The objective of this research is comparative analysis of several standard and one new seismic post- and pre-stack inversion methods and Amplitude Variation with Offset (AVO) attribute analysis in application to the CREWES Blackfoot 3D dataset. To prepare the data to the inversion, I start with processing the dataset by using ProMAX software. This processing, in general, includes static and refraction corrections, velocity analysis and stacking the data. The results show good quality images, which are suitable for inversion.<p> Five types of inversion methods are applied to the dataset and compared. Three of these methods produce solutions for the post-stack Acoustic Impedance (AI) and are per-formed by using the industry-standard Hampson-Russell software. The fourth method uses our in-house algorithm called SILC and implemented in IGeoS seismic processing system. In the fifth approach, the pre-stack gathers are inverted for elastic impedance by range-limited stacking of the common-midpoint (CMP) gathers in offsets and/or angles and then performing independent inversion of angle stack. Further, simultaneous inversion is applied to pre-stack seismic data to invert for both the P- and S-wave impedances. These im-pedances are used to extract the Lamé parameters multiplied by density (LMR), and used to extract the ratios between the P- and S-wave velocities. In addition, CMP gathers are used to produce AVO attribute images, which are good indicators of gas reservoirs. Fi-nally, the results of the different inversion techniques are interpreted and correlated with well-log data and used to characterize the reservoir.<p> The different inversion results show clearly the reservoir with its related low im-pedance within the channel. The post-stack inversion gives the best results; in particular, the model-based inversion shows smoothed images of it while SILC provides a different, higher-resolution image. The elastic impedance also gives results similar to the post-stack inversion. Pre-stack inversion and AVO attributes give reasonable results in cross sections near the center of study area. In other areas, performance of pre-stack inversion is poorer, apparently because of reflection aperture limitations.

The objective of this research is comparative analysis of several standard and one new seismic post- and pre-stack inversion methods and Amplitude Variation with Offset (AVO) attribute analysis in application to the CREWES Blackfoot 3D dataset. To prepare the data to the inversion, I start with processing the dataset by using ProMAX software. This processing, in general, includes static and refraction corrections, velocity analysis and stacking the data. The results show good quality images, which are suitable for inversion.<p> Five types of inversion methods are applied to the dataset and compared. Three of these methods produce solutions for the post-stack Acoustic Impedance (AI) and are per-formed by using the industry-standard Hampson-Russell software. The fourth method uses our in-house algorithm called SILC and implemented in IGeoS seismic processing system. In the fifth approach, the pre-stack gathers are inverted for elastic impedance by range-limited stacking of the common-midpoint (CMP) gathers in offsets and/or angles and then performing independent inversion of angle stack. Further, simultaneous inversion is applied to pre-stack seismic data to invert for both the P- and S-wave impedances. These im-pedances are used to extract the Lamé parameters multiplied by density (LMR), and used to extract the ratios between the P- and S-wave velocities. In addition, CMP gathers are used to produce AVO attribute images, which are good indicators of gas reservoirs. Fi-nally, the results of the different inversion techniques are interpreted and correlated with well-log data and used to characterize the reservoir.<p> The different inversion results show clearly the reservoir with its related low im-pedance within the channel. The post-stack inversion gives the best results; in particular, the model-based inversion shows smoothed images of it while SILC provides a different, higher-resolution image. The elastic impedance also gives results similar to the post-stack inversion. Pre-stack inversion and AVO attributes give reasonable results in cross sections near the center of study area. In other areas, performance of pre-stack inversion is poorer, apparently because of reflection aperture limitations.

Reservoir models are generally constructed from seismic, well logs and other related datasets using inversion methods and geostatistics. It has already been recognized by the geoscientists that such a process is prone to non-uniqueness. Practical methods for estimation of uncertainty still remain elusive. In my dissertation, I propose two new methods to estimate uncertainty in reservoir models from seismic, well logs and well production data. The first part of my research is aimed at estimating reservoir impedance models and their uncertainties from seismic data and well logs. This constitutes an inverse problem, and we recognize that multiple models can fit the measurements. A deterministic inversion based on minimization of the error between the observation and forward modeling only provides one of the best-fit models, which is usually band-limited. A complete solution should include both models and their uncertainties, which requires drawing samples from the posterior distribution. A global optimization method called very fast simulated annealing (VFSA) is commonly used to approximate posterior distribution with fast convergence. Here I address some of the limitations of VFSA by developing a new stochastic inference method, named Greedy Annealed Importance Sampling (GAIS). GAIS combines VFSA with greedy importance sampling (GIS), which uses a greedy search in the important regions located by VFSA to attain fast convergence and provide unbiased estimation. I demonstrate the performance of GAIS on post- and pre-stack data from real fields to estimate impedance models. The results indicate that GAIS can estimate both the expectation value and the uncertainties more accurately than using VFSA alone. Furthermore, principal component analysis (PCA) as an efficient parameterization method is employed together with GAIS to improve lateral continuity by simultaneous inversion of all traces. The second part of my research involves estimation of reservoir permeability models and their uncertainties using quantitative joint inversion of dynamic measurements, including synthetic production data and time-lapse seismic related data. Impacts from different objective functions or different data sets on the model uncertainty and model predictability are investigated as well. The results demonstrate that joint inversion of production data and time-lapse seismic related data (water saturation maps here) reduces model uncertainty, improves model predictability and shows superior performance than inversion using one type of data alone. / text

Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have an inaccurate update direction leading the inversion to converge into what we refer to as local minima of the objective function. In this thesis, I first look into the subject of full model wavenumber to analysis the root of local minima and suggest the possible ways to avoid this problem. And then I analysis the possibility of recovering the corresponding wavenumber components through the existing inversion and migration algorithms. Migration can be taken as a generalized inversion method which mainly retrieves the high wavenumber part of the model. Conventional impedance inversion method gives a mapping relationship between the migration image (high wavenumber) and model parameters (full wavenumber) and thus provides a possible cascade inversion strategy to retrieve the full wavenumber components from seismic data. In the proposed approach, consider a mild lateral variation in the model, I find an analytical Frechet derivation corresponding to the new objective function. In the proposed approach, the gradient is given by the oriented time-domain imaging method. This is independent of the background velocity. Specifically, I apply the oriented time-domain imaging (which depends on the reflection slope instead of a background velocity) on the data residual to obtain the geometrical features of the velocity perturbation. Assuming that density is constant, the conventional 1D impedance inversion method is also applicable for 2D or 3D velocity inversion within the process of FWI. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reflection response. To eliminate the cross-talk artifacts between different parameters, I utilize what I consider being an optimal parameterization. To do so, I extend the prestack time-domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practical. Results based on synthetic data of isotropic and anisotropic case examples illustrate the benefits and limitations of this method.

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.