Seismic Ray Impedance Inversion

This thesis investigates a prestack seismic inversion scheme implemented in the ray parameter domain. Conventionally, most prestack seismic inversion methods are performed in the incidence angle domain. However, inversion using the concept of ray impedance, as it honours ray path variation following the elastic parameter variation according to Snell’s law, shows the capacity to discriminate different lithologies if compared to conventional elastic impedance inversion. The procedure starts with data transformation into the ray-parameter domain and then implements the ray impedance inversion along constant ray-parameter profiles. With different constant-ray-parameter profiles, mixed-phase wavelets are initially estimated based on the high-order statistics of the data and further refined after a proper well-to-seismic tie. With the estimated wavelets ready, a Cauchy inversion method is used to invert for seismic reflectivity sequences, aiming at recovering seismic reflectivity sequences for blocky impedance inversion. The impedance inversion from reflectivity sequences adopts a standard generalised linear inversion scheme, whose results are utilised to identify rock properties and facilitate quantitative interpretation. It has also been demonstrated that we can further invert elastic parameters from ray impedance values, without eliminating an extra density term or introducing a Gardner’s relation to absorb this term. Ray impedance inversion is extended to P-S converted waves by introducing the definition of converted-wave ray impedance. This quantity shows some advantages in connecting prestack converted wave data with well logs, if compared with the shearwave elastic impedance derived from the Aki and Richards approximation to the Zoeppritz equations. An analysis of P-P and P-S wave data under the framework of ray impedance is conducted through a real multicomponent dataset, which can reduce the uncertainty in lithology identification.Inversion is the key method in generating those examples throughout the entire thesis as we believe it can render robust solutions to geophysical problems. Apart from the reflectivity sequence, ray impedance and elastic parameter inversion mentioned above, inversion methods are also adopted in transforming the prestack data from the offset domain to the ray-parameter domain, mixed-phase wavelet estimation, as well as the registration of P-P and P-S waves for the joint analysis. The ray impedance inversion methods are successfully applied to different types of datasets. In each individual step to achieving the ray impedance inversion, advantages, disadvantages as well as limitations of the algorithms adopted are detailed. As a conclusion, the ray impedance related analyses demonstrated in this thesis are highly competent compared with the classical elastic impedance methods and the author would like to recommend it for a wider application

Joint inversion of seismic PP- and PS-waves in the ray parameter domain

Seismic inversion is a quantitative analysis technique in reservoir geophysics to reveal subsurface physical properties from surface-recorded seismic data. But the most widely used inversion in oil and gas exploration for decades is PP-wave based. P-to-S converted wave, which has shown great success in the imaging of gas clouds, has a different response to rocks and pore-fluids from the PP-wave. A joint use of the PS-wave and PP-wave in the inversion can reduce the ill-posedness of the inverse problem and in particular enables simultaneous inversion for three independent elastic parameters. Conventionally, prestack seismic inversion is based on the incidence angle-dependent reflection coefficients. In my research, I define the seismic reflections and impedances along the ray paths of wave propagation, and these ray paths obey Snell’s law. I adopt the ray-impedance concept, which is a frequency-dependent parameter and is sensitive to fluid contents. Joined interpretation of PP- and PS-wave ray impedances can identify reservoirs, and also has potential in fluid discrimination. Joint inversion of PP- and PS-waves is performed on the constant ray parameter (CRP) profiles. For a constant ray parameter, a pair of PP- and PS-wave traces has exactly the same ray path between the source and the reflection point, which means the PP- and PS-wave reflection events represent exactly the same reflection point, in the horizontal direction. Therefore, PP and PS-wave calibration transforms PS-wave reflection events from PS-wave time to the corresponding PP-wave time, and reflections events in a pair of PP- and calibrated PS-wave traces with a constant ray parameter should correspond to each other, sample by sample, both horizontally and vertically. I also present a procedure which preserves the original wavelets in the transformed PS-wave trace. I use a bending ray-tracing method to construct the common image point (CIP) gathers in the ray-parameter domain. I estimate mixed-phase wavelets for each constant ray-parameter (CRP) profile through a frequency domain high-order statistical method, and then invert for the reflectivity series using weighted constraints. From the reflectivity sections, I estimate PP- and PS-wave ray impedances separately and also estimate three elastic parameters simultaneously in a joint inversion. I have applied the entire procedure to a couple of field data sets, to verify the robustness and effectiveness of the method, and to demonstrate the great potential of joint inversion in ray-parameter domain

High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy

A new inversion method to estimate high-resolution amplitude-versus-angle attributes (AVA) attributes such as intercept and gradient from prestack data is presented. The proposed technique promotes sparse-spike reflectivities that, when convolved with the source wavelet, fit the observed data. The inversion is carried out using a hybrid two-step strategy that combines fast iterative shrinkagethresholding algorithm (FISTA) and a standard least-squares (LS) inversion. FISTA, which can be viewed as an extension of the classical gradient algorithm, provides sparse solutions by minimizing the misfit between the modeled and the observed data, and the l1-norm of the solution. FISTA is used to estimate the location in time of the main reflectors. Then, LS is used to retrieve the appropriate reflectivity amplitudes that honor the data. FISTA, like other iterative solvers for l1-norm regularization, does not require matrices in explicit form, making it easy to apply, economic in computational terms, and adequate for solving large-scale problems. As a consequence, the FISTA+LS strategy represents a simple and cost-effective new procedure to solve the AVA inversion problem. Results on synthetic and field data show that the proposed hybrid method can obtain highresolution AVA attributes from noisy observations, making it an interesting alternative to conventional methods.Facultad de Ciencias Astronómicas y Geofísica

Machine learning applications for seismic processing and interpretation

During the past few years, exploration seismology has increasingly made use of machine learning algorithms in several areas including seismic data processing, attribute analysis, and computer aided interpretation. Since machine learning is a data-driven method for problem solving, it is important to adopt data which have good quality with minimal bias. Hidden variables and an appropriate objective function also need to be considered. In this dissertation, I focus my research on adapting machine learning algorithms that have been successfully applied to other scientific analysis problems to seismic interpretation and seismic data processing. Seismic data volumes can be extremely large, containing Gigabytes to Terrabytes of information. Add to these volumes the rich choice of seismic attributes, each of which has its own strengths in expressing geologic patterns, and the problem grows larger still. Seismic interpretation involves picking faults and horizons and identifying geologic features by their geometry, morphology, and amplitude patterns seen on seismic data. For the seismic facies classification task, I tested multiple attributes as input and built an attribute subset that can best differentiate the salt, mass transport deposits (MTDs), and conformal reflector seismic patterns using a suite of attribute selection algorithms. The resulting attribute subset differentiates the three classes with high accuracy and has the benefit of reducing the dimensionality of the data. To maximize the use of unlabeled data as well as labeled data, I provide a workflow for facies classification based on a semi-supervised learning approach. Compared to using only labeled data, I find that the addition of unlabeled data for learning results in higher performance of classification.. In seismic processing, I propose a deep learning approach for random and coherent noise attenuation in the frequency – space domain. I find that the deep ResNet architecture speeds up the process of denoising and improves the accuracy, which efficiently separates the noise from signals. Finally, I review geophysical inversion and machine learning approaches in an aspect of solving inverse problems and show similarities and differences of these approaches in both mathematical formulation and numerical tests

A marine geophysical investigation of the continental margin of east Greenland (63(^º)n to 69(^º) n)

During late July and August 1977, a marine geophysical investigation of the continental margin off East Greenland between latitudes 63(^º)N and 69.1(^º)N was undertaken by the University of Durham using the research vessel, R.R.S. Shackleton. Nearly 3500 km of continuously recorded bathymetric, magnetic and gravity data and approximately 2000 km of multi-channel seismic reflection data were recorded in a series of nearly parallel profiles perpendicular to the assumed strike of the continental margin. Disposable sonobuoy work was also carried out. The reduction, processing and interpretation of the geophysical data are described. In particular, the application of the maximum entropy method (MEM) of spectral estimation (using Burg's algorithm) to the problem of estimating the depth to buried magnetic sources is assessed. The principal geophysical results include: 1. The location of the ocean-continent boundary is inferred Fran seismic reflection data and the recognition of marine magnetic anomalies. Oceanic anomalies 22 through 24 are truncated by the continental margin. The marine anomaly sequence 13 through 21 is tentatively extrapolated northwards through the Denmark Straits and stops against the Denmark Straits fracture zone. 2. It is proposed that the Tertiary plateau basalts of the Blosseville coast do not terminate abruptly offshore but are down-faulted and continue eastwards, overlain by a prograded sequence of Tertiary sediments. 3. An interpretation of one processed, GDP stacked seismic section north of the Greenland-Iceland Ridge is presented. Several unconformities are recognised on the basis of seismic stratigraphic analysis. Two seismic horizons showing distinctive of flap against oceanic basement are tentatively dated at 30 Ma and 22 Ma respectively. No evidence is found for the presence of Mesozoic sediments offshore. 4. Gravity modelling indicates that the prograded wedge of Tertiary sediments observed north and south of the Greenland-Iceland Ridge is not isostatically compensated

Investigating the internal structure of glaciers and ice sheets using Ground Penetrating Radar

Ice penetrating radar (IPR) is a key tool in understanding the internal geometry and nature of glaciers and ice sheets, and has widely been used to derive bed topography, map internal layers and understand the thermal state of the cryosphere. Modern glacier and ice-sheet models facilitate increased assimilation of observations of englacial structure, including glacier thermal state and internal-layer geometry, yet the products available from radar surveys are often under-utilised. This thesis presents the development and assessment of radar processing strategies to improve quantitative retrievals from commonly acquired radar data. The first major focus of this thesis centres on deriving englacial velocities from zero-offset IPR data. Water held within micro- and macro-scale pores in ice has a direct influence on radar velocity, and significantly reduces ice viscosity and hence impacts the long-term evolution of polythermal glaciers. Knowledge of the radar velocity field is essential to retrieve correct bed topography from depth conversion processing, yet bed topography is often estimated assuming constant velocity, and potential errors from lateral variations in the velocity field are neglected. Here I calculate the englacial radar velocity field from common offset IPR data collected on Von Postbreen, a polythermal glacier in Svalbard. I first extract the diffracted wavefield using local coherent stacking, then use the focusing metric of negative entropy to deduce a local migration velocity field from constant-velocity migration panels and produce a glacier-wide model of local radar velocity. I show that this velocity field is successful in differentiating between areas of cold and temperate ice and can detect lateral variations in radar velocity close to the glacier bed. The effects of this velocity field in both migration and depth-conversion of the bed reflection are shown to result in consistently lower ice depths across the glacier, indicating that diffraction focusing and velocity estimation are crucial in retrieving correct bed topography in the presence of temperate ice. For the thesis’ second major component I undertake an assessment of automated techniques for tracing and interpreting ice-sheet internal stratigraphy. Radar surveys across ice sheets typically measure numerous englacial layers that can be often be regarded as isochrones. Such layers are valuable for extrapolating age-depth relationships away from ice-core locations, reconstructing palaeoaccumulation variability, and investigating past ice-sheet dynamics. However, the use of englacial layers in Antarctica has been hampered by underdeveloped techniques for characterising layer continuity and geometry over large distances, with techniques developed independently and little opportunity for inter-comparison of results. In this paper, we present a methodology to assess the performance of automated layer-tracking and layer-dip-estimation algorithms through their ability to propagate a correct age-depth model. We use this to assess isochrone-tracking techniques applied to two test case datasets, selected from CreSIS MCoRDS data over Antarctica from a range of environments including low-dip, continuous layers and layers with terminations. We find that dip-estimation techniques are generally successful in tracking englacial dip but break down in the upper and lower regions of the ice sheet. The results of testing two previously published layer-tracking algorithms show that further development is required to attain a good constraint of age-depth relationship away from dated ice cores. I make the recommendation that auto-tracking techniques focus on improved linking of picked stratigraphy across signal disruptions to enable accurate determination of the Antarctic-wide age-depth structure. The final aspect of the thesis focuses on Finite-Difference Time-Domain (FDTD) modelling of IPR data. I present a sliced-3D approach to FDTD modelling, whereby a thin 3D domain is used to replicate modelling of full 3D polarisation while reducing computational cost. Sliced-3D modelling makes use of perfectly matched layer (PML) boundary conditions, and requires tuning of PML parameters to minimise non-physical reflections from the model-PML interface. I investigate the frequency dependence of PML parameters, and establish a relationship between complex frequency stretching parameters and effective wavelength. The resultant parameter choice is shown to minimise propagation errors in the context of a simple radioglaciological model, where 3D domains may be prohibitively large, and for a near-surface cross-borehole survey configuration, a case where full waveform inversion may typically be used

Nonlinear design of geophysical surveys and processing strategies

The principal aim of all scientific experiments is to infer knowledge about a set of parameters of interest through the process of data collection and analysis. In the geosciences, large sums of money are spent on the data analysis stage but much less attention is focussed on the data collection stage. Statistical experimental design (SED), a mature field of statistics, uses mathematically rigorous methods to optimise the data collection stage so as to maximise the amount of information recorded about the parameters of interest. The uptake of SED methods in geophysics has been limited as the majority of SED research is based on linear and linearised theories whereas most geophysical methods are highly nonlinear and therefore the developed methods are not robust. Nonlinear SED methods are computationally demanding and hence to date the methods that do exist limit the designs to be either very simplistic or computationally infeasible and therefore cannot be used in an industrial setting. In this thesis, I firstly show that it is possible to design industry scale experiments for highly nonlinear problems within a computationally tractable time frame. Using an entropy based method constructed on a Bayesian framework I introduce an iteratively-constructive method that reduces the computational demand by introducing one new datum at a time for the design. The method reduces the multidimensional design space to a single-dimensional space at each iteration by fixing the experimental setup of the previous iteration. Both a synthetic experiment using a highly nonlinear parameter-data relationship, and a seismic amplitude versus offset (AVO) experiment are used to illustrate that the results produced by the iteratively-constructive method closely match the results of a global design method at a fraction of the computational cost. This new method thus extends the class of iterative design methods to nonlinear problems, and makes fully nonlinear design methods applicable to higher dimensional industrial scale problems. Using the new iteratively-constructive method, I show how optimal trace profiles for processing amplitude versus angle (AVA) surveys that account for all prior petrophysical information about the target reservoir can be generated using totally nonlinear methods. I examine how the optimal selections change as our prior knowledge of the rock parameters and reservoir fluid content change, and assess which of the prior parameters has the largest effect on the selected traces. The results show that optimal profiles are far more sensitive to prior information about reservoir porosity than information about saturating fluid properties. By applying ray tracing methods the AVA results can be used to design optimal processing profiles from seismic datasets, for multiple targets each with different prior model uncertainties. Although the iteratively-constructive method can be used to design the data collection stage it has been used here to select optimal data subsets post-survey. Using a nonlinear Bayesian SED method I show how industrial scale amplitude versus offset (AVO) data collection surveys can be constructed to maximise the information content contained in AVO crossplots, the principal source of petrophysical information from seismic surveys. The results show that the optimal design is highly dependant on the model parameters when a low number of receivers is being used, but that a single optimal design exists for the complete range of parameters once the number of receivers is increased above a threshold value. However, when acquisition and processing costs are considered I find that, in the case of AVO experiments, a design with constant spatial receiver separation is close to optimal. This explains why regularly-spaced, 2D seismic surveys have performed so well historically, not only from the point of view of noise attenuation and imaging in which homogeneous data coverage confers distinct advantages, but also as providing data to constrain subsurface petrophysical information. Finally, I discuss the implications of the new methods developed and assess which areas of geophysics would benefit from applying SED methods during the design stage