint methods, time reversal andbanana-doughnut kernels.Geophysical Journal International, 160(1):195–216.
Verschuur, D. and Berkhout, A. (1992).Surface-related multiple elimination: practical aspects.In SEG Technical Program Expanded Abstracts 1992, pages1100–1103. Society of Exploration Geophysicists.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 22 / 23
References IV
Virieux, J. (1986).P-sv wave propagation in heterogeneous media: Velocity-stressfinite-difference method.Geophysics, 51(4):889–901.
Javier Abreu, Roland Martin, Jose Darrozes (Geosciences Environment Toulouse)3D high order seismic imaging salt domes in the context of RTM algorithm using adjoint-based methods.May 2020 23 / 23