Description: Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space $\mathbb {R}^{3}$ is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Description: Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space $\mathbb {R}^{3}$ is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Description: A sequence of large earthquakes occurred along the North Anatolian fault in the 20th century. These earthquakes, including the 1999 Izmit/Düzce earthquakes, generally propagated westward towards the Marmara Sea, defining the Main Marmara fault as a potential seismic gap. It is important to conduct a detailed assessment of the seismic hazards along the main Marmara fault because the megacity Istanbul lies only approximately 10 km north of the eastern segment of the Main Marmara fault, which is referred to as the Princes’ Islands Fault segment (PIF). Here, we study the locking status of this fault segment to evaluate the seismic hazard potential. For the first time, combined ascending and descending Interferometric Synthetic Aperture Radar and Global Positioning System observations were used to investigate the crustal deformation associated with the PIF. After careful corrections of the estimated ground velocity, a deformation pattern relating to fault locking near the Princes’ Islands was identified. The modeling results revealed that the slip rate and locking depth of the fault segment show a clear trade-off, which were estimated as 18.9 ± 7.2 mm yr –1 and 12.1 ± 7.0 km, respectively. With a moment accumulation rate of 1.7 ± 0.4  x  10 17 Nm yr –1 (proportional to the product of slip rate and locking depth), our results imply a build-up of a geodetic moment on the PIF and therefore a potential for earthquake hazards in the vicinity of the Istanbul megacity.

Description: Large tectonic earthquakes lead to significant deformations in the months and years thereafter. These so-called post-seismic deformations include contributions mainly from afterslip and viscoelastic relaxation, quantification of their relative influence is of importance for understanding the evolution of post-seismic crustal stress, strain and aftershocks. Here, we investigate the post-seismic deformation processes following the 2011 M w 9.0 Tohoku earthquake using surface displacement data as observed by the onshore global positioning system network in the first ~1.5 yr following the main shock. We explore two different inversion modelling strategies: (i) we simulate pure afterslip and (ii) we simulate the combined effect of afterslip and viscoelastic relaxation. By assuming that the afterslip is solely responsible for the observed post-seismic deformation, we find most afterslip activities to be located close to the downdip area of the coseismic rupture at 20–80 km depth with a maximum cumulative slip of ~3.8 m and a seismic moment of 2.3 10 22 Nm, equivalent in moment to an M w 8.84 earthquake. By assuming a combination of afterslip and viscoelastic components, the best data fit is found for an afterslip portion that is spatially consistent with the pure afterslip model, but reveals a decreased seismic moment of 2.1 10 22 Nm, or M w 8.82. In addition, the combined model suggests an effective thickness of the elastic crust of ~50 km overlying an asthenosphere with a Maxwell viscosity of 2 10 19 Pa s. Temporal analysis of our model inversions suggests that the rate of afterslip rapidly decreases with time, consistent with the state- and rate-strengthening frictional law. The spatial pattern of afterslip coincides with the locations of aftershocks, and also with the area of coseismically increased Coulomb failure stress (CFS). Only a small part of the coseismically increased CFS was released by the afterslip in 564 d after the event. The effect of the viscoelastic relaxation within this initial stage only plays a secondary role, but it shows an increasing tendency, that is, the contribution of viscoelastic relaxation increases with time. Further geodetic observations are needed for a robust quantification of the role of the viscoelastic relaxation in the post-seismic deformation.

Description: Volcanic crises are often preceded and accompanied by volcano deformation caused by magmatic and hydrothermal processes. Fast and efficient model identification and parameter estimation techniques for various sources of deformation are crucial for process understanding, volcano hazard assessment and early warning purposes. As a simple model that can be a basis for rapid inversion techniques, we present a compound dislocation model (CDM) that is composed of three mutually orthogonal rectangular dislocations (RDs). We present new RD solutions, which are free of artefact singularities and that also possess full rotational degrees of freedom. The CDM can represent both planar intrusions in the near field and volumetric sources of inflation and deflation in the far field. Therefore, this source model can be applied to shallow dikes and sills, as well as to deep planar and equidimensional sources of any geometry, including oblate, prolate and other triaxial ellipsoidal shapes. In either case the sources may possess any arbitrary orientation in space. After systematically evaluating the CDM, we apply it to the co-eruptive displacements of the 2015 Calbuco eruption observed by the Sentinel-1A satellite in both ascending and descending orbits. The results show that the deformation source is a deflating vertical lens-shaped source at an approximate depth of 8 km centred beneath Calbuco volcano. The parameters of the optimal source model clearly show that it is significantly different from an isotropic point source or a single dislocation model. The Calbuco example reflects the convenience of using the CDM for a rapid interpretation of deformation data.

Description: The description of static displacements associated with earthquakes is traditionally achieved using GPS, EDM or InSAR data. In addition, displacement histories can be derived from strong-motion records, allowing an improvement of geodetic networks at a high sampling rate and a better physical understanding of earthquake processes. Strong-motion records require a correction procedure appropriate for baseline shifts that may be caused by rotational motion, tilting and other instrumental effects. Common methods use an empirical bilinear correction on the velocity seismograms integrated from the strong-motion records. In this study, we overcome the weaknesses of an empirically based bilinear baseline correction scheme by using a net-based criterion to select the timing parameters. This idea is based on the physical principle that low-frequency seismic waveforms at neighbouring stations are coherent if the interstation distance is much smaller than the distance to the seismic source. For a dense strong-motion network, it is plausible to select the timing parameters so that the correlation coefficient between the velocity seismograms of two neighbouring stations is maximized after the baseline correction. We applied this new concept to the KiK-Net and K-Net strong-motion data available for the 2011 M w 9.0 Tohoku earthquake. We compared the derived coseismic static displacement with high-quality GPS data, and with the results obtained using empirical methods. The results show that the proposed net-based approach is feasible and more robust than the individual empirical approaches. The outliers caused by unknown problems in the measurement system can be easily detected and quantified.

Description: The voluminous ash-flow eruptive products in the Central Andes imply that there are major magma bodies; however, how these magma bodies develop and change in time and space are not understood. In this study, we analyse the deformation activity of the Uturuncu Volcano, SW Bolivia, from 2003 to 2009 using a satellite radar interferometry (InSAR) data set. We find that the strength and the pattern of the present deformation can be explained by a pressurized source, such as an inflating flat-topped magma body at ~22 ± 9 km depth below the surface. Furthermore, we examine the optical remote sensing data to perform a lineament analysis, which shows in a geographic information system (GIS) that a girdle of river streams and faults encircle the volcano at radial distance of approximately 15 km. Using numerical stress models, we locate a magma body beneath the volcano and find that the lineaments are best explained by a deflating flat-topped magma body at approximately 18 ± 2 km depth, which is consistent with the InSAR study. Thus, both the independent analysis of InSAR and lineament data suggest the presence of a horizontally extended, flat-topped magma body beneath Uturuncu. The location depth is in agreement with, or just above, a prominent seismic low velocity zone. Consequently, although the sign of deformation caused by the herein constrained magma body differs, the similar geometry and similar location suggest them to be similar, possibly indicating longevity of a magma storage region.

Description: A sequence of large earthquakes occurred along the North Anatolian fault in the 20th century. These earthquakes, including the 1999 Izmit/Düzce earthquakes, generally propagated westward towards the Marmara Sea, defining the Main Marmara fault as a potential seismic gap. It is important to conduct a detailed assessment of the seismic hazards along the main Marmara fault because the megacity Istanbul lies only approximately 10 km north of the eastern segment of the Main Marmara fault, which is referred to as the Princes’ Islands Fault segment (PIF). Here, we study the locking status of this fault segment to evaluate the seismic hazard potential. For the first time, combined ascending and descending Interferometric Synthetic Aperture Radar and Global Positioning System observations were used to investigate the crustal deformation associated with the PIF. After careful corrections of the estimated ground velocity, a deformation pattern relating to fault locking near the Princes’ Islands was identified. The modeling results revealed that the slip rate and locking depth of the fault segment show a clear trade-off, which were estimated as 18.9 ± 7.2 mm yr –1 and 12.1 ± 7.0 km, respectively. With a moment accumulation rate of 1.7 ± 0.4  x  10 17 Nm yr –1 (proportional to the product of slip rate and locking depth), our results imply a build-up of a geodetic moment on the PIF and therefore a potential for earthquake hazards in the vicinity of the Istanbul megacity.

Description: During the 20th century, a series of devastating earthquakes occurred along the North Anatolian Fault. These generally propagated westwards, such that the main fault segment beneath the Marmara Sea appears as a seismic gap. For the nearby megacity Istanbul, rapid seismic hazard assessment is currently of great importance. A key issue is how a strong earthquake in the Marmara Sea can be characterized reliably and rapidly using the seismic network currently operating in this region. In order to investigate this issue, several scenario earthquakes on the main Marmara fault are simulated through dynamic modelling based on a 3-D structure model. The synthetic datasets are then used to reconstruct the source processes of the causal events with a recently developed iterative deconvolution and stacking method based on simplified 1-D Earth structure models. The results indicate that, by using certain a priori information about the fault geometry and focal mechanism, the tempo-spatial slip patterns of the input scenarios can be well resolved. If reasonable uncertainties are considered for the a priori information, the key source parameters, such as moment magnitude, fault size and slip centroid, can still be estimated reliably, while the detailed tempo-spatial rupture pattern may reveal significant variations. To reduce the effect induced by employing the inaccurate event location and focal mechanism, a new approach for absolute source imaging is proposed and tested. We also investigate the performance of the new source imaging tool for near real-time source inversion under the current network configuration in the Marmara Sea region. The results obtained are meaningful particularly for developing the rapid earthquake response system for the megacity Istanbul.