scholarly journals De riesgos y metáforas. En torno a «Los sótanos del universo»

2018 ◽  
Vol 3 (1) ◽  
Author(s):  
Juan Meléndez Sánchez
Keyword(s):  
Inverse Problem ◽  
The Earth

Resumen: Dos ecos galileanos percibidos en Los sótanos del universo: (1) La epistemología del riesgo que preconiza Juan Arana se prefigura en el cálculo de errores que inaugura (al menos conceptualmente) Galileo, y que se opone al paradigma del rigor escolástico que sigue arraigado en la filosofía de Descartes y sus sucesores. (2) La metáfora del conocimiento como resultado del “problema inverso” que resuelven los geólogos, infiriendo la estructura de la Tierra de los ecos de los terremotos, sugiere un paralelismo con el “subsuelo matemático” en el que residen las teorías para Galileo, y nos hace especular sobre la naturaleza matemática de la realidad última.Palabras clave: Epistemología, Galileo, Escolástica, Descartes, Ciencia, Cálculo de errores, Matemáticas.Abstract: Two Galilean echoes perceived in Los Sótanos del Universo: (1) The epistemology of risk precognised by Juan Arana is prefigured in the calculus of errors that Galileo inaugurate (conceptually at least) and that is opposed to the paradigm of scholastic rigour which is found in Descartes and in his successors’ philosophy. (2) The metaphor of knowledge as result of the “inverse problem”, which geologists solve deducing the estructure of the Earth from the echoes produced by earthquakes, suggests a similarity with the “underground of mathematics” where the theories are according to Galileo and that make us questioning about the mathematical nature of the final reality.Keywords: Epistemology, Galileo, Scholasticism, Descartes, Science, Calculus of Errors, Mathematics.Recibido: 18 de diciembre de 2012. Aprobado: 12 de diciembre de 2013.

Inversion of induced polarization data

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1327-1341 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Effective Conductivity ◽  
Optimization Theory ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Earth Structure ◽  
Nonlinear Inverse Problem ◽  
Polarization Data ◽  
The Earth

We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effect of chargeability is to alter the effective conductivity when current is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP responses to be numerically modeled by carrying out two forward modelings using a DC resistivity algorithm. The intimate connection between DC and IP data means that inversion of IP data is a two‐step process. First, the DC potentials are inverted to recover a background conductivity. The distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation and solving a linear inverse problem, (2) manipulating the conductivities obtained after performing two DC resistivity inversions, and (3) solving a nonlinear inverse problem. Our procedure for performing the inversion is to divide the earth into rectangular prisms and to assume that the conductivity σ and chargeability η are constant in each cell. To emulate complicated earth structure we allow many cells, usually far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a “model” (either the distribution of σ or η)is sought that minimizes the objective function subject to adequately fitting the data. Generalized subspace methodologies are used to solve both inverse problems, and positivity constraints are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configuration of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and by inverting dipole‐dipole data taken in Quebec.

Seismic Rays

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Inverse Problem ◽  
Seismic Tomography ◽  
Seismic Waves ◽  
Seismic Station ◽  
Three Dimensional ◽  
Arrival Times ◽  
The Earth ◽  
Straight Lines ◽  
Ray Path ◽  
Uniform Composition

This chapter focuses on the underlying mathematics of seismic rays. Seismic waves caused by earthquakes and explosions are used in seismic tomography to create computer-generated, three-dimensional images of Earth's interior. If the Earth had a uniform composition and density, seismic rays would travel in straight lines. However, it is broadly layered, causing seismic rays to be refracted and reflected across boundaries. In order to calculate the speed along the wave's ray path, the time it takes for a seismic wave to arrive at a seismic station from an earthquake needs to be determined. Arrival times of different seismic waves allow scientists to define slower or faster regions deep in the Earth. The chapter first presents the relevant equations for seismic rays before discussing how rays are propagated in a spherical Earth. The Wiechert-Herglotz inverse problem is considered, along with the properties of X in a horizontally stratified Earth.

scholarly journals Two optimization methods for solving the inverse gravimetrical problem

2021 ◽  
Vol 2092 (1) ◽  
pp. 012017
Author(s):  
Merey Kenzhebayeva
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Numerical Analysis ◽  
Gravity Field ◽  
Gradient Method ◽  
Optimization Problems ◽  
Mineral Exploration ◽  
Optimization Methods ◽  
The Earth

Abstract Mineral exploration, in particular, increasing the accuracy of calculations up to now is one of the urgent problems of geophysics. It is necessary to restore the density of a given inhomogeneity after considering the results of measuring the potential and its gradient on the surface of the earth. One of the measured values, the potential or the gradient of the gravity field, is chosen beyond the boundary condition, and the second corresponds to the minimized functional, i.e. one in-verse problem can be put in correspondence two different optimization problems. Both problems are solved based on the same gradient method. Based on the numerical analysis, two methods for solving the inverse problem are compared.

scholarly journals A project of creating atlas aftershocks of strong earthquakes

2019 ◽  
pp. 79-84
Author(s):  
A. V. Guglielmi ◽  
A. D. Zavyalov ◽  
O. D. Zotov
Keyword(s):  
Inverse Problem ◽  
Strong Earthquake ◽  
Main Shock ◽  
Earthquake Source ◽  
Problem Solution ◽  
Strong Earthquakes ◽  
Omori Law ◽  
The Earth ◽  
Interesting Possibility ◽  
Source Physics

The Omori Law, which describes the repeated underground shocks after a strong earthquake, is written in the form of a nonlinear differential equation. An idea of the focal deactivation coefficient after the main shock is introduced. Two advantages of the new wording of the Omori Law are given. Firstly, there is an interesting possibility to naturally take into account exogenous and endogenous triggers affecting the earthquake source. Endogenous triggers in the form of round-the-world seismic echo and free oscillations of the Earth, excited by the main shock, are especially noted. The second advantage is that the differential aftershock equation makes it possible to put the reverse problem of the earthquake source physics. The essence of the inverse problem is to determine the deactivation coefficient from the data on the observed aftershock frequency. Examples of inverse problem solution are given. The project of creation of the Atlas of aftershocks on the basis of the solution of the inverse problem of the source, cooling down after a strong earthquake is offered.

Inversion of magnetotelluric data using localized conductivity constraints

Geophysics ◽  
1986 ◽  
Vol 51 (8) ◽  
pp. 1603-1607 ◽  
Author(s):  
Kenneth P. Whittall
Keyword(s):  
Inverse Problem ◽  
Integral Form ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Physical Constraints ◽  
Direct Inversion ◽  
The Earth ◽  
External Sources ◽  
The One ◽  
Conductivity Models

I present an algorithm for the one‐dimensional magnetotelluric inverse problem of finding conductivity as a function of depth in the earth. The algorithm uses linear programming to solve an integral form of a nonlinear Riccati equation. This iterative scheme sacrifices the efficiency of direct inversion for the overwhelming advantages of incorporating localized conductivity constraints. I use localized conductivity constraints in two ways to combat the nonuniqueness of the nonlinear inverse problem. First, I impose physical constraints derived from external sources to restrict the nonuniqueness and construct conductivity models that are closer to reality. Second, I impose arbitrary constraints in an effort to assess the extent of nonuniqueness and explore the range of acceptable profiles. The first technique enhances the reliability of an interpretation, and the second measures the plausibility of particular conductivity features.

scholarly journals Monitoring near-Earth-object discoveries for imminent impactors

2018 ◽  
Vol 616 ◽  
pp. A176 ◽  
Author(s):  
Otto Solin ◽  
Mikael Granvik
Keyword(s):  
Inverse Problem ◽  
Probability Density Function ◽  
Orbital Element ◽  
Automated System ◽  
Data Sets ◽  
Earth Object ◽  
The Earth ◽  
Highly Nonlinear ◽  
The Impact ◽  
Probability Density Function Pdf

Aims. We present an automated system called NEORANGER that regularly computes asteroid-Earth impact probabilities for objects on the Minor Planet Center’s (MPC) Near-Earth-Object Confirmation Page (NEOCP) and sends out alerts of imminent impactors to registered users. In addition to potential Earth-impacting objects, NEORANGER also monitors for other types of interesting objects such as Earth’s natural temporarily-captured satellites. Methods. The system monitors the NEOCP for objects with new data and solves, for each object, the orbital inverse problem, which results in a sample of orbits that describes the, typically highly-nonlinear, orbital-element probability density function (PDF). The PDF is propagated forward in time for seven days and the impact probability is computed as the weighted fraction of the sample orbits that impact the Earth. Results. The system correctly predicts the then-imminent impacts of 2008 TC3 and 2014 AA based on the first data sets available. Using the same code and configuration we find that the impact probabilities for objects typically on the NEOCP, based on eight weeks of continuous operations, are always less than one in ten million, whereas simulated and real Earth-impacting asteroids always have an impact probability greater than 10% based on the first two tracklets available.

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