Figure 10 - uploaded by Jan Dettmer
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Examples of non-stationary data covariance matrix estimates for the same stations as shown in Fig. 9. Note that the range of time lags varies for the various matrices.
Source publication
This paper develops a probabilistic Bayesian approach to the problem of inferring the spatiotemporal evolution of earthquake rupture on a fault surface from seismic data with rigorous uncertainty estimation. To date, uncertainties of rupture parameters are poorly understood, and the effect of choices such as fault discretization on uncertainties ha...
Citations
... Subsequently, spatial data are binned via KNN clustering to estimate covariance terms. The approach also includes hierarchical scaling 65,66 to lower the dependence of covariance matrix estimates on the iterative scheme. ...
An earthquake sequence in western Canada exhibits resurgent aftershocks, possibly in response to persistent, post-mainshock saltwater disposal. Here, we reduce uncertainty in mainshock source parameters with joint inference of interferometric synthetic aperture radar and seismic waveform data, showing that the mainshock nucleated at about 5-km depth, propagating up-dip toward the injection source, and arresting at about 2-km depth. With precise hypocenter relocations and Bayesian inference, we reveal that four subparallel faults were reactivated, likely part of a regional, basement-rooted graben system. The reactivated faults appear to be truncated by a conjugate fault that is misoriented for slip in the present-day stress regime. The nearest saltwater disposal well targets a permeable Devonian reef in direct contact with Precambrian basement, atop a ridge-like uplift. Our observations show that a fault system can be activated more than a decade after saltwater disposal initiation, and continued disposal may lead to a resurgence of seismicity.
... We then tessellate the inferred rupture surface into a "watertight" mesh of finite slip patches. Here we use a triangular tessellation for simplicity, but the geometry of slip patches in general can be arbitrary, defined e.g. by Voronoi cells (Voronoi, 1908;Dettmer et al., 2014). A desirable quality of the discretized model is that slip patches are as small as necessary to fit the data, but as large as needed to be well resolved -that is, the model resolution matrix is as close as possible to the identity matrix (e.g., Backus & Gilbert, 1968;Fialko, 2004b;M. ...
We use Sentinel‐1 and ALOS‐2 Interferometric Synthetic Aperture Radar (InSAR), and Global Navigation Satellite System (GNSS) data to investigate the mechanisms of coseismic and postseismic deformation due to the 2021 M7.4 Maduo (China) earthquake. We present a refined coseismic slip model constrained by the rupture trace and precisely located aftershocks. The InSAR time series corrected for the atmospheric and decorrelation noise reveal postseismic line of sight displacements up to ∼0.1 m. The displacements are discontinuous along the fault trace, indicating shallow afterslip and velocity‐strengthening friction in the top 2–3 km of the upper crust. The magnitude of shallow afterslip is however insufficient to compensate for the coseismic slip deficit, implying substantial off‐fault yielding. The observed surface deformation does not exhibit obvious features that could be attributed to poroelastic effects. We developed a fully coupled model that accounts for both stress‐driven creep on a deep localized shear zone and viscoelastic relaxation in the bulk of the lower crust. The mid‐ to near‐field data can be reasonably well explained by deep afterslip and/or non‐Maxwellian visco‐elasticity. Our results suggest a power‐law stress exponent of ∼4–4.5 assuming a power‐law rheology, and transient and steady‐state viscosities of 10¹⁸ and 10¹⁹ Pa s, respectively, assuming a bi‐viscous (Burgers) rheology. However, a good fit to the GNSS data cannot be achieved assuming the bulk viscoelastic relaxation alone, and requires a contribution of deep afterlip and/or a localized shear zone extending through much of the lower crust.
... Those multiple datasets of InSAR and GPS allow us to reduce the ambiguities that exist in each dataset. In this study, we introduce a joint inversion using a trans-dimensional Bayesian method (Dettmer et al. 2014) to estimate the slip distribution of the earthquake. This approach has the advantage that it solves for the contiguous area of the fault that is allowed to slip in the inversion whilst also solving for the magnitude. ...
This study investigates the distribution of coseismic slip of the 19th August 2018 Mw 7.2 Lombok earthquakes, Indonesia, using Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) data. Two look directions on ascending, with a maximum displacement of 27 cm and 35 cm, and one on descending of Sentinel-1 SAR data, with a maximum displacement of 12 cm, are used. In addition, static offsets from the GPS data, which are located at the most western part of the island and the northern part of the island, detect ~ 2 cm and ~ 5 cm coseismic displacement due to the earthquake. Using combined InSAR and GPS data, this study estimates the fault location, fault geometry and the coseismic slip distribution by a joint inversion using a trans-dimensional Bayesian method. This method solves for the contiguous area of the fault that is allowed to slip in the inversion whilst also solving for the magnitude. This dampens the spurious smoothing that can occur in distributed slip solutions, in particular with far-field geodetic data or deep sources. The maximum slip of ~ 3.5 m is located at deeper portion of the fault at ~ 21 km, adjacent to the epicenter of the earthquake. This study demonstrates that the coseismic slip of the 19th August 2018 earthquakes occurred on a structure further south towards Lombok, a parallel fault structure with Flores back arc thrust.
... Key to this pragmatic inversion protocol is to re-partition the model into Voronoi polygons with cell density adapted to the coda-wave sensitivity kernels. Voronoi Diagrams have been adopted in various geophysical applications including in the Neighborhood Algorithm (Sambridge, 1999a(Sambridge, , 1999b and transdimensional inversions (Bodin & Sambridge, 2009;Dettmer et al., 2014;Zhang et al., 2018). Based on the station distribution in Figure 2a, we calculate the coda-wave sensitivity kernels for all station pairs within 50 km distance at 6 lapse times. ...
Reconstructions of Green's functions by ambient noise interferometry enable the imaging of the Earth's subsurface. Coda waves from reconstructed Green's functions can be utilized to perform time‐dependent imaging of processes that vary substantially at daily to monthly time scales in the crust. Time‐lapse Coda‐Wave Imaging (CWI) can detect tiny changes in seismic velocity with high temporal resolution. While previous studies on CWI have mainly focused on the descriptions of coda waves' propagation, little attention has been paid to choosing effective inversion algorithms that are suitable for CWI. Here we address this issue by developing a pragmatic inversion approach based on Voronoi tessellation with mesh cells adapted to coda‐wave sensitivity kernels. Using seismic stations in Central California, we present both synthetic and real data imaging to demonstrate that this approach stabilizes the inversion, is computationally efficient, and provides spatially adaptive resolution. We further propose a heuristic approach for a quantitative assessment of spatial resolution based on multi‐scale checkerboard tests.
... This approach allows for a comprehensive analysis of the locking degree by incorporating the variability and uncertainty inherent in the estimation process. In our approach, the spatial distribution of locking is discretized by Voronoi cells (Dettmer et al., 2014). The number and location of Voronoi cell centers are not fixed, but are allowed to vary according to a stochastic process. ...
Plain Language Summary
Deformation along plate boundaries can occur seismically (i.e. through earthquakes) as well as aseismically (i.e. slipping slowly), and it is important to understand where each of these modes is dominant. Along the Chilean subduction contact, North‐Central Chile is the only place where aseismic deformation episodes have been observed so far. In order to study these processes in detail, we deployed and operated dense geodetic and seismological networks in this region. Analyzing the data collected by these networks, we find notable relationships between seismic and aseismic processes. Thousands of small earthquakes are found at the boundaries of locked regions, whereas no small earthquakes are found at their interior. Thus, implying such regions are mechanically coupled, that is, currently accumulating elastic deformation energy that will 1 day be released during a large earthquake. Along the North‐Central Chilean plate boundary, there is one region (around 27.5°S) that shows many signs of aseismic deformation. It is located where a chain of seamounts is being subducted, which is likely responsible for the different behavior of this segment.
... com/AlTarFramework/altar, Jolivet, Simons, et al., 2015;Minson et al., 2013). Doing so, we explore the range of models that explain the data without the use of any form of regularization (i.e., smoothing) apart from the choice of the geometry of the fault (i.e., as opposed to trans-dimensional methods, Dettmer et al., 2014). AlTar uses parallel tempering to let the sample set slowly converge toward the posterior PDF. ...
Slow, aseismic slip plays a crucial role in the initiation, propagation, and arrest of large earthquakes along active faults. In addition, aseismic slip controls the budget of elastic strain in the crust, hence the amount of energy available for upcoming earthquakes. The conditions for slow slip include specific material properties of the fault zone, pore fluid pressure, and geometrical complexities of the fault plane. Fine scale descriptions of aseismic slip at the surface and at depth are key to determine the factors controlling the occurrence of slow, aseismic versus rapid, seismic fault slip. We focus on the spatial and temporal distribution of aseismic slip along the North Anatolian Fault, the plate boundary accommodating the 2 cm/yr of relative motion between Anatolia and Eurasia. Along the eastern termination of the rupture trace of the 1944 M7.3 Bolu‐Gerede earthquake lies a segment that slips aseismically since at least the 1950s. We use Sentinel 1 time series of displacement and GNSS data to provide a spatio‐temporal description of the kinematics of fault slip. We show that aseismic slip observed at the surface is coincident with a shallow locking depth and that slow slip events with a return period of 2.5 years are restricted to a specific section of the fault. In the light of historical measurements, we discuss potential rheological implications of our results and propose a simple alternative model to explain the local occurrence of shallow aseismic slip at this location.
... The trans-dimensional idea has been applied to a wide variety of geoscience problems, including source (e.g Dettmer et al., 2014) and structural (Burdick & Lekić, 2017;Galetti et al., 2017;Guo et al., 2020) studies using seismic data, in geomagnetism (Livermore et al., 2018) and in hydrology (Enemark et al., 2019). It can be particularly effective in settings where basis functions form a natural hierarchy of scale lengths, such as with wavelets and spherical harmonics, although keeping track of information creates computational challenges (Hawkins & Sambridge, 2015). ...
In this chapter, we survey some recent developments in the field of geophysical inversion. We aim to provide an accessible general introduction to the breadth of current research, rather than focussing in depth on particular topics. We hope to give the reader an appreciation for the similarities and connections between different approaches, and their relative strengths and weaknesses.
... The wavelet tree parameterisation used here is not the only parameterisation that can be used for a trans-dimensional MCMC. Indeed, a popular choice in many geophysical applications is to use Voronoi cells (Voronoï 1908;Bodin et al. 2012;Young et al. 2013;Dettmer et al. 2014;Zhang et al. 2018), where the image space is divided into cells defined by a node location such that all the points in a given cell are closer to their cell node than any other cell node. The value of the field for which one is inverting is generally taken to be constant in each cell. ...
... com/AlTarFramework/altar, Jolivet, Simons, et al., 2015;Minson et al., 2013). Doing so, we explore the range of models that explain the data without the use of any form of regularization (i.e., smoothing) apart from the choice of the geometry of the fault (i.e., as opposed to trans-dimensional methods, Dettmer et al., 2014). AlTar uses parallel tempering to let the sample set slowly converge toward the posterior PDF. ...
Slow, aseismic slip plays a crucial role in the initiation, propagation and arrest of large earthquakes along active faults. In addition, aseismic slip controls the budget of elastic strain in the crust, hence the amount of energy available for upcoming earthquakes. The conditions for slow slip include specific material properties of the fault zone, pore fluid pressure and geometrical complexities of the fault plane. Fine scale descriptions of aseismic slip at the surface and at depth are key to determine the factors controlling the occurrence of slow, aseismic versus rapid, seismic fault slip. We focus on the spatial and temporal distribution of aseismic slip along the North Anatolian Fault, the plate boundary accommodating the 2 cm/yr of relative motion between Anatolia and Eurasia. Along the eastern termination of the rupture trace of the 1944 M7.3 Bolu-Gerede earthquake lies a segment that slips aseismically since at least the 1950’s. We use Sentinel 1 time series of displacement and GNSS data to provide a spatio-temporal description of the kinematics of fault slip. We show that aseismic slip observed at the surface is coincident with a shallow locking depth and that slow slip events with a return period of 2.5 years are restricted to a specific section of the fault. In the light of historical measurements, we discuss potential rheological implications of our results and propose a simple alternative model to explain the local occurrence of shallow aseismic slip at this location.
... In this research, it was found that "small" additive noise resulted in poor estimation of the parameter posteriors; this observation was consistent with other Since it is difficult to calibrate the behavior of the AEM system in the presence of negative response values caused by IP effects, it is to be expected that there will be some model misspecification caused by the "theoretical error" of adopting the above empirical noise model. There are hierarchical Bayesian approaches that deal in resolving this issue in other geophysical research (Bodin et al. 2012;Vasyura-Bathke et al. 2021;Dettmer et al. 2014) that could be applied in the future for estimating AEM system noise in the presence of IP effects. ...
Detection of induced polarisation effects in airborne electromagnetic measurements does not yet have an established methodology. This work contributes a Bayesian approach to the IP-detectability problem using decoupled transdimensional layered-models and applies an approach novel to geophysics whereby transdimensional proposals are used within the embarrassingly parallelisable and robust sequential Monte Carlo class of algorithms for the simultaneous inference of parameters and models. This algorithm allows for adaptivity considerations for multiple models and proposal types. Methodological contributions to solid Earth geophysics include the decoupled layered-model approach and proposal of a statistic that uses posterior model odds for IP detectability. A case study is included investigating the detectability of IP effects in airborne electromagnetic data at a broad scale.
