Browsing by Author "Araya, Rodolfo"

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    A posteriori error estimates for a mixed-FEM formulation of a non-linear elliptic problem
    (2002) Araya, Rodolfo; Barrios, Tomás P.; Gatica, Gabriel N.; Heuer, Norbert
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    A supervised machine learning approach for estimating plate interface locking: Application to Central Chile
    (2024) Barra, Sebastian; Moreno, Marcos; Ortega-Culaciati, Francisco; Benavente, Roberto; Araya, Rodolfo; Bedford, Jonathan; Calisto, Ignacia
    Estimating locking degree at faults is important for determining the spatial distribution of slip deficit at seismic gaps. Inverse methods of varying complexity are commonly used to estimate fault locking. Here we present an innovative approach to infer the degree of locking from surface GNSS velocities by means of supervised learning (SL) algorithms. We implemented six different SL regression methods and apply them in the Central Chile subduction. These methods were first trained on synthetic distributions of locking and then used to infer the locking from GNSS observations. We tested the performance of each algorithm and compared our results with a least squares inversion method. Our best results were obtained using the Ridge regression, which gives a root mean square error (RMSE) of 1.94 mm/yr compared to GNSS observations. The ML -based locking degree distribution is consistent with results from the EPIC Tikhonov regularized least squares inversion and previously published locking maps. Our study demonstrates the effectiveness of machine learning methods in estimating fault locking and slip, and provides flexible options for incorporating prior information to avoid slip instabilities based on the characteristics of the training set. Exploring uncertainties in the physical model during training could improve the robustness of locking estimates in future research efforts.
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    Convergence analysis of pressure reconstruction methods from discrete velocities
    (2023) Araya, Rodolfo; Bertoglio, Cristobal; Carcamo, Cristian; Nolte, David; Uribe, Sergio
    Magnetic resonance imaging allows the measurement of the three-dimensional velocity field in blood flows. Therefore, several methods have been proposed to reconstruct the pressure field from such measurements using the incompressible Navier-Stokes equations, thereby avoiding the use of invasive technologies. However, those measurements are obtained at limited spatial resolution given by the voxel sizes in the image. In this paper, we propose a strategy for the convergence analysis of state-of-the-art pressure reconstruction methods. The methods analyzed are the so-called Pressure Poisson Estimator (PPE) and Stokes Estimator (STE). In both methods, the right-hand side corresponds to the terms that involving the field velocity in the Navier-Stokes equations, with a piecewise linear interpolation of the exact velocity. In the theoretical error analysis, we show that many terms of different order of convergence appear. These are certainly dominated by the lowest-order term, which in most cases stems from the interpolation of the velocity field. However, the numerical results in academic examples indicate that only the PPE may profit of increasing the polynomial order, and that the STE presents a higher accuracy than the PPE, but the interpolation order of the velocity field always prevails. Furthermore, we compare the pressure estimation methods on real MRI data, assessing the impact of different spatial resolutions and polynomial degrees on each method. Here, the results are consistent with the academic test cases in terms of sensitivity to polynomial order as well as the STE showing to be potentially more accurate when compared to reference pressure measurements.
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    Recurrence time and size of Chilean earthquakes influenced by geological structure
    (2024) Julve, Joaquin; Barbot, Sylvain; Moreno, Marcos; Tassara, Andres; Araya, Rodolfo; Catalan, Nicole; Crempien, Jorge G. F.; Becerra-Carreno, Valeria
    In 1960, the giant Valdivia earthquake (moment magnitude, Mw, 9.5), the largest earthquake ever recorded, struck the Chilean subduction zone, rupturing the entire depth of the seismogenic zone and extending for 1,000 km along strike. The first sign of new seismic energy release since 1960 occurred in 2017 with the Melinka earthquake (Mw 7.6), which affected only a portion of the deepest part of the seismogenic zone. Despite the recognition that rupture characteristics and rheology vary with depth, the mechanical controls behind such variations of earthquake size remain elusive. Here we build quasi-dynamic simulations of the seismic cycle in southern Chile including frictional and viscoelastic properties, drawing upon a compilation of geological and geophysical insights to explain the recurrence times of recent, historic, and palaeoseismic earthquakes and the distribution of fault slip and crustal deformation associated with the Melinka and Valdivia earthquakes. We find that the frictional and rheological properties of the forearc, which are primarily controlled by the geological structure and fluid distribution at the megathrust, govern the magnitude and recurrence patterns of earthquakes in Chile.
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    Relation Between Oceanic Plate Structure, Patterns of Interplate Locking and Microseismicity in the 1922 Atacama Seismic Gap
    (2023) Gonzalez-Vidal, Diego; Moreno, Marcos; Sippl, Christian; Baez, Juan Carlos; Ortega-Culaciati, Francisco; Lange, Dietrich; Tilmann, Frederik; Socquet, Anne; Bolte, Jan; Hormazabal, Joaquin; Langlais, Mickael; Morales-Yanez, Catalina; Melnick, Daniel; Benavente, Roberto; Muenchmeyer, Jannes; Araya, Rodolfo; Heit, Benjamin
    We deployed a dense geodetic and seismological network in the Atacama seismic gap in Chile. We derive a microseismicity catalog of >30,000 events, time series from 70 GNSS stations, and utilize a transdimensional Bayesian inversion to estimate interplate locking. We identify two highly locked regions of different sizes whose geometries appear to control seismicity patterns. Interface seismicity concentrates beneath the coastline, just downdip of the highest locking. A region with lower locking (27.5 & DEG;S-27.7 & DEG;S) coincides with higher seismicity levels, a high number of repeating earthquakes and events extending toward the trench. This area is situated where the Copiapo Ridge is subducted and has shown previous indications of both seismic and aseismic slip, including an earthquake sequence in 2020. While these findings suggest that the structure of the downgoing oceanic plate prescribes patterns of interplate locking and seismicity, we note that the Taltal Ridge further north lacks a similar signature.