The purpose of Bayesian seismic inversion is to combine information derived from seismic data and prior geological knowledge to determine a posterior probability distribution over parameters describing the elastic and geological properties of the subsurface. Typically the subsurface is modelled by a cellular grid model containing thousands or millions of cells within which these parameters are to be determined. Thus such inversions are computationally expensive due to the size of the parameter space (being proportional to the number of grid cells) over which the posterior is to be determined. Therefore, in practice approximations to Bayesian seismic inversion must be considered. A particular, existing approximate workflow is described in this thesis: the so-called two-stage inversion method explicitly splits the inversion problem into elastic and geological inversion stages. These two stages sequentially estimate the elastic parameters given the seismic data, and then the geological parameters given the elastic parameter estimates, respectively. In this thesis a number of methodologies are developed which enhance the accuracy of this approximate workflow. To reduce computational cost, existing elastic inversion methods often incorporate only simplified prior information about the elastic parameters. Thus a method is introduced which transforms such results, obtained using prior information specified using only two-point geostatistics, into new estimates containing sophisticated multi-point geostatistical prior information. The method uses a so-called deep neural network, trained using only synthetic instances (or `examples') of these two estimates, to apply this transformation. The method is shown to improve the resolution and accuracy (by comparison to well measurements) of elastic parameter estimates determined for a real hydrocarbon reservoir. It has been shown previously that so-called mixture density network (MDN) inversion can be used to solve geological inversion analytically (and thus very rapidly and efficiently) but only under certain assumptions about the geological prior distribution. A so-called prior replacement operation is developed here, which can be used to relax these requirements. It permits the efficient MDN method to be incorporated into general stochastic geological inversion methods which are free from the restrictive assumptions. Such methods rely on the use of Markov-chain Monte-Carlo (MCMC) sampling, which estimate the posterior (over the geological parameters) by producing a correlated chain of samples from it. It is shown that this approach can yield biased estimates of the posterior. Thus an alternative method which obtains a set of non-correlated samples from the posterior is developed, avoiding the possibility of bias in the estimate. The new method was tested on a synthetic geological inversion problem; its results compared favourably to those of Gibbs sampling (a MCMC method) on the same problem, which exhibited very significant bias. The geological prior information used in seismic inversion can be derived from real images which bear similarity to the geology anticipated within the target region of the subsurface. Such so-called training images are not always available from which this information (in the form of geostatistics) may be extracted. In this case appropriate training images may be generated by geological experts. However, this process can be costly and difficult. Thus an elicitation method (based on a genetic algorithm) is developed here which obtains the appropriate geostatistics reliably and directly from a geological expert, without the need for training images. 12 experts were asked to use the algorithm (individually) to determine the appropriate geostatistics for a physical (target) geological image. The majority of the experts were able to obtain a set of geostatistics which were consistent with the true (measured) statistics of the target image.

This thesis describes new interferometric imaging methods for migration and waveform inversion. The key idea is to use reflection events from a known reference reflector to ”naturally redatum” the receivers and sources to the reference reflector. Here, ”natural redatuming” is a data-driven process where the redatuming Green’s functions are obtained from the data. Interferometric imaging eliminates the statics associated with the noisy overburden above the reference reflector. To mitigate the defocussing caused by overburden errors I first propose the use of interferometric least-squares migration (ILSM) to estimate the migration image. Here, a known reflector is used as the reference interface for ILSM, and the data are naturally redatumed to this reference interface before imaging. Numerical results on synthetic and field data show that ILSM can significantly reduce the defocussing artifacts in the migration image. Next, I develop a waveform tomography approach for inverting the velocity model by mitigating the velocity errors in the overburden. Unresolved velocity errors in the overburden velocity model can cause conventional full-waveform inversion to get stuck in a local minimum. To resolve this problem, I present interferometric full-waveform inversion (IFWI), where conventional waveform tomography is reformulated so a velocity model is found that minimizes the objective function with an interferometric crosscorrelogram misfit. Numerical examples show that IFWI, compared to FWI, computes a significantly more accurate velocity model in the presence of a nearsurface with unknown velocity anomalies. I use IFWI and ILSM for 4D imaging where seismic data are recorded at different times over the same reservoir. To eliminate the time-varying effects of the near surface both data sets are virtually redatumed to a common reference interface before migration. This largely eliminates the overburden-induced statics errors in both data sets. Results with synthetic and field data show that ILSM and IFWI can suppress the artifacts caused by non-repeatability in time-lapse surveys. This can lead to a much more accurate characterization of the movement of fluids over time. In turn, this information can be used to optimize the extraction of resources in enhanced oil recovery (EOR) operations.

Natural gas and oil from characteristically complex unconventional reservoirs, such as organic shale, tight gas and oil, coal-bed methane; are transforming the global energy market. These conventional reserves exist in complex geologic formations where conventional seismic techniques have been challenged to successfully image the subsurface. To acquire maximum benefits from these unconventional reserves, seismic anisotropy must be at the center of our modeling and inversion workflows. I present algorithms for fast traveltime computations in anisotropic media. Both ray-based and finite-difference solvers of the anisotropic eikonal equation are developed. The proposed algorithms present novel techniques to obtain accurate traveltime solutions for anisotropic media in a cost-efficient manner. The traveltime computation algorithms are then used to invert for anisotropy parameters. Specifically, I develop inversion techniques by using diffractions and diving waves in the seismic data. The diffraction-based inversion algorithm can be combined with an isotropic full-waveform inversion (FWI) method to obtain a high-resolution model for the anellipticity anisotropy parameter. The inversion algorithm based on diving waves is useful for building initial anisotropic models for depth-migration and FWI. I also develop the idea of 'effective elliptic models' for obtaining solutions of the anisotropic two-way wave equation. The proposed technique offers a viable alternative for wavefield computations in anisotropic media using a computationally cheaper wave propagation operator. The methods developed in the thesis lead to a direct cost savings for imaging and inversion projects, in addition to a reduction in turn-around time. With an eye on the next generation inversion methods, these techniques allow us to incorporate more accurate physics into our modeling and inversion framework.

The main goal in seismic exploration is to identify locations of hydrocarbons reservoirs and give insights on where to drill new wells. Therefore, estimating an Earth model that represents the right physics of the Earth's subsurface is crucial in identifying these targets. Recent seismic data, with long offsets and wide azimuth features, are more sensitive to anisotropy. Accordingly, multiple anisotropic parameters need to be extracted from the recorded data on the surface to properly describe the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic data to anisotropy parameters. Then, I use a frequency domain scattering integral approach to invert for the optimal parameterization. The scattering integral approach is based on the explicit computation of the sensitivity kernels. I present a new method to compute the traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. I show that the new kernels are a better alternative to conventional cross-correlation/Rytov kernels. I also derive and analyze the sensitivity kernels for a transversely isotropic model with a vertical axis of symmetry. The kernels structure, for various opening/scattering angles, highlights the trade-off regions between the parameters. For a surface recorded data, I show that the normal move-out velocity vn, ƞ and δ parameterization is suitable for a simultaneous inversion of diving waves and reflections. Moreover, when seismic data is inverted hierarchically, the horizontal velocity vh, ƞ and ϵ is the parameterization with the least trade-off. In the frequency domain, the hierarchical inversion approach is naturally implemented using frequency continuation, which makes vh, ƞ and ϵ parameterization attractive. I formulate the multi-parameter inversion using the scattering integral method. Application to various synthetic and real data examples show accurate inversion results. I show that a good background ƞ model is required to accurately recover vh. For 3-D problems, I promote a hybrid approach, where efficient ray tracing is used to compute the sensitivity kernels. The proposed method highly reduces the computational cost.

Full Waveform Inversion (FWI) is a non-linear optimization problem aimed to estimating subsurface parameters by minimizing the misfit between modeled and recorded seismic data using gradient descent methods, which are the only practical choice because of the size of the problem. Due to the high non-linearity of the problem, gradient methods will converge to a local minimum if the starting model is not close to the true one. The accuracy of the long-wavelength components of the initial model controls the level of non-linearity of the inversion. In order for FWI to converge to the global minimum, we have to obtain the long wavelength components of the model before inverting for the short wavelengths. Ultra-low temporal frequencies are sensitive to the smooth (long wavelength) part of the model, and can be utilized by waveform inversion to resolve that part. Unfortunately, frequencies in this range are normally missing in field data due to data acquisition limitations. The lack of low frequencies can be compensated for by utilizing wide-aperture data, as they include arrivals that are especially sensitive to the long wavelength components of the model. The higher the scattering angle of a 5 recorded event, the higher the model wavelength it can resolve. Based on this property, a scattering-angle filtering algorithm is proposed to start the inversion process with events corresponding to the highest scattering angle available in the data, and then include lower scattering angles progressively. The large scattering angles will resolve the smooth part of the model and reduce the non-linearity of the problem, then the lower ones will enhance the resolution of the model. Recorded data is first migrated using Pre-stack Exploding Reflector Migration (PERM), then the resulting pre-stack image is transformed into angle gathers to which an angle filtering process is applied to remove events below a certain cut-off angle. The filtered pre-stack image cube is then demigrated (forward modeled) to produce filtered surface data that can be used in waveform inversion. Numerical tests confirm the feasibility of the proposed filtering algorithm. However, the accuracy of the filtered section is limited by PERM’s singularity for horizontally-traveling waves, which in turn is dependent on the velocity model used for migration and demigration

[pt] O problema de Inversão Sísmica envolve a determinação das propriedades físicas da superfície a partir de dados amostrados na superfície. A construção de um modelo matemático da resposta da subsuperfície à excitação de uma fonte sísmica, tendo como parâmetros as propriedades físicas da subsuperfície, fornece um modelo sintético desta resposta para determinados valores dos parâmetros. Isto permite comparar dados amostrados e modelos sintético. A perturbação do modelo pela variação dos seus parâmetros pode aproximar dados amostrados e sintéticos e colocar o problema da Inversão como um problema de minimização de uma função de erro que os ajuste de forma adequada. Usualmente, os métodos que tentam minimizar a medida a medida de erro supõem um comportamento linear entre a perturbação do modelo e esta medida. Na maioria dos problemas geofísicos, esta medida apresenta um alto grau de não linearidade e uma grande quantidade de mínimos locais. Isto torna estes métodos baseados em aproximações lineares muito sensíveis à escolha de uma boa solução inicial, o que nem sempre está disponível. Como resolver este problema sem uma boa solução inicial? A teoria da Inferência Bayesiana oferece uma solução pelo uso de informação a priori sob o espaço dos parâmetros. O problema de Inversão volta então a ser um problema de otimização onde se precisa maximizar a probabilidade a posteriori dos parâmetros assumirem um certo valor dado que se obteve o resultado da amostragem dos dados. Este problema é resolvido pelo método do Simulated Annealing (SA), método de otimização global que faz uma busca aleatória direcionada no espaço de solução. Este método foi proposto por uma analogia entre o recozimento física de sólidos e problemas de otimização. O SA, na sua variante Very Fast Simulated Annealing (VFSA), é aplicado na solução de problemas de Inversão Sísmica 1 D para modelos acústico e elásticos gerados sinteticamente. A avaliação do desempenho do SA usando medidas de erro com diferentes normas é realizada para um modelo elástico adicionado de ruído aleatório. / [en] The seismic inverse problem involves determining the subsurface physical properties from data sampled at Earth`s surface. A mathematical model of the response of the subsurface excited by a seismic source, having physical properties as parameters, provides a synthetic model for this response. This makes possible to compare sampled and synthetic data. The perturbation in the model due to the variation of its parameters can approximate these data and states the inversion problem as the minimization of an error function that fits them adequately. Usually, the methods which attempt to minimize this error assume that a perturbation in the model is linearly relates with a perturbation in the measured response. Most geophysical inverse problems are highly nonlinear and are rife with local minima. Therefore these methods are very sensitive to the choice of the initial model and good starting solutions may not be available. What should be done, if there is no basis for an initial guess? The theory of Bayesian inference provides an answer to this question taking into account the prior information about the parameter space. The inverse problem can then be stated as an optimization problem whose goal is to maximize the posterior probability that the set of parameters has a certain value once given the result of the sample. This problem is solved by the Simulated Annealing method, a global optimization method that executes a oriented random search in the solution space. This method comes from an analogy between the physical annealing of solids and optimization problems. The Very Fast Simulated Annealing (VFSA), a variant of SA, is applied to the solution of 1 D seismic inverse problems generated synthetically by acoustic and alastic done by a elastic model with additive noise.

Pore type variations account for complex velocity-porosity relationship and intensive permeability heterogeneity and consequently low oil and gas recovery in carbonate reservoir. However, it is a challenge for geologist and geophysicist to quantitatively estimate the influences of pore type complexity on velocity variation at a given porosity and porosity-permeability relationship. A new rock physics-based integrated approach in this study was proposed to quantitatively characterize the diversity of pore types and its influences on wave propagation in carbonate reservoir. Based on above knowledge, permeability prediction accuracy from petrophysical data can be improved compared to conventional approach. Two carbonate reservoirs with different reservoir features, one is a shallow carbonate reservoir with average high porosity (>10%) and another one is a supper-deep carbonate reservoir with average low porosity (<5%), are used to test the proposed approach. Paleokarst is a major event to complicate carbonate reservoir pore structure. Because of limited data and lack of appropriate study methods, it is a difficulty to characterize subsurface paleokarst 3D distribution and estimate its influences on reservoir heterogeneity. A method by integrated seismic characterization is applied to delineate a complex subsurface paleokarst system in the Upper San Andres Formation, Permian basin, West Texas. Meanwhile, the complex paleokarst system is explained by using a carbonate platform hydrological model, similar to modern marine hydrological environments within carbonate islands. How to evaluate carbonate reservoir permeability heterogeneity from 3D seismic data has been a dream for reservoir geoscientists, which is a key factor to optimize reservoir development strategy and enhance reservoir recovery. A two-step seismic inversions approach by integrating angle-stack seismic data and rock physics model is proposed to characterize pore-types complexity and further to identify the relative high permeability gas-bearing zones in low porosity reservoir (< 5%) using ChangXing super-deep carbonate reservoir as an example. Compared to the conventional permeability calculation method by best-fit function between porosity and permeability, the results in this study demonstrate that gas zones and non-gas zones in low porosity reservoir can be differentiated by using above integrated permeability characterization method.

Seismic inversion is the leading method to map and quantify changes in time-lapse (4D) seismic datasets, with applications ranging from monitoring hydrocarbon-producing fields to geological CO2 storage. However, the process of inverting seismic data for reservoir properties is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data. This comes with additional challenges for 4D applications, given the inaccuracies in the repeatability of time-lapse acquisition surveys. Consequently, adding prior information to the inversion process in the form of properly crafted regularization terms is essential to obtain geologically meaningful subsurface models and 4D effects. In this thesis, I propose a joint inversion-segmentation algorithm for 4D seismic inversion, which integrates total variation and segmentation priors as a way to counteract the missing frequencies and noise present in 4D seismic data. I validate the algorithm with synthetic and field seismic datasets and benchmark it against state-of-the-art 4D inversion techniques. The proposed algorithm shows three main advantages: 1. it produces high-resolution baseline and monitor acoustic impedance models, 2. by leveraging similarities between multiple seismic datasets, the proposed algorithm mitigates the non-repeatable noise and better highlights the real seismic time-lapse changes, and 3. it simultaneously provides a volumetric classification of the acoustic impedance 4D difference model based on user-defined classes, i.e., percentages of seismic time-lapse changes. Such advantages may enable more robust stratigraphic/structural and quantitative 4D seismic interpretation and provide more accurate inputs for dynamic reservoir simulations.

[pt] A inversão sísmica é o processo de transformar dados de Sísmica de Reflexão em valores quantitativos de propriedades petroelásticas das rochas. Esses valores, por sua vez, podem ser correlacionados com outras propriedades ajudando os geocientistas a fazer uma melhor interpretação que resulta numa boa caracterização de um reservatório de petróleo. Existem vários algoritmos tradicionais para Inversão Sísmica. Neste trabalho revisitamos a Inversão Colorida (Impedância Relativa), a Inversão Recursiva, a Inversão Limitada em Banda e a Inversão Baseada em Modelos. Todos esses quatro algoritmos são baseados em processamento digital de sinais e otimização. O presente trabalho busca reproduzir os resultados desses algoritmos através de uma metodologia simples e eficiente baseada em Redes Neurais e na pseudo-impedância. Este trabalho apresenta uma implementação dos algoritmos propostos na metodologia e testa sua validade num dado sísmico público que tem uma inversão feita pelos métodos tradicionais. / [en] Seismic inversion is the process of transforming Reflection Seismic data into quantitative values of petroleum rock properties. These values, in turn, can be correlated with other properties helping geoscientists to make a better interpretation that results in a good characterization of an oil reservoir.There are several traditional algorithms for Seismic Inversion. In this work we revise Color Inversion (Relative Impedance), Recursive Inversion, Bandwidth Inversion and Model-Based Inversion. All four of these algorithms are based on digital signal processing and optimization. The present work seeks to reproduce the results of these algorithms through a simple and efficient methodology based on Neural Networks and pseudo-impedance. This work presents an implementation of the algorithms proposed in the methodology and tests its validity in a public seismic data that has an inversion made by the traditional methods.

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