212 research outputs found
Fully nonlinear inversion of fundamental mode surface waves for a global crustal model
No full textWe use neural networks to find 1-dimensional marginal probability density functions (pdfs) of global crustal parameters. The information content of the full posterior and prior pdfs can quantify the extent to which a parameter is constrained by the data. We inverted fundamental mode Love and Rayleigh wave phase and group velocity maps for pdfs of crustal thickness and independently of vertically averaged crustal shear wave velocity. Using surface wave data with periods T > 35 s for phase velocities and T > 18 s for group velocities, Moho depth and vertically averaged shear wave velocity of continental crust are well constrained, but vertically averaged shear wave velocity of oceanic crust is not resolvable. The latter is a priori constrained by CRUST2.0. We show that the resulting model allows to compute global crustal corrections for surface wave tomography for periods T > 50 s for phase velocities and T > 60 s for group velocities
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
Subsonic near-surface P-velocity and low S-velocity observations using propagator inversion
No full textDetailed knowledge of near-surface P- and S-wave velocities is important for processing and interpreting multicomponent land seismic data because (1) the entire wavefield passes through and is influenced by the near-surface soil conditions, (2) both source repeatability and receiver coupling also depend on these conditions, and (3) near-surface P- and S-wave velocities are required for wavefield decomposition and demultiple methods. However, it is often difficult to measure these velocities with conventional techniques because sensitivity to shallow-wave velocities is low and because of the presence of sharp velocity contrasts or gradients close to the earth's free surface. We demonstrate that these near-surface P- and S-wave velocities can be obtained using a propagator inversion. This approach requires data recorded by at least one multicomponent geophone at the surface and an additional multicomponent geophone at depth. The propagator between them then contains all information on the medium parameters governing wave propagation between the geophones at the surface and at depth. Hence, inverting the propagator gives local estimates for these parameters. This technique has been applied to data acquired in Zeist, the Netherlands. The near-surface sediments at this site are unconsolidated sands with a thin vegetation soil on top, and the sediments considered are located above the groundwater table. A buried geophone was positioned 1.05 m beneath receivers on the surface. Propagator inversion yielded low near-surface velocities, namely, 270 ± 15 m/s for the compressional-wave velocity, which is well below the sound velocity in air, and 150 ± 9 m/s for the shear velocity. Existing methods designed for imaging deeper structures cannot resolve these shallow material properties. Furthermore, velocities usually increase rapidly with depth close to the earth's surface because of increasing confining pressure. We suspect that for this reason, subsonic near-surface P-wave velocities are not commonly observed
Probabilistic tomography using body wave, normal-mode and surface wave data. Geologica Ultraiectina (325)
No full textOver the last three decades a vast number of tomographic images has been produced, but the quantitative assessment of their accuracy and uniqueness has only just started. A relatively recent technique in this direction has been made by (Trampert et al., 2004) using probabilistic tomography. It is based on a full model space search, the Neighbourhood Algorithm (NA), with which to solve the inverse problem. This provides a representation of seismic constraints as probability density functions (pdfs) from which one can easily calculate the most likely model and its associated uncertainty. Since a full model space search quickly limits the dimension of the explorable parameter space, an essential condition to apply the NA is to have a small number of unknowns. Probabilistic tomography has been applied to invert surface waves and normal-modes. The aim of this thesis was to incorporate body wave data to increase the depth resolution in the lowermost mantle. The first step, therefore, was to establish a formalism which allows us to treat body waves as surface waves and free oscillations and, thus, separate the inverse problem into its lateral and radial components. In a spherically layered Earth using the path-average approximation, body wave delay times can be inverted in two steps. The first step is the construction of vertical travel-time residual maps as a function of ray parameter. The second step is their depth inversion, less well constrained than the first step but characterized by a small number of parameters and, hence, suitable to be solved by the NA. Such a procedure, called path-average approach, works well for long wavelength structure for the forward and inverse problem. Combing a body wave dataset characterized by a good resolution between 2441 and 2891 km and the advantages of the path-average approach, we provided a new insight into the lowermost mantle based on lateral variations of P-, S-seismic velocities and the corresponding seismologically observed ratio without an explicit depth inversion for seismic wave velocities variation. Following a robust statistical approach, we are able to link these seismic heterogeneities to mineral physics and provide evidence for the existence of post-perovskite near the core-mantle boundary. In the framework of probabilistic tomography, applying the path-average approach we inverted body wave vertical travel-time residual maps, normal-mode splitting functions and surface wave phase velocity maps locally for depth using the NA. We constructed a shear wave, compressional wave, bulk sound speeds and density perturbation model with associated uncertainty. The estimation of the correlation between parameters and the RMS amplitude of seismic variations clearly indicates a thermal and chemical nature of heterogeneity in the lower mantle. Furthermore, our models fully confirm the conclusions achieved by the model of Resovsky & Trampert (2003), produced without body waves. One strength of probabilistic tomography is the possibility to convert easily the pdfs of seismic velocities and density perturbations into pdfs of thermal and compositional anomalies. We constructed a model of temperature, iron and perovskite variations combining mineral physics data with the shear, bulk sound wave-speeds and density variation models described above
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
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