A relative moment tensor inversion technique applied to seismicity induced by mining

Three hybrid moment tensor inversion methods were developed for seismic sources originating from a small source region. These techniques attempt to compensate for various types of systematic error (or noise) that influence seismograms recorded in the underground environment in order to achieve an accurate and robust measure of the seismic moment tensor. The term 'hybrid' was used to distinguish between the relative method proposed by Dahm (1995) and the methods developed in this thesis. The hybrid methods were essentially weighting schemes designed to enhance the accuracy of the computed moment tensors by decreasing the influence of any low quality observations, to damp (or amplify) any signals that have been overestimated (or underestimated) due to local site effects, and to correct for raypath focussing or defocussing that results from inhomogeneities in the rockmass. The weighting or correction applied to a particular observation was derived from the residuals determined when observed data were compared with corresponding theoretical data (for a particular geophone site, sensor orientation and wave phase) and were calculated using a cluster of events rather than a single event. The first and second weighting schemes were indirectly related to the mean and the median of the residuals where the residuals were defined as the ratio of the theoretical to observed data. In the third scheme, the residuals were defined as the difference between the observed and theoretical data and the weights were based on the distance of a data point (measured in standard deviations) from the mean residual. In each of the weighting schemes, the correction was applied iteratively until the standard error of the least-squares solution (normalised to the scalar seismic moment) was a minimum. The schemes were non-linear because new weights were calculated for each iteration. A number of stability tests using synthetic data were carried out to quantify the source resolving capabilities of the hybrid methods under various extreme conditions. The synthetic events were pure double-couple sources having identical fault-plane orientations, and differing only in rake. This similarity in the mechanisms was chosen because the waveforms of tightly grouped events recorded underground often show high degrees of similarity. For each test, the results computed using the three hybrid methods were compared with one another and with those computed using the single event, absolute method and two relative methods (with and without a reference mechanism). In the noise-free situation, it was found that the relative method without reference mechanism showed the highest resolution of mechanisms, provided that the coverage of the focal sphere was not too sparse (> 3 stations). The hybrid method using a median correction was found to be the most robust of all the methods tested in the most extreme case of poor coverage (2 stations) of the focal sphere. When increasing levels of pseudo-random noise were applied to the data, the absolute moment tensor inversion method, the hybrid method using a median correction, and the hybrid method using a weighted mean correction all showed similar robustness and stability in extreme configurations concerning network coverage of the focal sphere and noise level. When increasing levels of systematic noise were added to the data, the hybrid methods using a median correction and weighted mean correction were found to exhibit similar robustness and stability in extreme configurations concerning network coverage of the focal sphere and systematic noise. In all situations investigated, these two hybrid methods outperformed the relative and absolute methods. The hybrid moment tensor inversion methods using a median and weighted mean correction were applied to a cluster of 14 events, having remarkably similar waveforms, recorded at Oryx Gold Mine. For comparative purposes, the absolute method was also applied. The inputs to the inversion methods consisted of the spectral plateaus of both P- and S-waves at frequencies below the comer frequency of the time-integrated displacement traces. The polarities of dominant motion were used as an additional constraint and were determined from cross-correlation of observed with synthetic P- or S-waves. The solutions computed using the hybrid moment tensor inversion using a median correction displayed a distinct improvement after the iterative residual correction procedure was applied. The radiation patterns and faultplane solutions showed a high degree of similarity, and are probably more accurate reflections of reality than those computed using the absolute moment tensor inversion methods. These observations are very encouraging and point towards the method's potential for use as a standard processing tool for mine seismicity. The implications of this work are a better understanding of the focal mechanisms of seismic events induced by mining activities, ultimately leading to improved safety underground

A lunar density model consistent with topographic, gravitational, librational, and seismic data

A series of models of the lunar interior are derived from topographic, gravitational, librational, and seismic data. The librational parameters and low-degree gravity harmonics result primarily from surface height variations and only secondarily from lateral density variations. The moon departs from isostasy, even for the low-degree harmonics, with a maximum superisostatic stress of 200 bars under the major mascon basins. The mean crustal thicknesses under different physiographic regions are: mascons, 30–35 km; irregular maria, 50–60 km; and highlands, 90–110 km. A possible composition consistent with our model is an anorthositic crust, underlain by a predominantly forsterite upper mantle which grades into a refractory rich lower mantle surrounding a pyrrhotite core

Scattering of elastic waves using non-orthagonal expansions

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1996.Includes bibliographical references (p. 270-284).by Matthias Georg Imhof.Ph.D

Partitioned simulation of the interaction between an elastic structure and free surface flow

Currently, the interaction between free surface flow and an elastic structure is simulated with monolithic codes which calculate the deformation of the structure and the liquid–gas flow simultaneously. In this work, this interaction is calculated in a partitioned way with a separate flow solver and a separate structural solver using the interface quasi-Newton algorithm with approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS). The interaction between an elastic beam and a sloshing liquid in a rolling tank is calculated and the results agree well with experimental data. Subsequently, the impact of both a rigid cylinder and a flexible composite cylinder on a water surface is simulated to assess the effect of slamming on the components of certain wave-energy converters. The impact pressure on the bottom of the rigid cylinder is nearly twice as high as on the flexible cylinder, which emphasizes the need for fluid–structure interaction calculations in the design process of these wave-energy converters. For both the rolling tank simulations and the impact simulations, grid refinement is performed and the IQN-ILS algorithm requires the same number of iterations on each grid. The simulations on the coarse grid are also executed using Gauss-Seidel coupling iterations with Aitken relaxation which requires significantly more coupling iterations per time step

On friction in forming : an experimental-numerical method to quantify contact behaviour

xii+138hlm.;24c

Finite Element Models of Volcano Deformational Systems Having Structural Complexity

[spa] El objetivo principal de este trabajo es la construcción de modelos de elementos finitos (FEMs) 3-D con complejidades estructurales con el fin de simular sistemas volcánicos de manera más realista. Como ejemplo de aplicación se ha escogido la caldera de Rabaul, un sistema volcánico cuya dinámica no se comprende por completo. Invirtiendo los datos de InSAR recogidos durante los años 2007-2010, investigamos las fuentes de desplazamiento de la superficie y proporcionamos claves de relevancia sobre el sistema magmático superficial real. Incluyendo características realistas, como la topografía y heterogeneidades mecánicas, usamos las informaciones geofísicas y geológicas para construir modelos de FEMs complejos en 3D. En última instancia, proporcionamos una estrategia para llevar a cabo una inversión lineal basada en una matriz de fuentes que nos permite identificar una distribución de flujo de fluido a través de un volumen de posibles fuentes responsables de los cambios de presión en el medio según lo dictado por los datos, sin imponer a priori una forma de fuente específica y su profundidad. Los resultados permiten generar imágenes de la forma compleja de la fuente que da lugar a la deformación, en el espacio y en el tiempo, sin tener que utilizar ninguna fuente con una forma excesivamente simplificada a priori. Esto lleva el modelado de fuentes un paso adelante hacia modelos más realistas. En el caso de Rabaul, la aplicación de la metodología discutida anteriormente, muestra un sistema magmático superficial formado por dos lóbulos interconectados localizados bajo la caldera y en posiciones diametralmente opuestas. La interconexión y la distribución espacial de las fuentes encuentran correspondencia en la petrología de los productos descritos en literatura y en la dinámica de las erupciones que caracterizan la caldera. Los resultados obtenidos mediante la aplicación del método son satisfactorios y demuestran que la inversión lineal basada en la matriz de fuentes de FE propuesta puede ser considerada adecuada para generar modelos de sistemas magmáticos. Se puede aplicar fácilmente a cualquier volcán, ya que tiene en cuenta la deformación del edificio sin tener que especificar la forma de la fuente de deformación antes de la inversión.[eng] The main focus of this work is to build 3-D FEM models with structural complexities in order to simulate volcanic systems in a more realistic way. We use Rabaul as an example to show the application of the methods and strategies proposed to an active volcano. Rabaul caldera is a volcanic system whose dynamics still need to be understood to effectively predict the behavior of future eruptions. In comparison to the simplified analytic models used so far, more realistic models, such as Finite Elements Models (FEMs), are needed to more accurately explain recent deformation and understand the magmatic system. By inverting InSAR data collected between 2007 and 2010 (using linear inversions based on FEMs), we investigate the sources of surface displacement and provide insights about the actual shallow magmatic system. FEMs are numerical models that let us include realistic features such as topography and mechanical heterogeneities. We provide strategies to use geophysical and geological information to build complex 3-D parts and assemble them into 3-D models. We then compare the effects of different material properties configurations and of different source shapes on the deformational signal and on the strength source estimates (fluid flux or pressure). Ultimately, we provide a strategy for performing a linear inversion based on an array of FEM sources that allows us to identify a distribution of flux of fluid (or change in pressure) over a volume, without imposing an a-priori source shape and depth. We use Rabaul as an example to show the 3-D model’s validity and applicability to active volcanic areas. The methodology is based on generating a library of forward numerical displacement solutions, where each entry is the displacement generated by injecting a mass of fluid of known density and bulk modulus into a source of the array. The sources are simulated as fluid-filled cavities that can accept a specified flux of magma. As the array of sources is an intrinsic geometric aspect of all forward models and the sources are activated one at a time, the domain only needs to be discretized once. This strategy precludes the need for remeshing for each activated source and greatly reduces computational requirements. By using an array of sources, we are not investigating the geometric and pressure parameters of a simplified, unique source with a regular shape. Instead, we are investigating a distribution of flux of fluids over a volume of potential sources responsible for the pressure changes in the medium as dictated by the data. The results allow us to image the complex shape of the deformation source without having to use any a-priori or simplified sources. This takes source modeling a step towards more realistic source models. The application of the methodology to Rabaul shows a shallow magmatic system under the caldera made of two interconnected lobes located at the two opposite sides of the caldera. These lobes are suggested to be the feeding reservoirs of the ongoing Tavuvur volcano eruption, on the eastern side, and of the past Vulcan volcano eruptions, on the western side. The interconnection and spatial distribution of sources find correspondence in the petrography of the products described in literature and in the dynamics of the single and twin eruptions that characterize the caldera. The good results obtained from the application of the method show that the proposed linear inversion based on the FEM array of sources can be considered suitable for generating models of the magmatic system. It can be easily applied to any volcano, because it accounts for volcano deformation without having to specify the shape of the deformation source prior to inversion

Spatial Interaction Patterns

An algebraic examination of spatial models leads to the conclusion that a convenient description of the pattern of flows implicit in a geographical interaction table is obtained by displaying a field of vectors computed from the relative net exchanges. The vector field approximates the gradient of a scalar potential, and this may be invoked to explain the flows. The method can be applied to asymmetrical tables of a non-geographical nature

Eighth DOD/NASA/FAA Conference on Fibrous Composites in Structural Design, Part 2

Papers presented at the conference are compiled. The conference provided a forum for the scientific community to exchange composite structures design information and an opportunity to observe recent progress in composite structures design and technology. Part 2 contains papers related to the following subject areas: the application in design; methodology in design; and reliability in design