1. Department of Geotechnology and Geohydraulics
Computational and practical Issues of 3D SSH-inversion with Aplications to the Analysis of the anisotropic lithospheric Structure and regional Hypocenters beneath Germany.
Dr. M. Koch
Department of Geotechnology and Geohydraulics
University of Kassel
Lecture 2 / 41st INSC (2016)

2. Abstract
There is ample evidence that large sections of the upper mantle underneath Europe and Germany, in particular, are anisotropic. Using regional earthquake travel times, Song et al. [2001] and Song et al. [2004] by means of a 1D time-term analysis and a full 2D Pn anisotropic inversion showed that an anisotropic velocity ellipse with the “fast” axis in the direction of ~N250E and an anisotropy level of ~3.5 reduces significantly the data variance, and that geologically meaningful upper mantle Pn-velocity perturbations could only be obtained if anisotropy was included.
Employing a modified version of the method of simultaneous inversion for structure and hypocenters (SSH) of Koch [1993], including a priori known upper mantle anisotropy, the analyses of Song et al. [2001, 2004] are extended here to a full simultaneous inversion for 3D crustal and upper mantle structure and regional hypocenters underneath Germany. Regional travel times from local earthquakes occurring between are included in the study.
First of all improved 1D P-wave velocity models are derived assuming an isotropic as well as an anisotropic upper mantle. In addition of a slightly better model fit for the anisotropic than for the isotropic model, the latter gives also a somewhat too low Pn-velocity of ~7.90 km/s, compared with ~8.0 km/s for the former. This indicates that inclusion of upper mantle anisotropy into the model is required to obtain physically reasonable Pn-velocities.
Significant improvements for both the isotropic and anisotropic upper mantle cases are obtained. for full 3D SSH inversion models. Similar to the 1D Pn-velocity models there are remarkable differences in the lateral Pn-velocities, depending whether the lithosphere is corrected for anisotropy or not. Finally the manifold of structural seismological results obtained from the SSH-inversion for both crust and upper mantle will be interpreted in terms of the present-day knowledge on the geology and the tectonics of the central European Variscides.

3. Overview 1. Introduction and previous work
D anisotropic Pn time term analysis of Song et al. (2001)
D anisotropic Pn time term analysis of Song et al. (2004)
2. Data used in present study
2.1 Sources and selection criteria
2.2 Event distribution and ray coverage
3. Method of simultaneous inversion for structure and hypocenters
4. 1D vertically inhomogeneous P-wave velocity models
5. 3D laterally inhomogeneous P-wave velocity models
5.1 9x9 models
x15 models
x35 models
6. Geological and tectonic interpretation
7. Conclusions

4. 1. Previous work ( Song et al., 2001, 2004)
Top: Earthquakes and explosions (circles)
recorded between 1975 and 1999 at seismic station
(triangles) in Germany and neighboring countries.
Middle: Coverage for Pn rays
Bottom: Refraction profiles of Enderle et al. (1996)

5. 1. 1 Previous work: 1D anisotropic Pn time term analysis of Song et al
Top: Traveltime residuals as a function of epicentral distances for the straight line fit
Middle: Residuals for classical time term method
Bottom: : Residuals for anisotropic time term method
Note the systematic decrease of the data variance with increasing complexity of the analysis method
Anisotropy-ellipsoid with major axis in N26.7°E
and velocity contrast of 3,5%
So ist die Refraktor-slowness

6. 1. 2 Previous work: 2D anisotropic Pn time-term analysis of Song et al
Anisotropic Pn velocity model
more realistic Pn-velocities ~8km/s
Isotropic Pn velocity model
Pn velocities too low <7.8 km/s

7. Overview 1. Introduction and previous work
D anisotropic Pn time term analysis of Song et al. (2001)
D anisotropic Pn time term analysis of Song et al. (2004)
2. Data used in present study
2.1 Sources and selection criteria
2.2 Event distribution and ray coverage
3. Method of simultaneous inversion for structure and hypocenters
4. 1D vertically inhomogeneous P-wave velocity models
5. 3D laterally inhomogeneous P-wave velocity models
5.1 9x9 models
x15 models
x35 models
6. Geological and tectonic interpretation
7. Conclusions

8. 2. Data used in present study 2.1 Sources and selection criteria
Data Catalogue of Earthquakes of BGR (Henger & Leydecker) Events with P + S -Phases recorded between – 2003
Preprocessing
Selection of best hypocentral localisations
Assume that local networks (LED, BNS etc.) have best localisations
Selection criteria
At least 8 recording stations phases per event
Azimuthatl gap < 180°
 events with P-Phases

9. 2. Data used in present study 2.2 Event distribution and ray-coverage
(GAP < 180° und Nobs > 7)
All rays
Only Pn-rays

10. Overview 1. Introduction and previous work
D anisotropic Pn time term analysis of Song et al. (2001)
D anisotropic Pn time term analysis of Song et al. (2004)
2. Data used in present study
2.1 Sources and selection criteria
2.2 Event distribution and ray coverage
3. Method of simultaneous inversion for structure and hypocenters
4. 1D vertically inhomogeneous P-wave velocity models
5. 3D laterally inhomogeneous P-wave velocity models
5.1 9x9 models
x15 models
x35 models
6. Geological and tectonic interpretation
7. Conclusions

11. 3. Method of simultaneous inversion for structure and hypocenters
Nonlinear iterative solution to minimize the objective function
F = ∑(tobs – tmod) 2
Matrix formulation of the linearized tomographic inverse problem:
with
G= Fréchet (Jacobian) matrix
= tobs – tmod n-dimensional travel-time residual vector;
Δ m = (Δ mH, Δ mv) m-dimensional unknown, incremental model vector of
hypocentral parameters mH and velocity parameters mv
Solution through minimization of linear constrained (regularized) objective function
=> Linear system of equations for solution vector
Updated travel-time t(n+1)mod = tmod(mn + Δ m(n+1)sol) computed by nonlinear
ray tracing (Koch, 1992, 1993; Koch et al., 2001, 2004)

12. Overview 1. Introduction and previous work
D anisotropic Pn time term analysis of Song et al. (2001)
D anisotropic Pn time term analysis of Song et al. (2004)
2. Data used in present study
2.1 Sources and selection criteria
2.2 Event distribution and ray coverage
3. Method of simultaneous inversion for structure and hypocenters
4. 1D vertically inhomogeneous P-wave velocity models
5. 3D laterally inhomogeneous P-wave velocity models
5.1 9x9 models
x15 models
x35 models
x25 models
6. Geological and tectonic interpretation
7. Conclusions

13. 4. 1D vertically inhomogeneous P-wave velocity models
TSS (Total Sum of residuals Squared) as a function of azimuth of anisotropy axis
Note the minimum of the TSS for an azimuth in the range of degrees
Mehrere Inversionsrechnungen im Winkelbereich von 19° bis 31°
Das Minimum des TSS liegt zwischen 25° und 27°
Aufgrund der sehr flachen Kurve kann, trotz des Minimums bei 26° kann momentan keine exakte Aussage getroffen werden.

14. 4. 1D vertically inhomogeneous P-wave velocity models
Reduction of residuals after correction with Pn-anisotropy
Only raytracing
First iteration

15. 4. 1D vertically inhomogeneous P-wave velocity models
Isotropic upper mantle
Anisotropic upper mantle
RMS = 1.35s, TSS = s² RMS = 1.30s, TSS = s²
too low Pn-velocity ~ 7.9 km/s Pn-velocity ~8.1 km/s

16. 4. 1D vertically inhomogeneous P-wave velocity models
Relocations of simultaneously inverted hypocenters
Isotropic mantle
Anisotropic mantle

17. Overview 1. Introduction and previous work
D anisotropic Pn time term analysis of Song et al. (2001)
D anisotropic Pn time term analysis of Song et al. (2004)
2. Data used in present study
2.1 Sources and selection criteria
2.2 Event distribution and ray coverage
3. Method of simultaneous inversion for structure and hypocenters
4. 1D vertically inhomogeneous P-wave velocity models
5. 3D laterally inhomogeneous P-wave velocity models
5.1 9x9 models
x15 models
x35 models
x25 models
6. Geological and tectonic interpretation
7. Conclusions

18. 5. 3D P-wave velocity models / 9x9 block models
Isotrop: , vp-mittel =
Anisotrop: , vp-mittel =
isotropic model
anisotropic model
TSS = s², RMS = 1.22 s TSS = s², RMS = 1.16 s

19. 5.1 9x9 models: Checkerboard resolution tests
no noise: TSS = 18 s², RMS = s noise  = 0.3 s, TSS = 2005 s², RMS = 0.30 s

20. 5.2 3D P-wave /15x15 block models
Isotrop: RMS-Vpn = 7.975km/s
Anisotrop
Isotropic inversion
TSS = => s²
Vpn (av) = 7.97km/s
Anisotropic inversion
TSS = =>30948 s²
Vpn (av)= 8.00 km/s

21. 5.2 15x15 P-wave models: Checkerboard resolution tests
Hier die besten Lösungen aus Iteration 1 und 4
Ich werde die Bilder aus Iteration 4 mit und ohne Rauschen auf eine Folie packen.
no noise, TSS = 561 s², RMS = s I noise  = 0.3 s, TSS = 1856 s²,RMS = s

22. 5.3 35x35 P-wave models TSS = 56960 => 30638 s²,
Hier die besten Lösungen aus Iteration 1 und 4
Ich werde die Bilder aus Iteration 4 mit und ohne Rauschen auf eine Folie packen.
anisotropic mantle
TSS = => s²,
RMS = 1.15 s
isotropic mantle,
TSS = => s²,
RMS = 1.16 s

23. 5.3 35x35 models: checkerboard resolution tests
Hier die besten Lösungen aus Iteration 1 und 4
Ich werde die Bilder aus Iteration 4 mit und ohne Rauschen auf eine Folie packen.
no noise: TSS = 52.0s², RMS = 0.05s noise  = 0.1s: TSS =250 s², RMS =0.10 s

24. 5.4 25x25 models: Isotropic versus anisotropic models
Hier die besten Lösungen aus Iteration 1 und 4
Ich werde die Bilder aus Iteration 4 mit und ohne Rauschen auf eine Folie packen.

25. 5.4 25x25 models: Isotropic resolution test
Hier die besten Lösungen aus Iteration 1 und 4
Ich werde die Bilder aus Iteration 4 mit und ohne Rauschen auf eine Folie packen.

26. Overview 1. Introduction and previous work
D anisotropic Pn time term analysis of Song et al. (2001)
D anisotropic Pn time term analysis of Song et al. (2004)
2. Data used in present study
2.1 Sources and selection criteria
2.2 Event distribution and ray coverage
3. Method of simultaneous inversion for structure and hypocenters
4. 1D vertically inhomogeneous P-wave velocity models
5. 3D laterally inhomogeneous P-wave velocity models
5.1 9x9 models
x15 models
x35 models
x25 models
6. Geological and tectonic interpretation
7. Conclusions

27. 6. Geological and tectonic implications
Tectonical map of Germany
Optimal 15x 15 model, first layer (0-10km)

28. 7. Conclusions
Anisotropic models show better fit of data (smaller residuals) than isotropic ones
Incorporation of anisotropy is necessary for obtaining geologically meaningful upper mantle Pn-velocities ~8 km/s
Travel time data provide for an independent resolution of the crust and upper mantle over most of the study region.
Upper crust well resolved but large sections of the lower crust show poor lateral resolution, due to a paucity of earthquakes here
Various upper crustal tectonic (petrological) features retrieved in the 3D models:
* Molasse region in the Alpine foreland
* volcanic and metamorphic roots in the Black Forest, the Vosges, and parts
of northern Rhinegraben
6. Effects of anisotropy on relocated hypocenters marginal
Future study: Analysis of anisotropy in the crust

29. References (of the author only)
Publications, Projects and Presentations of Research
>> Curriculum Vitae, Prof. Dr. M. Koch