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It 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.

This thesis reports on studies that have been carried out to better image the crustal and upper mantle shear velocity structure around the Gulf of California, Mexico. The Gulf of California forms a part of the plate boundary between the Pacific and North-American plates, where transform motion in the North converts into oceanic spreading in the South. Although currently oblique extension occurs within the gulf, in the past subduction of the oceanic Farallon plate took place along a trench west of what is currently the Baja California Peninsula. Around 12 Ma subduction and spreading ceased and the remaining parts of the Farallon plate were captured by the Pacific plate. After this the Gulf of California started to develop and around 5 Ma the Pacific-North America plate boundary shifted to its present location within the gulf. The study is subdivided into three parts. In the first part we use a spectral-element code to model seismic wave propagation and the adjoint technique to calculate finite-frequency sensitivity kernels for two-station surface wave measurements. We found a dominant sensitivity in the interstation region, close to what is assumed in the two-station method. However, we also show that anomalous structures even far from the assumed propagation path can significantly affect the measurements. To improve regional tomographic inversions using the two-station method, sensitivity kernels should therefore be taken into account. At the regional scale we are interested in this requires high computational costs, which are difficult to reach in practice. In the second part, instead of improving the lateral resolution using the method described above, we improve the vertical resolution by 1-D joint inversions of surface wave and receiver function data recorded by NARS-Baja stations. We use a Neighbourhood Algorithm to obtain shear velocity models beneath the stations. We are able to find sediment and crustal thicknesses below the stations in the area. In the upper mantle we find indications for the presence of subducted plate remnants below the middle and southern parts of the Baja California Peninsula and we identify the top as a sharp interface. The absence of plate remnants below the northern part explains why the middle and southern parts of the Baja California Peninsula move faster to the Northwest with respect to the North-American plate than the northern part. In the third part we investigate the effects of dipping crustal layers on the receiver functions. We find that azimuthal differences is the receiver function data can be explained by a westward dipping Moho below the Baja California Peninsula, and a dipping mid-crustal layer throughout the entire area. For detailed crustal imaging of the Baja California area using receiver functions more complex modelling than a 1-D inversion is recommended.

Numerous problems in the field of seismology require the determination of parameters of a physical model that are compatible with a set of observations and prior assumptions. This type of problem is generally termed inverse problem. While, in many cases, we are able to predict observations, given a particular set of parameters with high accuracy and precision using numerical and analytical methods, often we are unable to directly infer model parameters from observations. This has lead to the development of a large number of inverse methodologies. For many applications it is necessary not only to obtain a set of best fitting parameters, but also an estimate of the attached uncertainties, which arise from the fact that any observation is subject to measurement uncertainties and from other sources of uncertainty that may be present due to numerical limitations or simplifying assumptions. Often, the situation is further complicated by the non-linear nature of many inverse problems, leading to non-Gaussian and possibly non-unique posterior distributions. An important seismological inverse problem is the determination of earthquake source parameters. Source parameters are on one hand needed as an input for subsequent investigations, such as tomographic imaging or finite fault studies. On the other hand source parameter estimates are required in order to provide information to the public as quickly as possible after a new earthquake has initiated - a field known as earthquake early warning. We have developed a methodology for rapid probabilistic moment tensor point source inversions able to cope with a wide variety of data types. Accurate and computationally expensive synthetic forward modelling can be incorporated without significantly altering the time required for the inversions. Our methodology is based on finding an approximation to the conditional posterior probability of source models given observations by smoothly interpolating a set of prior samples. The interpolation is obtained using ensembles of Mixture Density Networks (MDNs) - a class of artificial neural networks, whose output are the parameters of a Gaussian mixture model. Once an ensemble has been constructed, new observations can be inverted within the fraction of a second on a standard desktop computer. The method is therefore well suited for earthquake early warning, where new observations must be inverted routinely and rapidly. We apply the method to two scenarios in Southern California using both synthetic and observed datasets. We invert regional static and dynamic GPS displacement data for the 2010 M 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth, and focal mechanism. Moreover, we show how accurate 3-D spectral element simulations can be incorporated into the rapid inversion scheme by means of a model scenario focussing on the 2008 M 5.4 Chino Hills earthquake. We discuss general implications, advantages and limitations of the method and suggest directions for potential future research.

The 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.

Seismic reflection methods are widely used for the detection of hydrocarbons in subsurface structures up to several kilometers depth. However, since most data are acquired at or close to the Earth's surface, it is essential to understand the influence of the near-surface on the acquired data in order that its effects are not interpreted as pertaining to the reservoir. The near-surface effect on seismic data has two main origins: (i) near-surface wave propagation and (ii) wavefield acquisition. Wavefield acquisition comprises both wavefield excitation and wavefield measurement, i.e. source and receiver effects. Since both P- and S-wave velocities are observed to vary rapidly close to the Earth's surface, wave propagation in the near-surface is often very complex. In order to improve our understanding of near-surface wave propagation, we investigated and developed methods to determine near-surface P- and S-wave velocities. For this purpose, we used dense recording geometries including buried geophones, since these material properties cannot be resolved with a conventional acquisition geometry using geophones only at the free surface. One of the methods developed is based on the estimation and inversion of the propagator matrix, and therefore referred to as propagator inversion. The propagator inversion was applied to data which we acquired in Zeist, The Netherlands. We obtained a low near-surface P velocity, namely 270 ± 15 m/s, which is well below the sound velocity in air, and 150 ± 9 m/s for the S velocity. The buried geophone was located at approximately 1.0 m depth, thus the obtained velocities are only representative of the top meter of the near-surface. The second part of this thesis is devoted to the influence of wavefield acquisition. Corrections for source and receiver perturbations are necessary when their behaviour changes within a given survey, and should be performed in the early stages of processing. However, existing techniques, such as surface-consistent deconvolution, require prior processing before even they can be applied. We developed an alternative approach to compensate for source and receiver amplitude perturbations which has the advantage of being purely a raw data preprocessing step. It is applicable to the whole seismic trace, and does not impose additional assumptions on the subsurface. The approach is based on reciprocity of the medium response. This implies that differences between normal and reciprocal traces can be attributed to the source and receiver perturbations. We successfully demonstrated the procedure to compensate for these perturbations on both synthetic and field data. The field data were acquired in Manistee County, Michigan (courtesy of WesternGeco). Along the acquisition line, near-surface conditions change from moist-to-wet sediments to dry sands. The obtained source corrections are strongly correlated to these changing near-surface conditions, whereas the receiver corrections vary more strongly from geophone to geophone. Compensation of the recorded data for the source and receiver perturbations resulted in a significant improvement of the signal-to-noise ratio, both on prestack and poststack data. Finally, the receiver response we found did not agree with the generally accepted damped harmonic oscillator model, implying that this model need to be revised.