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Full Waveform Inversion. The quest for resolution in earthquake seismology - Application to lithospheric imaging from teleseismic data

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October 12, 2015

Full Waveform Inversion. The quest for resolution in earthquake seismology - Application to lithospheric imaging from teleseismic data

Présentation de Stéphane Operto (Géoazur) aux 2èmes Rencontres Scientifiques et Techniques Résif | 12-14 octobre 2015, La Grande Motte

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@Résif

October 12, 2015
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  1. Full Waveform Inversion The quest for resolution in earthquake seismology

    Application to lithospheric imaging from teleseismic data S. Beller1, V. Monteiller1, L. Combe1, G. Nolet1, S. Operto1 1 UMR 7329 Géoazur – Sophia-Antipolis – UNS – CNRS – OCA – IRD https://geoazur.oca.eu/ – e-mail: beller@geoazur.unice.fr http://seiscope2.osug.fr La Grande Motte France, 12-14 October, 2015 SEISCOPE
  2. Content 1 Lithospheric imaging from teleseismic data: principles and motivation

    2 Principles of FWI and resolution power 3 Application to a realistic synthetic case study 4 Application to CIFALPS data 5 Conclusions & perspectives 6 References Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 2 / 21
  3. Lithospheric imaging from teleseismic data: principles and motivation Motivation: Build

    high-resolution elastic (VP, VS , ρ) models of lithospheric targets with a spatial resolution ∼ λ Conventional approaches: 1 Traveltime tomography lacks spatial resolution. 2 Receiver function analysis lacks accuracy in complex area. 3 Least-squares ray+Born migration (Bostock et al., 2001) Methodological approach: Full Waveform Inversion (FWI) of teleseismic data. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 3 / 21
  4. Principles of FWI and resolution power Motivation: exploit the full

    information content of seismograms (Tarantola, 1984; Gauthier et al., 1986; Mora, 1988). Seismological references: (Tromp et al., 2005; Tape et al., 2010; Fichtner et al., 2013) Numerical optimization: minimizes a distance between recorded and modeled seismograms C(m) = 1 2 s r t (dcal(s, r, t) − dobs(s, r, t))2 = 1 2 ∆d 2, mVP ,VS ,ρ denotes the elastic parameters discretizing the lithospheric target. Forward problem: full wavefield methods, e.g., the spectral element method (Komatitsch and Tromp, 1999). A minimum of C is found by local optimization (gradient methods) m(k+1) = m(k) + ∆m(k), with ∆m(k) = −γ(k)(H(k))−1∇mC(k). ∇mC and H are the first (gradient) and second (Hessian) derivative of C .wrt. m. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 4 / 21
  5. FWI gradient Gradient: zero-lag correlation between the data residuals ∆d

    and the partial derivative of the seismograms .wrt. the parameters. ∇mC(k) = s r t ∂dcal(s, r, t) ∂m (k) ∆d(s, r, t)(k) Physical meaning: ∂dcal (s,r,t) ∂m (k) and ∆d(s, r, t)(k) as wavefields (single-)scattered by the missing heterogeneities in mk (conceptually, represented by a fine grid of point diffractors) and recorded at the receiver positions. The zero-lag correlation between ∆d(k) and ∂dcal (s,r,t) ∂m (k) tests whether a missing heterogeneity located at the diffractor point m generated the residual ∆d(s, r, t)(k). The result of the zero-lag correlation is used to update ∇mC(k) at the position of m. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 5 / 21
  6. Resolution power - Relationship between λ, θ and wavenumber vector

    k k = 2π(2/λ) cos(θ/2)n 0 10 20 30 40 50 Depth (km) 0 20 40 60 80 100 Distance (km) k Backward scattering k Forward scattering θ θ Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 6 / 21
  7. A case study in exploration geophysics (Operto et al., 2015)

    0 1 2 3 4 4 6 8 10 12 14 16 18 4 6 8 10 Y(km) X(km ) Depth(km) Y (km) 3 4 5 6 7 8 9 10 11 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 X(km) Geology: Shallow-water environment (70m of water). Gas in the overburden, forming locally a gas cloud between 1km and 1.5km depth. Over-pressured, under-saturated Upper Cretaceous chalk reservoir at 2.5km depth (Barkved et al., 2010). Anisotropy as high as 16%. Acquisition: 2302 hydrophones, 49,954 shots (50m spacing) processed in a reciprocal way. Covered area: 16km × 9km = 145km2; Maximum depth: 4.5 km. Wave physics: Visco-acoustic VTI. Frequency band: 3.5Hz - 10Hz. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 7 / 21
  8. An illustration in exploration geophysics - Traveltime tomography model 3

    4 5 6 7 8 9 10 11 X (km) 3 5 7 9 11 13 15 17 Y (km) 1700 1800 1900 2000 m/s 3 4 5 6 7 8 9 10 11 X (km) 3 5 7 9 11 13 15 17 1700 1750 1800 1850 1900 1950 m/s 3 4 5 6 7 8 9 10 11 X (km) 3 5 7 9 11 13 15 17 1700 1800 1900 2000 2100 2200 m/s 0 1 2 3 4 Depth(km) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Y(km) 1500 2000 2500 3000 m/s 0 1 2 3 4 Depth(km) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1500 2000 2500 3000 m/s 0 1 2 3 4 Depth(km) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1500 2000 2500 3000 m/s z=175m z=500m z=1000m x=5575m x=6250m x=6475m Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 8 / 21
  9. An illustration in exploration geophysics - 10Hz FWI model 3

    4 5 6 7 8 9 10 11 X (km) 3 5 7 9 11 13 15 17 Y (km) 1700 1800 1900 2000 m/s 3 4 5 6 7 8 9 10 11 X (km) 3 5 7 9 11 13 15 17 1700 1750 1800 1850 1900 1950 m/s 3 4 5 6 7 8 9 10 11 X (km) 3 5 7 9 11 13 15 17 1700 1800 1900 2000 2100 2200 m/s 0 1 2 3 4 Depth(km) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Y(km) 1500 2000 2500 3000 m/s 0 1 2 3 4 Depth(km) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1500 2000 2500 3000 m/s 0 1 2 3 4 Depth(km) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1500 2000 2500 3000 m/s z=175m z=500m z=1000m x=5575m x=6250m x=6475m Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 9 / 21
  10. An illustration in exploration geophysics - Data anatomy & fit

    (TOMO) 0 2 4 6 8 10 O set(km) 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Time (s) -12 -10 -8 -6 -4 -2 O set(km) Recorded Modeled Time(s) -1 0 1 2 Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 10 / 21
  11. An illustration in exploration geophysics - Data anatomy & fit

    (FWI) 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Time (s) -12 -10 -8 -6 -4 -2 O set(km) Recorded 0 2 4 6 8 10 O set(km) Modeled Time(s) -1 0 1 2 Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 11 / 21
  12. Scale ratio between exploration geophysics and lithospheric imaging Acquisition Teleseismic

    FWI Exploration FWI Minimum frequency 0.05 Hz 3.5 Hz Maximum frequency 1 Hz 10 Hz Mean wavelength 5km 200m Target size 500km 20km Nλ 100 100 Sources Plane waves Point sources Scattering regime Transmission Reflection Fold - - - + + + Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 12 / 21
  13. Computer implementation: the Lithos code Main developer: S. Beller (PhD

    Geoazur). Collaborators: L. Combe (HPC research engineer), V. Monteiller (Post-doc Geoazur). Forward modeling: Coupling between AxiSEM (Nissen-Meyer et al., 2008) and a 3D spectral-element code (Komatitsch and Tromp, 1999) on unstructured grid through a grid injection technique (Alterman and Karal, 1968; Taflove and Hagness, 2005; Robertson and Chapman, 2000; Monteiller et al., 2013). Fully anisotropic elastic physics. Lacks attenuation. Numerical optimization: SEISCOPE optimization toolbox (Métivier and Brossier, 2016). MPI parallelism: source distribution + domain decomposition (combined with OpenMP). Source-signature independent (Choi and Alkhalifah, 2011). Manage multi subsurface parameterizations: (VP, Vs, ρ), (IP, IS , ρ), (λ, µ, ρ), ... Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 13 / 21
  14. A realistic synthetic example representative of the western Alps Target

    size: 400km x 400km x 200km. 201 stations at surface (5km spacing). 10 distant earthquakes (10o < incidence angle < 35o). Maximum frequency: 0.5Hz. Multiscale approch proceedind over broader frequency bandwidth (Bunks et al., 1995). Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 14 / 21
  15. Vz gather Late arrivals in sedimentary basins Early arrival and

    strong diffractions upon Ivrea body Multiples of the Ivrea body Vx gather Footprint of the Moho discontinuity Diffractions from Ivrea body and sedimentary basins Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 15 / 21
  16. Multiscale imaging - Maximum frequency: 0.5Hz Minimal period: 05s 200

    150 100 50 0 50 100 150 200 0 50 100 150 200 200 150 100 50 0 50 100 150 200 0 50 100 150 200 200 150 100 50 0 50 100 150 200 0 50 100 150 200 2600 2700 2800 2900 3000 3100 3200 3300 3400 Density in kg/m3 ρ in kg.m-3 200 150 100 50 0 50 100 150 200 0 50 100 150 200 200 150 100 50 0 50 100 150 200 0 50 100 150 200 200 150 100 50 0 50 100 150 200 0 50 100 150 200 4000 4500 5000 5500 6000 6500 7000 7500 8000 Vp in m/s Vp in m.s-1 200 150 100 50 0 50 100 150 200 0 50 100 150 200 200 150 100 50 0 50 100 150 200 0 50 100 150 200 200 150 100 50 0 50 100 150 200 0 50 100 150 200 2500 2750 3000 3250 3500 3750 4000 4250 4500 Vs in m/s Vs in m.s-1 Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 16 / 21
  17. Final residuals 0 20 40 60 80 100 120 140

    Time in seconds 0 10 20 30 40 50 60 70 Receivers Observed (black) and synthetic (red) vz data 0 20 40 60 80 100 120 140 Time in seconds 0 10 20 30 40 50 60 70 Receivers Misfit for vz data 0 20 40 60 80 100 120 140 Time in seconds 0 10 20 30 40 50 60 70 Receivers Observed (black) and synthetic (red) vx data 0 20 40 60 80 100 120 140 Time in seconds 0 10 20 30 40 50 60 70 Receivers Misfit for vx data Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 17 / 21
  18. CIFALPS experiment 43.5°N 44.5°N 45.5°N 43.5°N 44.5°N 45.5°N 4.5°E 5.5°E

    6.5°E 7.5°E 8.5°E CIFALPS array 0 25 50 km (scale factor 1.00 at 43.25°N, -352°E) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Meters For a maximum frequency of 1Hz, necessary ressources (cluster Occigen, CINES): Mesh: 875 000 elements. Domain decomposition: 480 cores, 20 nodes. Number of time steps: 15,000. Total number of cores for 10 sources: 4800 (200 nodes). Elapsed time for one modeling: 500s. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 18 / 21
  19. FWI model - VP , VS , ρ models (Freq.

    max: 0.5Hz) ρ(kg/m3) Vp(m/s) 3800 2100 4700 Vs(m/s) Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 19 / 21
  20. Detrending - High-wavenumber components of VS model 0 50 100

    150 200 X(km) 0 50 100 150 200 250 300 350 400 Y(km) Depth25km 0 50 100 150 200 X(km) 0 50 100 150 200 250 300 350 400 Y(km) Depth50km 0 50 100 150 200 X(km) 0 50 100 150 200 250 300 350 400 Y(km) Depth100km −200 −150 −100 −50 0 Depth (km) 100 200 300 Distance (km) −100 −90−80−70−60−50−40−30−20−10 0 10 20 30 40 50 60 70 80 90 100 Vs km/s Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 20 / 21
  21. Conclusions & perspectives A 3D massively parallel elastic anisotropic FWI

    code available for processing teleseismic data. Can be adapted for regional tomography from local earthquakes and controlled-source seismology. 2016 dedicated to more precise assessment of the method from synthetic and real data applications (resolution analysis, footprint of noise, footprint of acquisition geometry,...) 2017-2019: Application to AlpArrays. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 21 / 21
  22. Alterman, Z. and Karal, F. C. (1968). Propagation of elastic

    waves in layared media by finite-difference methods. Bulletin of the Seismological Society of America, 58:367–398. Barkved, O., Albertin, U., Heavey, P., Kommedal, J., van Gestel, J., Synnove, R., Pettersen, H., and Kent, C. (2010). Business impact of full waveform inversion at Valhall. In Expanded Abstracts, 91 Annual SEG Meeting and Exposition (October 17-22, Denver), pages 925–929. Society of Exploration Geophysics. Bostock, M. G., Rondenay, S., and Shragge, J. (2001). Multiparameter two-dimensional inversion of scattered teleseismic body waves 1. theory for oblique incidence. Journal of Geophysical Research, 106(12):30771–30782. Bunks, C., Salek, F. M., Zaleski, S., and Chavent, G. (1995). Multiscale seismic waveform inversion. Geophysics, 60(5):1457–1473. Choi, Y. and Alkhalifah, T. (2011). Source-independent time-domain waveform inversion using convolved wavefields: application to the encoded multisource waveform inversion. Geophysics, 76(5):R125–R134. Fichtner, A., Trampert, J., Cupillard, P., Saygin, E., Taymaz, T., Capdeville, Y., and nor, A. V. (2013). Multiscale full waveform inversion. Geophysical Journal International, 194:534–556. Gauthier, O., Virieux, J., and Tarantola, A. (1986). Two-dimensional nonlinear inversion of seismic waveforms: numerical results. Geophysics, 51(7):1387–1403. Komatitsch, D. and Tromp, J. (1999). Introduction to the spectral element method for 3D seismic wave propagation. Geophysical Journal International, 139:806–822. Métivier, L. and Brossier, R. (2016). The seiscope optimization toolbox: A large-scale nonlinear optimization library based on reverse communication. Geophysics, 81(2):F11–F25. Monteiller, V., Chevrot, S., Komatitsch, D., and Trom, J. (2013). A hybrid method to compute short period synthetic seismograms of teleseismic body waves in a 3-d regional model. Geophysical Journal International, 192(1):230–247. Mora, P. R. (1988). Elastic wavefield inversion of reflection and transmission data. Geophysics, 53:750–759. Nissen-Meyer, T., Fournier, A., and Dahlen, F. A. (2008). A 2-d spectral-element method for computing spherical-earth seismograms - ii. waves in solid-fluid media. Geophysical Journal International, 174:873–888. Operto, S., Miniussi, A., Brossier, R., Combe, L., Métivier, L., Monteiller, V., Ribodetti, A., and Virieux, J. (2015). Efficient 3-D frequency-domain mono-parameter full-waveform inversion of ocean-bottom cable data: application to Valhall in the visco-acoustic vertical transverse isotropic approximation. Geophysical Journal International, 202(2):1362–1391. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 21 / 21
  23. Robertson, J. O. A. and Chapman, C. H. (2000). An

    efficient method for calculating finite-difference seismograms after model alterations. Geophysics, 65(3):907–918. Taflove, A. and Hagness, S. C. (2005). Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, 3rd edition. Tape, C., Liu, Q., Maggi, A., and Tromp, J. (2010). Seismic tomography of the southern California crust based on spectral-element and adjoint methods. Geophysical Journal International, 180:433–462. Tarantola, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49(8):1259–1266. Tromp, J., Tape, C., and Liu, Q. (2005). Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International, 160:195–216. Beller (Géoazur – PhD student) Lithospheric Full-Waveform Inversion 14/10/2015 - RESIF 21 / 21