Uncertainty Quantification – From Data to Reliable Knowledge (UQ): GFZ

Uncertainty Quantification – From Data to Reliable Knowledge (UQ)

The estimation of seismic hazard, exploitation of the underground for mineral resources, geothermal energy generation and storage, and understanding of geodynamic processes require knowledge and interpretation of the structure of the subsurface. Seismic tomography is a technique that uses model inference of seismic waves either directly or in combinations of secondary measurements (e.g., surface wave dispersion curves, travel times, and preprocessed traces) to characterize the Earth’s interior. We will concentrate on methods based on secondary observables and simplified physics, as they are amenable to deal with large numbers of observations and direct search methods are feasible. A challenge here is that the underlying distribution of data uncertainty is poorly known and needs to be estimated as part of the analysis process. The distribution of the true data error as well as variability of the signal tend to have long tails. We will develop and test techniques for distinguishing outliers from extreme values resulting from structural variations. Additional uncertainty due to simplification of the physics of wave propagation can often be captured stochastically. In the analysis stage, additional physical insight is often used to guide the exploration of the posterior probability space. In this project, we will evaluate the implications of these additional constraints for UQ. Finally, the three-dimensional (3D) models resulting from the geophysical imaging pipeline are interpreted by geologists (visual interpretation) or inform numerical geodynamic models (quantitative interpretation). In both cases, it is crucial to adequately communicate uncertainties to avoid misinterpretations, while at the same time the representation of complex joint probability density functions needs to remain manageable.

In the first stage, we focus on uncertainty quantification in radial anisotropy based on the transdimensional hierarchical Bayesian method. The hierarchical transdimensional Bayesian approach is able to provide uncertainty estimates taking fully into account the nonlinearity of the forward problem. Under the Bayesian framework, the mean and the variance of the ensemble containing a large set of models are interpreted as the reference solution and a measure of the model error respectively. We then applied the method to a temporary broadband array covering all of Sri Lanka.

In the second stage, we propose a one-step 3-D direct inversion based on the reversible jump McMC and 3-D Voronoi tessellation. Joint inversion is usually performed in two steps: first invert for 2-D surface wave phase (or group) velocity maps and then invert 1-D surface wave and RFs jointly to construct a 3-D spatial velocity structure. However, in doing so, the valuable information of lateral spatial variations in velocity maps and dipping discontinuities in RFs may not be preserved and lead to biased 3-D velocity structure estimation. Hence, the lateral neighbours in the final 3-D model typically preserve little of the 2-D lateral spatial correlation information in the phase and group velocity maps. To improve the above issues, we inverted for 3-D spatial structure directly from frequency-dependent travel time measurements and receiver functions.

The figure shows the structure along an East-West profile across Sri Lanka based on joint inversion of receiver functions (RFs) and Rayleigh and Love wave dispersion data. The probability distribution functions for 1D variations of Vs and radial anisotropy below each station and the estimated data noise is estimated with a transdimensional Markov chain Monte Carlo approach applied to a 1D-Voronoi cell parametrization scheme (constant velocity layers). (A) shows inferred standard deviation of data noise for different observational classes. (B), (C), (D), and (E) shows mean values and standard deviations for Vs, radial anisotropy. Black solid curves indicate the interface probability. Black dashed lines indicate the interpreted main discontinuities: Moho and mid-crust. The Moho interface generally reflects the topography, i.e., higher crustal elevations correspond to larger Moho depths, corresponding to the expectations of Airy isostacy. *(F. Tilmann, GFZ)*

Time frame

2020 - 2024

Principal Investigator

F. Tilmann GFZ)
T. Ryberg (GFZ)

Staff

Kuan-Yu Ke (GFZ)

Funding

Gefördert durch die Helmholtz-Gemeinschaft als Pilotprojekt im Bereich der Informations- und Datenwissenschaften

Cooperation/Partner

Karlsruhe Institute of Technology (KIT) -Koordinator
Universität Bielefeld (Uni BI) - Koordinator
Alfred-Wegener-Institut (AWI)
Forschungszentrum Jülich (FZJ)
Helmholtz Institute for Functional Marine Biodiversity (HIFMB)
Carl von Ossietzky Universität Oldenburg (Uni OL)
Helmholtz Zentrum München (HMGU)
Helmholtz-Zentrum Geesthacht (HZG)
Helmholtz-Zentrum für Umweltforschung (UFZ)

Project website

Research Unit(s) (POF/MESI/GIPP)

Topic 3 - Restless Earth

Publication

Tilmann, F., Sadeghisorkhani, H., Mauerberger, A. (2020): Another look at the treatment of data uncertainty in Markov chain Monte Carlo inversion and other probabilistic methods. - Geophysical Journal International, 222, 1, 388-405. https://doi.org/10.1093/gji/ggaa168