Fossa Carolina: SH field data example. 47 sources and 48 ... 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8 time [s]. Data comparison shot no. 1 field data model data .... 2D visco-elastic time-domain SH-problem ρ. ∂vy. ∂t. = ∂σxy. ∂x. +. ∂σyz. ∂z. + fy ,.
Field Data Application: Simple Love wavefield with weak dispersion Dokter et al. 2017
SH-FWI of weak-dispersive Love wave field data
Sequential multi-parameter Vs-Density FWI of low-pass filtered data with fmax = [15], [20], [40], [80] Hz
Field Data Application: Complex Love wavefield with strong dispersion K¨ ohn et al. 2018
Connecting Rhine and Danube via Fossa Carolina canal
Fossa Carolina (2015 AD)
Fossa Carolina (2015 AD)
Question: Can we derive the canal structure by SH-FWI?
Fossa Carolina: SH field data example
47 sources and 48 receivers distributed on a 36 m long profile
Fossa Carolina: FATT model Fossa Carolina first arrival traveltimes
RMS TT error: 10 ms
0.1 0.05
field data FATT model data
0.0
450 400
1
300 250
3
200
4 5 6
150 100
FATT result 5
50 10
15
20 Distance [m]
25
30
35
Vs [m/ s]
350
2 Depth [m]
Time [s]
0.15
Data comparison (FATT model, elastic)
Data comparison shot no. 1
0.1
field data model data
0.2
time [s]
0.3
0.4
0.5
0.6
0.7
0.8 0
5
10
15
20
offset [m]
25
30
Data comparison (FATT model, Qs=30)
Data comparison shot no. 1
0.1
field data model data
0.2
time [s]
0.3
0.4
0.5
0.6
0.7
0.8 0
5
10
15
20
offset [m]
25
30
Data comparison (FATT model, Qs=15)
Data comparison shot no. 1
0.1
field data model data
0.2
time [s]
0.3
0.4
0.5
0.6
0.7
0.8 0
5
10
15
20
offset [m]
25
30
Data comparison (FATT model, Qs=10)
Data comparison shot no. 1
0.1
field data model data
0.2
time [s]
0.3
0.4
0.5
0.6
0.7
0.8 0
5
10
15
20
offset [m]
25
30
Data comparison (FATT model, Qs=10, dispersion corr.)
Data comparison shot no. 1
0.1
field data model data
0.2
time [s]
0.3
0.4
0.5
0.6
0.7
0.8 0
5
10
15
20
offset [m]
25
30
FATT model (dispersion corr.)
450 400
1
300 250
3
200
4 5 6
1
150 100
FATT result 5
50 10
15
20 Distance [m]
25
30
35
Sequential mono-parameter Vs-FWI of low-pass filtered data with fmax = [20], [30], [40], [50], [60], [70], [80] Hz
Vs [m/s]
Depth [m]
350 2
SH-FWI result (low-pass filter strategy)
450 400
1
300 250
3
200
4 5 6
1
150 100
FWI result (L workflow) 5
10
50 15
20 Distance [m]
25
30
35
Sequential mono-parameter Vs-FWI of low-pass filtered data with fmax = [20], [30], [40], [50], [60], [70], [80] Hz
Vs [m/s]
Depth [m]
350 2
FWI result (low + band-pass filter strategy)
450 400
1
300 250
3
200
4 5 6
2
Vs [m/s]
Depth [m]
350 2
150 100
FWI result (LB workflow) 5
10
50 15
20 Distance [m]
25
30
35
Sequential mono-parameter Vs-FWI of band-pass filtered data with fmin /fmax = [20, 80], [30, 80], [40, 80], [50, 80], [60, 80], [70, 80] Hz
FWI result (low + band + low-pass filter strategy)
450 400
1
300 250
3
200
4 5 6
3
150 100
FWI result (LBL workflow) 5
10
50 15
20 Distance [m]
25
30
35
Final mono-parameter Vs-FWI of low-pass filtered data with fmax = 80 Hz
Vs [m/s]
Depth [m]
350 2
Data comparison (FATT result, worst data fit)
0.1
field data model data
0.2
time [s]
0.3
0.4
0.5
0.6
0.7
0.8
−30
−25
−20
−15 offset [m]
−10
−5
0
Data comparison (LBL-FWI result, worst data fit)
0.1
field data model data
0.2
time [s]
0.3
0.4
0.5
0.6
0.7
0.8
−30
−25
−20
−15 offset [m]
−10
−5
0
FATT vs. FWI vs. Archaeological Excavation
Fossa Carolina: archaeological excavation
FATT vs. archaeological excavation
FATT vs. archaeological excavation
FWI L-workflow vs. archaeological excavation
FWI LBL-workflow vs. archaeological excavation
FWI LBL-workflow vs. archaeological excavation
Conclusions and Outlook
Conclusions Low-frequency Love wave dominates sequential FWI of low-pass filtered data. Resolution improvement by inversion of Love- and high-frequency refracted SH-data using LBL-workflow Structures in LBL-FWI result can be correlated with features from archaeological excavation Outlook 2D multi-parameter Vs-Qs FWI
Acknowledgements
The German Ministry of Education and Research (BMBF) for funding the ANGUS-II Project The European Union for funding the DESCRAMBLE project (grant agreement number 640573) The DFG for funding the SPP 1630 Harbours The forward modeling and FWI were performed on the NEC-cluster at the computing center of Kiel University
Thank you very much for your attention
Appendix
Fossa Carolina: Other FWI approaches 200000.0
Model roughness ||∆m||2
175000.0
L B MovB LB LBB LBL FATT
150000.0 125000.0 100000.0 75000.0 50000.0 25000.0 -2e-13 -1.8e-13 -1.6e-13 -1.4e-13 -1.2e-13 -1e-13 Misfit function E
FWI result (low + band + low-pass filter strategy)
450 400
1
300 250
3
200
4 5 6
150 100
FWI result (LBL workflow) 5
LBL approach
10
50 15
20 Distance [m]
25
30
35
Vs [m/s]
Depth [m]
350 2
FWI result (band-pass filter strategy)
450 400
1
300 250
3
200
4 5 6
Vs [m/s]
Depth [m]
350 2
150 100
FWI result (B workflow) 5
10
50 15
20 Distance [m]
25
30
35
Sequential FWI of band-pass filtered data with fmin /fmax = [20, 80], [30, 80], [40, 80], [50, 80], [60, 80], [70, 80] Hz
FWI result (moving band-pass filter strategy)
450 400
1
300 250
3
200
4 5 6
Vs [m/s]
Depth [m]
350 2
150 100
FWI result (MovB workflow) 5
10
50 15
20 Distance [m]
25
30
35
Sequential FWI of moving band-pass filtered data with fmin /fmax = [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80] Hz
FWI result (low + band + band-pass filter strategy)
450 400
1
300 250
3
200
4 5 6
150 100
FWI result (LBB workflow) 5
LBB approach
10
50 15
20 Distance [m]
25
30
35
Vs [m/s]
Depth [m]
350 2
The forward problem 2D visco-elastic time-domain SH-problem ∂vy ∂σxy ∂σyz = + + fy , ∂t ∂x ∂z X L ∂σxy ∂vy + rxyl , = µ0 ∂t ∂x l=1 ∂rxyl 1 ∂vy µl + rxyl , =− ∂t τσl ∂x
ρ
X L ∂σyz ∂vy + ryzl , = µ0 ∂t ∂z l=1 ∂ryzl 1 ∂vy µl + ryzl , =− ∂t τσl ∂z
with vy particle velocity, σxy , σyz shear stresses, fy source term
rxyl , ryzl memory variables, τσl relaxation times µl phase velocity corrected shear modulus
Realization of frequency-independent Qs by superposition of multiple Maxwell bodies (Blanch et al. 1995, Emmerich and Korn 1987):
P ω2 τ 2 1 + Ll=1 1+ω2σlτ 2 τs σl Qs (ω, τσl , τs ) = PL ωτσl l=1 1+ω 2 τ 2 τs σl
2D SH-waveform inversion
Inversion parameters 2D time-domain SH-waveform inversion P Pshots h ui,j ·di,j i Objective function E = rec − |ui,j ||di,j | i j ui,j = modelled data di,j = field data global correlation norm (Choi and Alkhalifah, 2012) Optimization method: preconditioned conjugate gradient Adjoint state gradients are calculated for the symmetrized visco-elastic forward problem (Yang et al. 2016, Fabien-Ouellet et al. 2017, Fabien-Ouellet, 2018) Application of 2D spatial Gaussian filter to the Vs-gradient
Multi-parameter SH FWI applicaton (Vs, density) Visco-elastic FWI results for different passive Qs models Qs=30
Qs=30 2 Depth [m]
Depth [m]
2 4
4 6
6
8
8
Qs=15
Qs=15 2 Depth [m]
Depth [m]
2 4
4 6
6
8
8
Qs=10
Qs=10 2 Depth [m]
Depth [m]
2 4
4 6
6 8
5
100
150
10
200
15 Distance x [m] 250 Vs [m/s]
20
300
from Dokter et al. 2017
25
350
400
8
900
5
1000
1100
10
1200
15 Distance x [m]
1300 1400 1500 Density [kg/m3]
20
1600
1700
25
1800
1900
Multi-parameter SH FWI applicaton (Vs, density) Visco-elastic FWI result (shear modulus parametrization) Shear modulus from Vs-density FWI Depth [m]
2 4 6 8 Shear modulus FWI Depth [m]
2 4 6 8
0
5
0.2
0.4
10
0.6
15 Distance x [m]
0.8 1 1.2 Shear modulus [Pa]
20
1.4
1.6
25
1.8
2 8
x 10
Multi-parameter SH FWI applicaton (Vs, density) Comparing data fits of different FWI approaches Data comp. shot no. 42
Data residuals
0.15 0.2
Time [s]
0.25 0.3 0.35 0.4 0.45
field data model data
elastic FWI
0.15 0.2
Time [s]
0.25 0.3 0.35 0.4 0.45
(visco)-elastic FWI (Qs=15)
0.15 0.2
Time [s]
0.25 0.3 0.35 0.4 0.45 −20
(visco)-elastic shear-modulus FWI (Qs=15) −15
−10 Offset [m]
−5
−20
−15
−10 Offset [m]
−5
Elastic multi-parameter FWI synthetic example Rayleigh vs. Love wave FWI (from Dokter et al. 2017) Vp [m/s]
True CTS model
Depth [m]
500 480
2
460 4 440 6
420 Vs [m/s]
Depth [m]
160 2 140 4
120
6
100
Depth [m]
80 Density [kg/m3]
2
1700
4
1600 1500
6 5
10
15 Distance [m]
20
25
1400
Elastic multi-parameter FWI synthetic example Rayleigh vs. Love wave FWI (from Dokter et al. 2017) Depth [m]
V [m/s]
CTS Love/SH FWI result
CTS Rayleigh/PSV FWI result
p
500 480
2
460
No Vp update
4
440
6
420 Vs [m/s]
Depth [m]
160 2
140
4
120 100
6
Depth [m]
80 Density [kg/m3]
2
1700
4
1600 1500
6 5
10
15 Distance [m]
Code SH PSV
20
25
5
10
15
20
25
Distance [m]
Computation Time/Iteration [minutes] 4.4 14.8
Memory [Gb] 1.59 2.56
1400