Seismic reverse-time migration in viscoelastic media

Seismic images are key to exploration seismology. They help identify structures in the subsurface and locate potential reservoirs. However, seismic images suffer from the problem of low resolution caused by the viscoelasticity of the medium. The viscoelasticity of the media is caused by the combination of fractured solid rock and fluids, such as water, oil and gas. This viscoelasticity of the medium causes attenuation of seismic waves, which includes energy absorption and velocity dispersion. These two attenuation effects significantly change the seismic data, and thus the seismic imaging. The aim of this thesis is to deepen the understanding of seismic wave propagation in attenuating media and to further investigate the method for high-resolution seismic imaging. My work, presented in this dissertation, comprises the following three parts. First, the determination of the viscoelastic parameters in the generalised viscoelastic wave equation. The viscoelasticity of subsurface media is succinctly represented in the generalised wave equation by a fractional temporal derivative. This generalised viscoelastic wave equation is characterised by the viscoelastic parameter and the viscoelastic velocity, but these parameters are not well formulated and therefore unfavourable for seismic implementation. The causality and stability of the generalised wave equation are proved by deriving the rate-of-relaxation function. On this basis, the viscoelastic parameter is formulated based on the constant Q model, and the viscoelastic velocity is formulated in terms of the reference velocity and the viscoelastic parameter. These two formulations adequately represent the viscoelastic effect in seismic wave propagation. Second, the development of a fractional spatial derivatives wave equation with a spatial filter. This development aims to effectively and efficiently solve the generalised viscoelastic wave equation with fractional temporal derivative, which is numerically challenging. I have transferred the fractional temporal derivative into fractional spatial derivatives, which can be solved using the pseudo-spectral implementation. However, this method is inaccurate in heterogeneous media. I introduced a spatial filter to correct the simulation error caused by the averaging in this implementation. The numerical test shows that the proposed spatial filter can significantly improve the accuracy of the seismic simulation and maintain high efficiency. Moreover, the proposed wave equation with fractional spatial derivatives is applied to compensate for the attenuation effects in reverse-time migration. This allows the dispersion correction and energy compensation to be performed simultaneously, which improves the resolution of the migration results. Finally, the development of reverse-time migration using biaxial wavefield decomposition to reduce migration artefacts and further improve the resolution of seismic images. In reverse-time migration, the cross-correlation of unphysical waves leads to large artefacts. By decomposing the wavefield both horizontally and vertically, and selecting only the causal waves for cross-correlation, the artefacts are greatly reduced, and the delicate structures can be identified. This decomposition method is also suitable for reverse-time migration with attenuation compensation. The migration results show that the resolution of the final seismic image is significantly improved, compared to conventional reverse-time migration.Open Acces

Quantitative tools for seismic stratigraphy and lithology characterization

Seismological images represent maps of the earth's structure. Apparent bandwidth limitation of seismic data prevents successful estimation of transition sharpness by the multiscale wavelet transform. We discuss the application of two recently developed techniques for (non-linear) singularity analysis designed for bandwidth limited data, such as imaged seismic reflectivity. The first method is a generalization of Mallat's modulus maxima approach to a method capable of estimating coarse-grained local scaling/sharpness/Hölder regularity of edges/transitions from data residing at essentially one single scale. The method is based on a non-linear criterion predicting the (dis)appearance of local maxima as a function of the data's fractional integrations/differentiations. The second method is an extension of an atomic decomposition technique based on the greedy Matching Pursuit Algorithm. Instead of the ordinary Spline Wavelet Packet Basis, our method uses multiple Fractional Spline Wavelet Packet Bases, especially designed for seismic reflectivity data. The first method excels in pinpointing the location of the singularities (the stratigraphy). The second method improves the singularity characterization by providing information on the transition's location, magnitude, scale, order and direction (anti-/causal/symmetric). Moreover, the atomic decomposition entails data compression, denoising and deconvolution. The output of both methods produces a map of the earth's singularity structure. These maps can be overlayed with seismic data, thus providing us with a means to more precisely characterize the seismic reflectivity's litho-stratigraphical information content.Massachusetts Institute of Technology. Industry Consorti

Full waveform inversion procedures with irregular topography

Full waveform inversion (FWI) is a form of seismic inversion that uses data residual, found as the misfit, between the whole waveform of field acquired and synthesized seismic data, to iteratively update a model estimate until such misfit is sufficiently reduced, indicating synthetic data is generated from a relatively accurate model. The aim of the thesis is to review FWI and provide a simplified explanation of the techniques involved to those who are not familiar with FWI. In FWI the local minima problem causes the misfit to decrease to its nearest minimum and not the global minimum, meaning the model cannot be accurately updated. Numerous objective functions were proposed to tackle different sources of local minima. The ‘joint deconvoluted envelope and phase residual’ misfit function proposed in this thesis aims to combine features of these objective functions for a comprehensive inversion. The adjoint state method is used to generate an updated gradient for the search direction and is followed by a step-length estimation to produce a scalar value that could be applied to the search direction to reduce the misfit more efficiently. Synthetic data are derived from forward modelling involving simulating and recording propagating waves influenced by the mediums’ properties. The ‘generalised viscoelastic wave equation in porous media’ was proposed by the author in sub-chapter 3.2.5 to consider these properties. Boundary layers and conditions are employed to mitigate artificial reflections arising from computational simulations. Linear algebra solvers are an efficient tool that produces wavefield vectors for frequency domain synthetic data. Regions with topography require a grid generation scheme to adjust a mesh of nodes to fit into its non-quadrilateral shaped body. Computational co-ordinate terms are implemented within wave equations throughout topographic models where a single point in the model in physical domain are represented by cartesian nodes in the computational domains. This helps to generate an accurate and appropriate synthetic data, without complex modelling computations. Advanced FWI takes a different approach to conventional FWI, where they relax upon the use of misfit function, however none of their proponents claims the former can supplant the latter but suggest that they can be implemented together to recover the true model.Open Acces

Desenvolvimento das representações integrais para as equações unidirecionais de onda acopladas e estratégias para a estimativa de parâmetros baseadas na migração e inversão conjuntas

Orientador: Joerg Dietrich Wilhelm SchleicherTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de GeociênciasResumo: Neste trabalho, nós investigamos as equações de onda unidirecionais acopladas e estratégias para a estimativa de parâmetros da subsuperfície a partir de dados sísmicos de reflexão medidos próximo à superfície terrestre. Na primeira parte, desenvolvemos em detalhe as equações de onda unidirecionais a partir da equação de movimento e da derivada temporal da lei de Hooke. Então, definimos as funções de Green unidirecionais de maneira consistente com a função equivalente para o caso completo. Na sequência, deduzimos originalmente as representações integrais das equações de onda unidirecionais. As expressões integrais formam a base conceitual do algoritmo de modelagem direta adotado. Na segunda parte, desenvolvemos e discutimos em detalhe formas de obter uma estimativa da imagem sísmica e o aprimoramento de um modelo de velocidades inicial, sempre aplicando o método de quadrados mínimos não-linear para o ajuste de dados. Considerando que o modelo de velocidades tem precisão suficiente para o imageamento, revisitamos a parametrização deste problema em função dos coeficientes de reflexão e obtemos uma expressão para o gradiente da função objetivo que sugere a modificação da condição de imagem convencional. Além disso, ainda neste contexto de modelo de velocidades suficiente para imagear, propomos a parametrização do problema de imageamento em profundidade em função da impedância. Então, a partir de uma seção de impedância homogênea inicial, estimamos as variações de impedância. Finalmente, incluímos atualizações do modelo de velocidades no procedimento de inversão, o que caracteriza o método de migração e inversão conjuntas que inspirou este trabalho. Propomos duas regularizações baseadas na imagem de forma que as atualizações do modelo de velocidades possam se beneficiar da informação de alta-frequência espacial da imagem. Os testes numéricos indicam que as metodologias investigadas são promissorasAbstract: We investigate the coupled one-way wave equations and develop strategies for the estimation of model parameters of the subsurface from seismic reflection data acquired near the Earth's surface. In the first part, we develop in detail the one-way wave equations from the movement and temporal derivative of Hooke's law. Then, we define one-way Green's functions consistently with the two-way counterpart. Next, we derive in an originally the integral representations of the one-way wave equations. These representations form the conceptual basis of the adopted modeling algorithm. In the second part, we develop approaches to estimate the seismic image and to improve an initial velocity model. All the methodologies for parameter estimation are built upon the nonlinear least-squares method for data fitting. Considering that the known velocity model is sufficiently precise for imaging, we revisit this problem parameterization as a function of the reflection coefficients. The expression obtained for the misfit-function gradient suggests a new imaging condition. Still in the context of a known precise velocity model, we propose the impedance parameterization of the imaging problem. Then, given an initial homogeneous impedance section, we estimate the relative acoustic impedance. Finally, we include updates of the velocity model in the inversion procedure, which characterizes the joint migration inversion methodology that inspired this work. We propose two regularizing functions based on the image such that the updates of the velocity model can benefit from the high spatial-frequency content in the image. The numerical tests indicate that the investigated methodologies are promisingDoutoradoReservatórios e GestãoDoutor em Ciências e Engenharia de Petróleo88887.161391/2017-0088887.161391/2017-00CAPESDAA

Improving the seismic image in reverse time migration by analysis of wavefields via continuous wavelet transform

During the last 50 years there has been a lot of effort to obtain subsurface structures on the oil and gas exploration. Some of them even if they are based on the mathematical formulation of the phenomenon, were not easily implemented due to the lack of computational power. Nevertheless, the problem is not only the algorithmic complexity but also, the uncertainty reduction of the scalar field that is obtained after the mathematical modeling and inversion procedures. Specifically, this thesis deals with the well known Reverse time migration (RTM) procedure, which is basically the two-way wave equation migration that is able to generate models with both great structural and velocity complexities, problems arise when the construction of subsurface models take into account seismic signals recorded on the surface. The data is mapped into the subsurface using the acoustic wave equation and the models obtained contain uncertainties that affect their subsequent interpretation. In order to reduce these uncertainties, we seek to improve the algorithm used in RTM before and after the generation of the final model looking for uncertainty reduction and improved scalar fields. We propose a set of strategies of extracting information from the seismic signals in order to obtain characteristics that allow a better and more refined representation of the subsurface structure model. Integral transforms are developed for this purpose. Inspired on the concept of information retrieval from data, we developed a signal procedure algorithm to determine in time-scale domain, the main features of the traveler wave in order to relate temporarily the inherent physics phenomena, locate complex structures by pointing the velocity field singularities due to the main changes on the frequency content revealed within the scalogram obtained by Gaussian wavelet family. Later on, a wavefield separation for the scalar field calculation is proposed based on the same principle and we called it Time Scale Wavefield Separation (TSWS). The space defined by Source wave propagation is decomposed on the subspaces and the analysis in time-domain time-scale of the subset of the wavefield is performed by selecting special features extracted by Wavelet Transform Modulus Maxima (WTMM) and a numerical algorithm is introduced for massive data [1]. Consequently, a Depth Scale Wavefield Separation (DSWS) is developed to the Receiver Wavefield separation by extracting the depth-domain scale-domain features of the relevant information of the reverse traveler wave [2]. Finally and taking into account the need for the proper structure definition for drilling purposes, we introduced the Laguerre Gauss Transform as final part of the Zero lag cross correlation imaging condition (ZL-CC-IC-LG) and provide a useful transformation of the final real scalar field into a complex scalar field with properties of spatial features enhancement

Scaling And Seismic Reflectivity: Implications Of Scaling On Avo

AVO analysis of seismic data is based on the assumption that transitions in the earth consist of jump discontinuities only. The generalization of this type of transition to a more realistic class of transitions shows a drastic change in observed AVO behavior, especially for the large angles currently attained by increasing cable lengths. We propose a simple approach that accounts for this anomalous behavior by renormalizing the observed AVO. This renormalization allows for a separation of the observed AVO effects in terms of a conventional Zoeppritz contribution and a scaling contribution in those cases where the transitions can no longer be considered as isolated jump discontinuities. After renormalization, the inverted fluctuations regain their relative magnitudes which, due to the scaling, may have been significantly distorted. An example of these distortions are tuning effects, often erroneously interpreted as bright spots.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumMassachusetts Institute of Technology. Earth Resources Laboratory. Reservoir Delineation Consortiu

Application of vertical seismic profiling for the characterisation of hard rock

Seismic imaging in hard rock environments is gaining wider acceptance as a mineral exploration technique and as a mine-planning tool. However, the seismic images generated from hard rock targets are complex due to high rock velocities, low contrasts in elastic rock properties, fractionated geology, complicated steep dipping structures and mineralogical alterations. In order to comprehend the complexity and utilise seismic images for structural mapping and rock characterisation, it is essential to correlate these images to known geology. An ideal tool for this purpose is Vertical Seismic Profiling or VSP. The VSP method can provide not only a means to correlate seismic images to geology but also to study the properties of the transmitted seismic field as it is modified by different rock formations, the origin of the reflected events and the corresponding reflector geometry. However, the VSP technique is rarely used in hard rock environments because of the cost and operational issues related to using clamping geophones in exploration boreholes, which are 96 mm or less in diameter. Consequently the main objective of this research is to produce an efficient VSP methodology that can be readily deployed for mineral exploration.An alternative to the clamping geophone is the hydrophone. Hydrophones are suspended in, and acoustically coupled to the borehole wall through, the borehole fluid. Borehole acoustic modes known as "tube-waves" are generated by seismic body waves passing the water column and are guided in the borehole due to the high acoustic impedance contrast between the rock and fluid. Tube-waves are 1-2 orders in magnitude higher in amplitude than seismic signal and mask reflected energy in hydrophone VSP profiles. As such the use of borehole hydrophone arrays to date has been restricted to direct body wave measurements only. I have effectively mitigated tube-waves in hydrophone VSP surveys with specific acquisition methodologies and refined signal processing techniques. The success of wavefield separation of tubewaves from hydrophone data depends critically upon; having high signal to noise ratio, well sampled data, pre-conditioning of the field data and processing in the field record (FFID) domain. Improvements in data quality through the use of high viscosity drilling fluids and baffle systems have been tested and developed. The increased signal to noise ratio and suppression of tube-wave energy through these technologies greatly enhances the performance of hydrophone VSP imaging.Non-standard wavefield separation techniques successfully removed strong coherent tube-wave noise. The additional wavefield separation steps required to remove high amplitude tube-waves does degrade the overall result with some fidelity and coherency being lost. However, a direct comparison of hydrophone and borehole clamping geophone VSP surveys has been conducted in the Kambalda nickel district and the two methodologies produced comparable results. The difference was that the hydrophone data were collected in a fraction of the time compared to clamping geophone equipment with significantly less risk of equipment loss and with reduced cost.The results of these field experiments and the data processing methodology used, demonstrate the potential of hydrophone VSP surveys in the small diameter boreholes typical of hard rock exploration. Thus, these results show that hydrophone VSP is a viable, cost effective and efficient solution that should be employed more routinely in hard rock environments in order to enhance the value of the surface seismic datasets being acquired