1,721,096 research outputs found
Resolvability of the 3D density structure of the Earth's mantle using normal mode theory
No full textWe performed an investigation of the large scale seismic wave speeds and density structure of the Earth’s mantle using free oscillations. Seismic free oscillations, or normal modes, are convenient for analysing low-frequency seismograms in a hetero- geneous Earth. To use these, we must address how to calculate exact seismograms using normal modes, and how to formulate the inverse problem to infer Earth’s 3D structure. The most important findings of this research are: • In order for seismograms to be theoretically exact, full mode coupling calcula- tions must involve an infinite set of modes. In practice, only a finite subset of modes can be used, introducing an error into the seismograms. We found that coupling modes 1-2 mHz above the highest frequency of interest is essential for having sufficiently accurate signals to infer density. • Observations of free oscillations provide important constraints on the heteroge- neous structure of the Earth. This inference problem has usually been addressed by the measurement and interpretation of splitting functions. These can be seen as secondary data extracted from low frequency seismograms. The measurement step necessitates the calculation of synthetic seismograms, but current imple- mentations rely on approximations referred to as self- or group-coupling and do not use fully accurate seismograms. We therefore investigated whether a systematic error might be present in currently published splitting functions. As is well known, the density signal is weak in low-frequency seismograms. Our results suggest this signal is of similar magnitude to the realistic uncertainties associated with currently published splitting functions. Thus, great care must be taken in any attempt to robustly infer details of Earth’s density structure using current splitting functions. • We investigated the problem of inferring density using currently published split- ting functions with properly calibrated uncertainties together with a novel prob- abilistic inversion technique, Hamiltonian Monte Carlo. Models are strongly dependent on damping. We found that shear wave speed models are statisti- cally significant in terms of misfit change, while density and compressional wave speeds are not. Therefore any interpretation of Earth’s mantle density based on splitting functions might be inaccurate. • A promising approach is the direct spectral inversion, which uses spectra di- rectly without the need of splitting functions. We found that misfit changes corresponding to the inferred models are statistically significant even for den- sity and compressional wave speed, but depend on a good starting model. We only used group coupling and relatively low frequency spectra for computa- tional reasons. Full coupling together with high frequencies might solve this long-lasting problem to infer density contrasts in the Earth’s mantle
Resolvability of the 3D density structure of the Earth's mantle using normal mode theory
No full textWe performed an investigation of the large scale seismic wave speeds and density structure of the Earth’s mantle using free oscillations. Seismic free oscillations, or normal modes, are convenient for analysing low-frequency seismograms in a hetero- geneous Earth. To use these, we must address how to calculate exact seismograms using normal modes, and how to formulate the inverse problem to infer Earth’s 3D structure. The most important findings of this research are: • In order for seismograms to be theoretically exact, full mode coupling calcula- tions must involve an infinite set of modes. In practice, only a finite subset of modes can be used, introducing an error into the seismograms. We found that coupling modes 1-2 mHz above the highest frequency of interest is essential for having sufficiently accurate signals to infer density. • Observations of free oscillations provide important constraints on the heteroge- neous structure of the Earth. This inference problem has usually been addressed by the measurement and interpretation of splitting functions. These can be seen as secondary data extracted from low frequency seismograms. The measurement step necessitates the calculation of synthetic seismograms, but current imple- mentations rely on approximations referred to as self- or group-coupling and do not use fully accurate seismograms. We therefore investigated whether a systematic error might be present in currently published splitting functions. As is well known, the density signal is weak in low-frequency seismograms. Our results suggest this signal is of similar magnitude to the realistic uncertainties associated with currently published splitting functions. Thus, great care must be taken in any attempt to robustly infer details of Earth’s density structure using current splitting functions. • We investigated the problem of inferring density using currently published split- ting functions with properly calibrated uncertainties together with a novel prob- abilistic inversion technique, Hamiltonian Monte Carlo. Models are strongly dependent on damping. We found that shear wave speed models are statisti- cally significant in terms of misfit change, while density and compressional wave speeds are not. Therefore any interpretation of Earth’s mantle density based on splitting functions might be inaccurate. • A promising approach is the direct spectral inversion, which uses spectra di- rectly without the need of splitting functions. We found that misfit changes corresponding to the inferred models are statistically significant even for den- sity and compressional wave speed, but depend on a good starting model. We only used group coupling and relatively low frequency spectra for computa- tional reasons. Full coupling together with high frequencies might solve this long-lasting problem to infer density contrasts in the Earth’s mantle
Studying global discontinuities using full waveforms
No full textSeismology aims at obtaining accurate tomographic images of the Earth’s interior by simulating models to create waveforms that fit recorded seismograms. The resolution of an acquired image greatly depends on the accuracy of the numerical tool used for modelling and the quality of observed data. Using a state-of-the art numerical wave propagation software, I study the structure of global discontinuities. I develop an iterative optimisation methodology for modelling the waveforms by minimising the misfit caused by the existence of topographic structure on discontinuities. Given that the disconti- nuity structure has mainly been studied in a ray theoretical framework, I only use synthetics in order to assess the reliability of conventional methods and to develop a novel approach based on full waveforms and non-linear min- imisation. My study also focuses on the sensitivity of waveforms related to discontinuity structure. Analyses of their exact sensitivity pave the way towards a better comprehension of real data and improvement of the inversion methodologies. To that extent, a new inversion method is proposed which relies on the iterative optimisation of boundary and structural models, with special focus on the structure of global discontinuities using boundary Fréchet derivatives for the first time in an inversion problem. Successive steps for the iterative optimisation of the model are: choose a starting model and select a misfit function to calculate the discrepancies between observed and synthetic data. The objective function is the most important step in the inversion. By computing the derivative of this function, employing time-reversal and adjoint methods, one creates a model update which should minimise the previous misfit. Adjoint methods rely on the inter- action between "forward" and "adjoint" wavefields, propagating from source to receivers and vice versa. This process is iterated until the global misfit value sufficiently reduces. In this thesis, it is shown that this novel approach for imaging discontinuities improves the inference of internal discontinuity structure and provides an integrated method for global seismology. The pro- posed full waveform methodology outperforms ray theory to a great extent and should be used in real data applications
Studying global discontinuities using full waveforms
No full textSeismology aims at obtaining accurate tomographic images of the Earth’s interior by simulating models to create waveforms that fit recorded seismograms. The resolution of an acquired image greatly depends on the accuracy of the numerical tool used for modelling and the quality of observed data. Using a state-of-the art numerical wave propagation software, I study the structure of global discontinuities. I develop an iterative optimisation methodology for modelling the waveforms by minimising the misfit caused by the existence of topographic structure on discontinuities. Given that the disconti- nuity structure has mainly been studied in a ray theoretical framework, I only use synthetics in order to assess the reliability of conventional methods and to develop a novel approach based on full waveforms and non-linear min- imisation. My study also focuses on the sensitivity of waveforms related to discontinuity structure. Analyses of their exact sensitivity pave the way towards a better comprehension of real data and improvement of the inversion methodologies. To that extent, a new inversion method is proposed which relies on the iterative optimisation of boundary and structural models, with special focus on the structure of global discontinuities using boundary Fréchet derivatives for the first time in an inversion problem. Successive steps for the iterative optimisation of the model are: choose a starting model and select a misfit function to calculate the discrepancies between observed and synthetic data. The objective function is the most important step in the inversion. By computing the derivative of this function, employing time-reversal and adjoint methods, one creates a model update which should minimise the previous misfit. Adjoint methods rely on the inter- action between "forward" and "adjoint" wavefields, propagating from source to receivers and vice versa. This process is iterated until the global misfit value sufficiently reduces. In this thesis, it is shown that this novel approach for imaging discontinuities improves the inference of internal discontinuity structure and provides an integrated method for global seismology. The pro- posed full waveform methodology outperforms ray theory to a great extent and should be used in real data applications
Applications of machine learning to mineral physics data and the inference of the thermochemical structure of the Earth's mantle.
No full textThe physical and chemical properties of the Earth’s mantle govern the cause of natural disasters, such as earthquakes and volcanoes. Since we do not have direct access to mantle materials, their properties are often inferred from laboratory measurements and surface observations (e.g. seismic data from earthquake recordings). This thesis addresses some key problems we face while utilising these data to constrain the thermal and chemical properties of the mantle. Firstly, we propose a data-driven approach based on machine learning to explain the laboratory measurements and quantify their uncertainties in the absence of an adequate physical model. Our results show that although conventional approaches based on fitting the measurements to an assumed model may appear better constrained, they could potentially provide biased results. Secondly, we use the data-driven approach to explore which thermochemical parameters can be constrained (and to what extent) with limited seismic observables- wave speeds and density. Our results show that these observables constrain temperature and major chemical parameters (silicon, magnesium, and iron), and they indicate the presence of thermochemical heterogeneities at the lowermost mantle. The dense and slow piles at the bottom of the lower mantle seen in seismic data can be explained by an enrichment in silica and iron content- characteristic feature of enstatite chondrites. The inferred heterogeneities have profound implications for the dynamics of the mantle and outer core. The methodology developed in this thesis is extremely efficient. It can easily incorporate additional observables and thus, has wide applications in the seismology and mineral physics community
Finding the patterns in mantle convection
No full textIt is very difficult to study mantle convection over periods of millions of years because convection is a non-linear process. In this thesis, I present a new method for studying the underlying statistics in convection patterns. I use neural networks to find patterns in these statistics to make inferences about the mantle and its history. I can make inferences about constant rheological parameters, evolving time dependent parameters, such as the development of LLSVPs, and the compositional, thermal and viscosity structure of the mantle. All of these parameters have important implications for the formation of Earth, evolution of plate tectonics and therefore life, interpretation of geophysical observations and understanding of dynamic processes. They are all current poorly constrained, making any new method potentially powerful. I also use neural networks as a predictive tool. Every inference is made using a Bayesian approach and is therefore fully probabilistic and includes uncertainty estimates. These uncertainty estimates are in themselve novel to geodynamics
Data-driven redatuming and compressive sensing in complex media for subsurface monitoring
No full textSeismic imaging of subsurface structures situated deep beneath complex overburden structures, such as sub-salt, remains challenging for researchers. However, the Marchenko method has offered a new and promising perspective on data-driven redatuming. While it has proven successful for media characterized by smoothly varying interfaces, it has shown only moderate success for complex media. To address this limitation, we present an alternative form of the Marchenko representation that retrieves only the unknown perturbations to both focusing functions and redatumed fields using a scattering framework. A second redatuming step is then used to reconstruct a local virtual response at a preset datum level, leveraging multidimensional deconvolution. We reformulate the problem in the time domain, which was previously believed to be computationally intractable, and introduce several physical constraints that naturally drive the inversion towards a reduced set of reliable and stable solutions. By solving the problem in the time domain, we were able to successfully reconstruct the overburden-free reflection response beneath a complex salt body from noise-contaminated data. This study is supplemented with low-rank interpolation techniques that aim at enabling large-scale 3D field surveys to be considered in current production flows. We propose a novel transform domain revealing the low-rank character of seismic data that prevents the inherent matrix enlargement introduced when the data are sorted in the midpoint-offset domain and develop a robust extension of the current matrix completion framework to account for lateral physical constraints that ensure a degree of proximity similarity among neighbouring points
Interpreting GPS observations of the megathrust earthquake cycle: insights from numerical models
Get PDFDuring a megathrust earthquake cycle, the plates accumulate strain in the interseismic stage due to locking of a portion of the megathrust that separates them. This strain is released during the earthquake and following rapid postseismic relaxation. As summarised in Chapter 1, this understanding was built through decades of seismological and geodetic observations and of advances in physics-based models. Models link properties and structures to observable quantities and are crucial to interpreting observed surface deformation in terms of the processes and materials in the inaccessible subsurface. However, different models can approximate the same observations roughly equally well. Furthermore, more sophisticated models do not necessarily reflect better the processes and properties of the subsurface; at the same time, simpler models that can explain some observations do not necessarily reflect the key processes occurring throughout one or multiple earthquake cycles. This thesis uses relatively simple three-dimensional models that still capture the key processes occurring during repeated earthquake cycles, without attempting to reproduce the structure or properties of specific subduction zones, to examine possible explanations of geodetic observations from global navigation satellite systems (GNSSs) at different stages of the cycle. Chapter 2 focuses on the interseismic, horizontal deformation of the overriding plate, which is in apparent contrast with observations of far-reaching coseismic displacement. We estimate the spatial patterns, with uncertainties, of GNSS velocities in South America, Southeast Asia, and northern Japan. Interseismic velocities with respect to the overriding plate generally decrease with distance from the trench with a steep gradient up to a “hurdle”, beyond which the gradient is distinctly lower and velocities are small. The hurdle is located 500-1000 km away from the trench for the trench-perpendicular velocity component, and either at the same distance or closer for the trench-parallel component. The trench-perpendicular hurdle generally follows major tectonic or geological boundaries and seismological contrasts. We formulate and test the hypothesis that both the interseismic hurdle and the coseismic response result from a mechanical contrast in the overriding plate. Our models show that overriding plates with a sufficient contrast respond to locked interseismic convergence similarly to observations. The compliance contrast is probably mainly responsible for the observed hurdle and in turn results from thermal, compositional and thickness contrasts. Chapter 3 is concerned with the increased landward velocities that were recorded onshore after 6 megathrust earthquakes in subduction zone regions adjacent to the ruptured portion. We investigate whether bending can be expected to reproduce this observed enhanced landward motion (ELM). We find that viscous relaxation, but not afterslip, produces ELM when a depth limit is imposed on afterslip. This ELM results primarily from in-plane elastic bending of the overriding plate due to trenchward viscous flow in the mantle wedge near the rupture. Modeled ELM is, however, incompatible with the observations, which are an order of magnitude greater and last longer. This conclusion does not significantly change when varying key model parameters. The observed ELM consequently appears to reflect faster slip deficit accumulation, implying a greater seismic hazard in lateral segments of the subduction zone. In Chapter 4, we study postseismic landward motion observed on the overriding plate in the vicinity of a major megathrust rupture. We argue that relocking of the megathrust, particularly at shallow depths, is needed for postseismic relaxation to produce landward motion on the tip of the overriding plate. We discuss how that this finding is consistent with previous simulations that implicitly relock the megathrust where afterslip is not included. We conclude that the Tohoku megathrust relocked within less than two months of the earthquake. This suggests that the shallow megathrust probably behaves as a true, unstably sliding asperity
Revisiting Earth's radial seismic structure using a Bayesian neural network approach
No full textThe gross features of seismic observations can be explained by relatively simple spherically symmetric (1-D) models of wave velocities, density and attenuation, which describe the Earth's average(radial) structure. 1-D earth models are often used as a reference for studies on Earth's thermo-chemical structure and dynamics, earthquake location determination and 3-D seismic tomographic models. Therefore, the quality of the latter is intrinsically linked to the robustness of the former. But what is the quality of such 1-D models? Seismic inverse problems are notoriously non-unique; different earth models can explain the data equally well, but may lead to incompatible interpretations of the nature of the Earth's interior and dynamics. Ideally, the assessment of solution quality is an integral part of any inverse method. The main motivation for this thesis was to investigate a means to simultaneously infer Earth structure and quantify the uncertainties in our estimates. A common (Bayesian) approach is to directly sample the posterior model probability density, as is done in Markov Chain Monte Carlo (MCMC) methods via a (guided) random walk. Here, I solve such seismological inference problems using pattern recognition and machine learning techniques. The method developed here, using articial neural networks, is exible and enables me to address specific hypotheses on Earth's structure in a robust, quantitative manner. Using normal mode splitting function coefficients and body wave travel times, I obtain complete statistical descriptions of features of radial Earth structure, in terms of elastic and anelastic structure, anisotropy and depths of major discontinuities. In general, I conclude that a lot can still be learned on 1-D Earth structure from seismic data; ideally, we do so prior to tackling the 3-D tomographic problem. An analysis of the information content suggests that the free oscillations constrain most parameters better than the body wave data. Spheroidal and toroidal mode data constrain the depth extent of the density excess in the lowermost mantle. Furthermore, I show, for the first time, that the average lower mantle is anisotropic below 1900 km depth, challenging the consensus that this part of the mantle is isotropic. It is possible to explain these seismic observations with currently available mineral physics data for lower mantle minerals. Therefore, seismic anisotropy, such as observed here, can provide constraints on mantle flow and deformation mechanisms. However, meaningful geodynamic interpretations require a full 3-D analysis to be made. Finally, I illustrate one pragmatic approach to data dimensionality reduction using autoencoder networks, as a first step towards non-linear seismic waveform inversion using encoded seismograms. The machine learning method adopted in this thesis is a pragmatic approach to solving non-linear Bayesian inverse problems. Their exibility and interpolation capabilities, in combination with the quantitative Bayesian framework, make neural networks well-suited for data sensitivity analysis and testing hypotheses on Earth structure. Rather than a replacement for Monte Carlo methods, I suggest that in the future they are used as a complementary tool, providing an initial assessment of data sensitivity and a lower bound on the information on model parameters that is contained in the data
Applications of machine learning to mineral physics data and the inference of the thermochemical structure of the Earth's mantle.
No full textThe physical and chemical properties of the Earth’s mantle govern the cause of natural disasters, such as earthquakes and volcanoes. Since we do not have direct access to mantle materials, their properties are often inferred from laboratory measurements and surface observations (e.g. seismic data from earthquake recordings). This thesis addresses some key problems we face while utilising these data to constrain the thermal and chemical properties of the mantle. Firstly, we propose a data-driven approach based on machine learning to explain the laboratory measurements and quantify their uncertainties in the absence of an adequate physical model. Our results show that although conventional approaches based on fitting the measurements to an assumed model may appear better constrained, they could potentially provide biased results. Secondly, we use the data-driven approach to explore which thermochemical parameters can be constrained (and to what extent) with limited seismic observables- wave speeds and density. Our results show that these observables constrain temperature and major chemical parameters (silicon, magnesium, and iron), and they indicate the presence of thermochemical heterogeneities at the lowermost mantle. The dense and slow piles at the bottom of the lower mantle seen in seismic data can be explained by an enrichment in silica and iron content- characteristic feature of enstatite chondrites. The inferred heterogeneities have profound implications for the dynamics of the mantle and outer core. The methodology developed in this thesis is extremely efficient. It can easily incorporate additional observables and thus, has wide applications in the seismology and mineral physics community
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