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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

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Data comparison (FATT model, elastic)

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Sequential mono-parameter Vs-FWI of low-pass filtered data with fmax = [20], [30], [40], [50], [60], [70], [80] Hz

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Sequential mono-parameter Vs-FWI of low-pass filtered data with fmax = [20], [30], [40], [50], [60], [70], [80] Hz

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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)

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Final mono-parameter Vs-FWI of low-pass filtered data with fmax = 80 Hz

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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)

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FWI result (LBL workflow) 5

LBL approach

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FWI result (band-pass filter strategy)

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FWI result (B workflow) 5

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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)

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FWI result (MovB workflow) 5

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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)

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FWI result (LBB workflow) 5

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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

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from Dokter et al. 2017

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Multi-parameter SH FWI applicaton (Vs, density) Visco-elastic FWI result (shear modulus parametrization) Shear modulus from Vs-density FWI Depth [m]

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Multi-parameter SH FWI applicaton (Vs, density) Comparing data fits of different FWI approaches Data comp. shot no. 42

Data residuals

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Elastic multi-parameter FWI synthetic example Rayleigh vs. Love wave FWI (from Dokter et al. 2017) Vp [m/s]

True CTS model

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Elastic multi-parameter FWI synthetic example Rayleigh vs. Love wave FWI (from Dokter et al. 2017) Depth [m]

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CTS Love/SH FWI result

CTS Rayleigh/PSV FWI result

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Code SH PSV

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Computation Time/Iteration [minutes] 4.4 14.8

Memory [Gb] 1.59 2.56

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