Vasso Saltogianni

Fault slip source models for the 2014 Mw 6.9 Samothraki‐Gökçeada earthquake (North Aegean Trough) combining geodetic and seismological observations

The 24 May 2014, Mw 6.9, Samothraki-Gokceada shallow (depth: 11 km) earthquake along the North Aegean Trough (NAT), at the westward extension of the North Anatolian Fault Zone (NAFZ), is investigated using constraints from seismological and geodetic data. A point source solution based on teleseismic long-period P and SH waveforms suggests an essentially strike-slip faulting mechanism consisting of two subevents, while from a finite fault inversion of broadband data the rupture area and slip history were estimated. Analysis of data from 11 permanent GPS stations indicated significant coseismic horizontal displacement but no significant vertical or postseismic slip. Okada-type inversion of horizontal slip vectors, using the new TOPological INVersion algorithm, allowed precise modeling of the fault rupture both as single and preferably as double strike-slip faulting reaching the surface. Variable slip models were also computed. The independent seismological and geodetic fault rupture models are broadly consistent with each other and with structural and seismological data and indicate reactivation of two adjacent fault segments separated by a bend of the NAT. The 2014 earthquake was associated with remote clusters of low-magnitude aftershocks, produced low accelerations, and filled a gap in seismicity along the NAT in the last 50 years; faulting in the NAT seems not directly related to the sequence of recent faulting farther east, along the NAFZ and the seismic gap in the Marmara Sea near Istanbul.

Time-space modeling of the dynamics of Santorini volcano (Greece) during the 2011–2012 unrest

The 2011–2012 unrest of Santorini (Thera) volcano (Aegean Sea, Greece) was associated with microseismicity confined to the Kameni Line (KL), a major tectonovolcanic lineament, and has been regarded as a single magmatic episode, produced by a spherical source derived from inversion of GPS data. However, such a source is a few kilometers away from the KL and cannot explain observed microseismicity. For this reason, we divided the unrest episode into five periods based on the fluctuations of seismicity and deformation rates and investigated the connection between seismicity and two spherical magmatic point sources for each period. Based on a new inversion algorithm and consistent GPS data, we recognized during the volcano unrest episode an unstable pattern of intrusions correlating with both the KL and Columbo Line (CL), a second major tectonovolcanic lineament. Intrusions correlating with CL appear relatively persistent, aseismic, small, and shallow, which is consistent with marine geophysical evidence for arrested shallow dykes and geodetic evidence from a previous inflation episode. During the two periods of intense seismicity, sources close to the KL, explaining seismicity, were obtained. This unstable pattern of intrusions explains both the well-observed location and timing of seismicity as well as ground deformation and is consistent with results of an Okada-type inversion for a sill and a dyke. The stress interactions between the two sources agree with Coulomb failure stress models. Santorini appears to be affected by concurrent offset magma pulses, and only recent activity from a magma pulse below the KL produced microseismic swarms.

Modeling the Mogi magma source centre of the Santorini (Thera) volcano, Aegean Sea, Greece, 1994–1999, based on a numerical-topological approach

The aim of this study is the refinement of the dynamics of a recent (1994–1999) minor, slow-inflation episode of the Santorini (Thera) volcano, famous for the Minoan (∼3600 B.C.) eruption and the identification of the parameters of the magmatic source responsible for the inflation. Based on the Mogi source equations, on geodetic observations of base-line changes, on a topological, grid-search approach and on the reasonable assumption that the magma source remained practically stable in map view during the inflation period, we have been able to refine the location and depth (approximately 2.7 km) of the magma center. A tendency for increase of the magma pressure with time, roughly corresponding to a sphere with radius between 30 and 60 m, and a short deflation interval were also documented. The overall modeling was based on a topological method of inversion in two steps and for a selected 4-D grid. At a first step the system of Mogi-source equations was approximated by the intersection of the 4-D subspaces (defined by sets of grid points) each satisfying one observation equation on the basis of a grid-search procedure. At a second step, the best estimate of the Mogi source solution and its full variance-covariance matrix were defined using a common stochastic approach. The overall approach leads to a solution of a system of equations focusing on a 4-D space bounding significant minima in the misfits between model and observed values, and not on solutions focusing on single points, usually trapped in local minima. This study is important to understand a new phase of volcanic unrest since January 2011, while the proposed methodology, inspired from traditional navigation methods may be useful for other inversion problems leading to redundant systems of highly non-linear equations with n unknowns (i.e. topological solutions in the n-D space).

Adjustment of highly non-linear redundant systems of equations using a numerical, topology-based approach

Abstract. The adjustment of systems of highly non-linear, redundant equations , deriving from observations of certain geophysical processes and geodetic data cannot be based on conventional least-squares techniques, and is based on various numerical inversion techniques. Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solution with poor error control. To overcome these problems, we propose an alternative numerical-topological approach inspired by lighthouse beacon navigation, usually used in 2-D, low-accuracy applications. In our approach, an m-dimensional grid G of points around the real solution (an m-dimensional vector) is at first specified. Then, for each equation an uncertainty is assigned to the corresponding measurement , and the sets of the grid points which satisfy the condition are detected. This process is repeated for all equations, and the common section A of the sets of grid points is defined. From this set of grid points, which define a space including the real solution, we compute its center of weight, which corresponds to an estimate of the solution, and its variance–covariance matrix. An optimal solution can be obtained through optimization of the uncertainty in each observation. The efficiency of the overall process was assessed in comparison with conventional least squares adjustment.

Topological inversion in geodesy-based, non-linear problems in geophysics

Geophysical phenomena such as volcanism and earthquake faulting are modeled on the basis of geodetic observations leading to redundant systems of highly non-linear equations. Still, such systems of equations cannot be solved using traditional analytical techniques. For this reason forward modeling or numerical inversion techniques are used, but these techniques have serious limitations. To overcome these problems, we propose a numerical/topological, grid-search based technique in the R^m space, a generalization and refinement of techniques used in some cases of low-accuracy 2-D positioning. In contrast to conventional solutions which tend to minimize a certain function and directly obtain a point solution of a system of equations, our algorithm has a different strategy. At first, an optimal R^m space which is defined by a grid and which contains the true solution is mapped as the intersection of grid spaces defined on the basis of the uncertainties of each observation. Then, the center of weight of this R^m space and its variance-covariance matrix are computed, and this point solution approximates the true solution of the system of equations. The efficiency of the proposed algorithm and its compatibility with conventional adjustment is demonstrated on the basis of two characteristic case studies.

Solution of underdetermined systems of equations with gridded a priori constraints

The TOPINV, Topological Inversion algorithm (or TGS, Topological Grid Search) initially developed for the inversion of highly non-linear redundant systems of equations, can solve a wide range of underdetermined systems of non-linear equations. This approach is a generalization of a previous conclusion that this algorithm can be used for the solution of certain integer ambiguity problems in Geodesy.The overall approach is based on additional (a priori) information for the unknown variables. In the past, such information was used either to linearize equations around approximate solutions, or to expand systems of observation equations solved on the basis of generalized inverses. In the proposed algorithm, the a priori additional information is used in a third way, as topological constraints to the unknown n variables, leading to an Rn grid containing an approximation of the real solution.The TOPINV algorithm does not focus on point-solutions, but exploits the structural and topological constraints in each system of underdetermined equations in order to identify an optimal closed space in the Rn containing the real solution. The centre of gravity of the grid points defining this space corresponds to global, minimum-norm solutions. The rationale and validity of the overall approach are demonstrated on the basis of examples and case studies, including fault modelling, in comparison with SVD solutions and true (reference) values, in an accuracy-oriented approach.

A new algorithm for modelling simple and double Mogi magma sources in active volcanoes: accuracy, sensitivity, limitations and implications

A new algorithm for modelling one or two Mogi magma sources in actively deforming volcanoes is proposed using Santorini (Thera, Greece) volcano as a test site. This algorithm is based on a quasi-deterministic grid-scan search followed by a topological inversion in Rn space. It avoids point solutions and local minima and is primarily designed for GPS observations. It can be extended to other types of magma sources defined by closed functions and to other types of data. A validation of the method used an accuracy-oriented approach: a comparison between ‘true’ or ‘reference’ and inverse-modelled magma sources, which revealed bias-free, precise magma source solutions. A validation of the algorithm for false alarms, i.e. for identification of non-existent sources produced by computation artefacts, was also made. Computed solutions correspond to point sources affecting idealized media (homogeneous elastic half spaces) and hence ignore errors induced by magma source and lithology complexities, which should be superimposed to obtain the total error budget. Still, the solutions allow modelling of the propagation of measurement errors because of the mathematical model adopted; this problem has previously been ignored. A sensitivity analysis of results obtained using this method permit us to predict and quantify expected bias and uncertainties in modelled magma sources as a function of their depth and of the observation networks. Increased bias and noise in solutions for specific observations, networks and types of data are inferred, and this may explain reported discrepancies in various magma-source models. Some implications for the Santorini volcano, which had an unrest episode in 2011–2012, are that the algorithm can lead to less noisy solutions of the Mogi sources, that the surface deformation may be recognized as resulting from inflation of two spherical sources and that differences in magma source models using different types of data may only indicate predictable uncertainties in the solutions.