Surface Wave Tomography

Transcription

1 Surface Wave Tomography Alexandra Mauerberger GEO-DEEP9300 course at CEED, University of Oslo Nov. 6 - Nov

2 Outline Recap General Methods Techniques to Derive Tomography Resolution Limits Perspectives

3 Love Waves Transversely polarized Constructive interference of up and down going multiple, total reected SH body waves Constructive only at certain j ω, where j=0 is fundamental mode j > 1 are higher modes (overtones) Do not exist in halfspace, need a shallow wave guide [Stein and Wysession, 2003]

4 Rayleigh Waves [Shearer, 2009] Coupled, inhomogeneous P and SV waves are trapped in an interface below free surface Radially polarized (vertical and radial motion) Exists also in a uniform halfspace but do not show dispersion! Displacement decays exponentially with depth, proportional to its horizontal wavelength u exp( k x z) Elliptical motion is retrograde at the surface, prograde below depth of λ x /5 with λ x = 2π/k x

5 Recap General Methods Techniques Resolution Limits Perspectives Dispersion Apparent velocities along surface are frequency dependent U= dω dk dc dc = c 1 k dω = c λ dλ Group velocity with which energy of wave group move (envelope) c(ω) = ω k(ω) Phase velocity of the individual wave peak with U < c [Stein and Wysession, 2003] gassner@gfz-potsdam.de SW Tomography GEO-DEEP9300 course

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8 Earth's Mode - Ray Duality Orbiting SW constructively interfere at resonant frequencies normal modes standing waves [Stein and Wysession, 2003]

9 Earth's Mode - Ray Duality Orbiting SW constructively interfere at resonant frequencies normal modes standing waves [Stein and Wysession, 2003] Rayleigh spheroidal mode Love toroidal mode (oscillation)

10 Earth's Mode - Ray Duality Orbiting SW constructively interfere at resonant frequencies normal modes standing waves [Stein and Wysession, 2003] Rayleigh spheroidal mode Love toroidal mode (oscillation) Excitation of modes depend on velocity structure, source depth, focal mechanism and frequency The deeper the source, the longer period is the fundamental mode High order modes penetrate deeper at any same frequency Long-period analyses using large EQ

11 Earth's Mode - Ray Duality Orbiting SW constructively interfere at resonant frequencies normal modes standing waves [Stein and Wysession, 2003] Rayleigh spheroidal mode Love toroidal mode (oscillation) Excitation of modes depend on velocity structure, source depth, focal mechanism and frequency The deeper the source, the longer period is the fundamental mode High order modes penetrate deeper at any same frequency Long-period analyses using large EQ Displacement are eigenfunctions spherical harmonics

12 Earth's Mode - Ray Duality [Kennett, 2002] Displacement are eigenfunctions spherical harmonics

13 Characteristics of Tomography Contribution of Rayleigh mode j to the vertical component of seismogram s with source amplitude A S epicentral distance X, frequency ω, slowness p j (ω) and Ψ j (ω) as source phase where phv C(ω) = 1/p j (ω) s(x, φ, 0, t) = + A S (p j (ω), ω) exp( iωt + i ωp j (ω)x }{{} + iψ j(ω) ) dω

14 Characteristics of Tomography Contribution of Rayleigh mode j to the vertical component of seismogram s with source amplitude A S epicentral distance X, frequency ω, slowness p j (ω) and Ψ j (ω) as source phase where phv C(ω) = 1/p j (ω) s(x, φ, 0, t) = + A S (p j (ω), ω) exp( iωt + i ωp j (ω)x }{{} + iψ j(ω) ) dω φ(ω, X) = ω }{{} path p j dx = ωp j X incremental phase

15 Characteristics of Tomography Group Velocity Tomography [Laske and Widmer-Schnidrig, 2015]

16 Characteristics of Tomography Group Velocity Tomography Pick maxima of narrow-band ltered envelopes (time-domain) [Laske and Widmer-Schnidrig, 2015]

17 Characteristics of Tomography Group Velocity Tomography [Laske and Widmer-Schnidrig, 2015] Pick maxima of narrow-band ltered envelopes (time-domain) Sliding time window and multiple ltering analyses (time-frequency domain) FTAN (Levshin et al. (1989)) determines also phase velocities Measurement error < 0.1 km/s Advantageous over phase velocities because of the source term Suitable for regional studies

18 Characteristics of Tomography Group Velocity Tomography Pick maxima of narrow-band ltered envelopes (time-domain) Sliding time window and multiple ltering analyses (time-frequency domain) FTAN (Levshin et al. (1989)) determines also phase velocities Measurement error < 0.1 km/s Advantageous over phase velocities because of the source term Suitable for regional studies [Laske and Widmer-Schnidrig, 2015]

19 Characteristics of Tomography Phase Velocity Tomography Crossing of multiple propagation paths 3D velocity inversion to reconstruct the lateral velocity perturbations [Kennett, 2002]

20 Characteristics of Tomography Phase Velocity Tomography Crossing of multiple propagation paths 3D velocity inversion to reconstruct the lateral velocity perturbations Body wave travel time residuals can be picked directly for any phase high-freq approx of ray theory [Kennett, 2002]

21 Characteristics of Tomography Phase Velocity Tomography Crossing of multiple propagation paths 3D velocity inversion to reconstruct the lateral velocity perturbations Body wave travel time residuals can be picked directly for any phase high-freq approx of ray theory [Kennett, 2002] SW frequency dependent phase shifts can be obtained to examine dispersion residuals Cross-correlation techniques

22 Characteristics of Tomography Phase Velocity Tomography The key note is to isolate the contribution from an individual mode and using the frequency variation to create a dispersion curve usually, a residual dispersion analysis is done dening a reference phase velocity C 0 (ω) model, where C(ω) = 1/p(ω) δψ(ω) Ψ(ω) 1 0 δc(ω,θ,φ) C 0(ω) dx Alternative notation of Eikonal equation C(ω) can be obtained from the inversion of measured phase delays (shifts)

23 Notes on Inversion Theory d = Gm linear LSQ m = (G T G) 1 G T d d data vector containing SW waveform information incl. phase dispersion results m model vector containing parameters to invert for, e.g. velocity distribution, density G linear operator to predict data from the model

24 Notes on Inversion Theory 1D reference model as start model parameterize a 3D model using Ray theory approach dividing a model into (uniform) velocity blocks or nodes (regional scale) Spherical harmonics parameterize lateral velocity perturbations (suitable for global scale) (Full)-Waveform inversion Joint inversion of various waves

25 from L.Boschi lecture notes Notes on Inversion Theory

26 Techniques Single-Station Approach Phase Dispersion: needs precise information about the source location and focal mechanism reference model required suitable for large-scale R and L fundamental mode dispersion

27 Recap General Methods Techniques Resolution Limits Perspectives Techniques Single-Station Approach [Ekstrom et al., 1997] SW Tomography GEO-DEEP9300 course

28 Techniques Single-Station Approach Group Dispersion: no information about source needed only location is important FTAN approach subtracting noisy mode contribution [Levshin et al., 1992]

29 Techniques Two-Station Approach Stations along common great circle Local and Regional Scale Cross-correlation (between two recordings or between real and synthetic waveforms) [Laske and Widmer-Schnidrig, 2015]

30 Techniques Two-Station Approach Stations along common great circle Local and Regional Scale Cross-correlation (between two recordings or between real and synthetic waveforms) Problems: [Laske and Widmer-Schnidrig, 2015] O great circle propagation (Error of ca. 6% for phv) Multipathing bent wavefronts in complex structure plane wave assumption invalid wavefront healing

31 Techniques Two Plane Wave Approach by [Forysth and Li, 2005] Assume incoming waveeld as sum of two plane waves Fitting two arriving plane waves to phase measurements Phase and amplitude must be considered for non-plane waves approaching

32 Techniques Many Others Non-plane wave solution using plolaritation analysis [Prindle and Tanimoto, 2006] Ambient noise cross-correlation (e.g. [Snieder and Wapenaar, 2010]) SWT beamforming (e.g. [Maupin, 2011]) N-Station method (e.g. [Jin and Gaherty, 2015]) Joint (dispersion, receiver function, etc) and waveform inversion analysis (e.g. [Schaeer and Lebedev, 2013])

33 Techniques Waveform Inversion Modeling of seismograms (including body and SW) Waveform tting between predicted and observered seismogram 3D Kernels needed for P, S velocity, density, phase, amplitude, arrival angle,... (e.g. [Tromp et al. 2005], [Tromp et al. 2010], [Fichtner et al., 2008]) Source properties must be reliable? Kernel relates the SW phase velocity to the shear velocity V S and other structural properties

34 Techniques Waveform Inversion Joint inversion of body, surface and higher mode waveforms Parameterized laterally in spherical harmonics [Mégnin and Romanowicz, 2000]

35 Absolute V S Models Joint inversion of S, SW and normal modes Schaeer and Lebedev (2013)

36 Diculties of Tomography ray paths are not straight and depend on the velocity model unequal distributed sources and receivers incoming waveeld not necessarily simple plane wave nite frequency eects uncertainty of source which may leads to trade-o with velocity model uncertainty of data processing (e.g. picking errors) many model parameters for inversion simple approximation of an average path Rayleigh fundamental mode is well separated from higher modes in contrast to Love Waves

37 Resolution Limits Absolute V S using joint ambient noise and SW tomography No constrain below 300 km depth using fundamental SW mode No/poor constrain above 50 km (multipathing in short-period SW, long-period SW do not sample shallow structures) Excitation of higher modes depend on source location and focal mechanism Worse lateral resolution than body waves Depth resolution 50 km: Poor resolution of sharp velocity changes with depth (gradient or discontinuity not distinguishable) V S decreases nonlinearly when reaching the melting temperature Poor constrained anisotropy (= ratio of V SV V SH ) due to ambiguous inversions methods [Kawakatsu and Utada, 2017]

38 Perspectives Including SW overtones into inversion: better depth resolution and sensitivity to V P structure Advances in (multi-observable) probabilistic inversion approaches (integration of seismic, magnetic, InSAR, gravity, etc. data) Advances Thermophysical models combining multiple geophysical and geodynamical data Combination of AN and SW tomography allows thermodynamic relations due to the information on absolute V S Full-waveform inversions using multiple observations [Afonso et al., 2016]

39 References I Afonso, J. C., Moorkamp, M., and Fullea, J. (2016). Imaging the Lithosphere and Upper Mantle: Where We Are At and Where We Are Going. Integrated Imaging of the Earth: Theory and Applications, Geophysical Monograph, 218: Ekstrom, G., Tromp, J., and Larson, E. W. F. (1997). Measurements and global models of surface wave propagation. Journal of Geophysical Research-Solid Earth, 102(B4): Forysth, D. W. and Li, A. (2005). Array analysis of two-dimensional variations in surface wave phase velocity and azimuthal anisotropy in the presence of multipathing interference. Seismic Earth: Array Analysis of Broadband Seismograms, pages Jin, G. and Gaherty, J. B. (2015). Surface wave phase-velocity tomography based on multichannel cross-correlation. Geophysical Journal International. Kawakatsu, H. and Utada, H. (2017). Seismic and Electrical Signatures of the LithosphereAsthenosphere System of the Normal Oceanic Mantle. Annual Review of Earth and Planetary Sciences, 45(1): Kennett, B. (2002). The Seismic Waveeld. Volume II. University of Cambridge. Laske, G. and Widmer-Schnidrig, R. (2015). Theory and Observations: Normal Mode and Surface Wave Observations. Treatise on Geophysics, pages Levshin, A., Ratnikova, L., and Berger, J. (1992). Peculiarities of surface-wave propagation across central Eurasia. Bulletin of the Seismological Society of America, 82(6):

40 References II Maupin, V. (2011). Upper-mantle structure in southern Norway from beamforming of Rayleigh wave data presenting multipathing. Geophysical Journal International, 185(2): Shearer, P. M. (2009). Introduction to Seismology. University of Cambridge, 2nd ed edition. Stein, S. and Wysession, M. (2003). An Introduction to Seismology, Earthquakes, and Earth Structure. Blackwell Publishing. Thurber, C. and Ritsema, J. (2015). Theory and Observations - Seismic Tomography and Inverse Methods.

41 Appendix Inversion +improve by randomly resample the data (jackknife or bootstrap), but time consuming -assuming noise-free data -constant amplitude anomalies

42 Finite-frequency tomography Appendix Inversion Theory: travel time anomalies are only accumulated along the geometrical ray path FFT: averaging of structure adjacent to the theoretical ray paths (acounting for the eects of the o-ray-path structure) can be examined using kernels (or Fréchet derivatives) Kernel show the sensitivity of travel time to velocity perturbations banana-doughnut: sensitivity is zero to velocity perturbations exactly at the geometrical ray path width of the kernel shrinks with decreasing frequency

43 Notes on Inversion Theory d = Gm linear LSQ m = (G T G) 1 G T d

44 Notes on Inversion Theory d = Gm linear LSQ m = (G T G) 1 G T d m = (G T C 1 nng + C 1 mm)(g T C 1 nn d C 1 nm[m m 0 ]) non-linear iterative LSQ [Forysth and Li, 2005] m: current model m 0 : starting model m: change to the model d: dierence between obs and pre data for the current model G: sensitivity matrix relating pre changes in d to perturbations in m C nn : a priori data C mm : model covariance matrices

45 Appendix Inversion Model Parameterization [Thurber and Ritsema, 2015]