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

3-D SEISMIC SURVEY DESIGN VIA MODELING AND REVERSE TIME MIGRATION: PIERCE JUNCTION SALT DOME, TEXAS

Seismic forward modeling studies are required for adequately imaging complex geological structures, such as folds, faults, and domes. Many U.S. Gulf Coast salt domes are used for oil and gas exploration, brine production, and underground hydrocarbon storage. For this reason, it is crucial to image the flank of the salt domes and surrounding sediments. Allied Geophysical Laboratories (AGL) carried out a 2-D seismic study in the Texas Brine Company facility to image the Pierce Junction salt dome. However, we were not able to image the salt flanks because of improper survey design. This led to the current study which proposes a 2-D and a 3-D seismic survey design using modeling and Reverse Time Migration (RTM) imaging. We gathered original 2-D seismic, topography, and gravity data to build 2-D and 3-D velocity models of the Pierce Junction salt dome area. We processed the original 2-D data and extracted the velocities of the cap rock and near surface sediments for use in velocity models. We modelled gravity data collected in a north-south direction and performed analyses on the synthetic seismic data to determine new 2-D conventional seismic survey parameters that could be achieved with the limited acquisition equipment of AGL. We modeled synthetic shot gathers by a finite difference method using the full (two-way) acoustic wave equation, and generated seismic images using the Reverse Time Migration (RTM) method. We determined the optimum parameters of the new 2-D seismic survey by reviewing the quality of the results. These parameters were able to adequately image the salt dome and its surrounding sediments. We then modified the 2-D parameters for a new 3-D survey, and obtained synthetic RTM images based on the 3-D velocity model. Optimal 2-D and 3-D seismic survey designs for the Pierce Junction salt dome area were achieved using seismic modeling and RTM imaging. We found RTM imaging to be a novel and powerful method for determining seismic survey parameters for complex geological structures.Earth and Atmospheric Sciences, Department o

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

Full waveform inversion of narrow-azimuth towed-streamer seismic data

Full waveform inversion (FWI) is a computational scheme that produces high-fidelity, high-resolution models of the Earth's subsurface from surface seismic data. FWI has become a standard tool in velocity-model building and performs well on full-azimuth long-offset ocean-bottom seismic datasets. However, the majority of marine seismic datasets use narrow-azimuth towed streamers (NATS) which often lack long-offset refracted energy. Here I explore the capability of conventional FWI when it is applied to marine deep-water reflection-dominated NATS field data. I applied FWI to three datasets: the first used a deep-towed 10-km cable and was specifically acquired for 2D FWI; the other two datasets were both 3D reflection-dominated surveys to which FWI had been previously applied with limited success - these datasets were from Gabon and Brazil, and were chosen specifically because FWI had been previously tried and had failed. Applying FWI to these datasets, I reached the following conclusions: 1) When the input data have adequate turning energy and adequate low-frequency energy, acoustic anisotropic FWI can generate accurate high-resolution velocity models of increasing complexity and resolution up to about 40 Hz. 2) Extending FWI to the full bandwidth of the field data produces minimal further change in the macro-velocity model, but nonetheless continues to improve resolution up to and perhaps beyond that which can be recovered by conventional Kirchhoff-based pre-stack depth migration. 3) Applying 2D and full-3D FWI to a single 2D sail line produces similar outcomes. 4) The Gabon dataset proved almost entirely resistant to FWI; the available evidence suggests that the nominally-raw field data were corrupt in some unknown way. 5) The Brazilian dataset was inverted using a third-party FWI code that assumed constant density; this assumption is detrimental to FWI.Open Acces

SEISMIC DATA CONDITIONING AND ANALYSIS FOR FRACTURED RESERVOIRS

The ability to identify the intensity and orientation of fractures within both unconventional and conventional resources can have a critical impact on oil field development. Fractures and faults are often the primary pathways for hydrocarbon migration and production. Because of their complexity and commercial importance, fractures have been studied by each of the main disciplines – geology, geophysics, petrophysics, and engineering. The focus of this dissertation is to present an understanding of how different geophysical technologies can be used to characterize fractures at different scales. Seismic attributes are one of the main tools to map the distribution of fractures and can be categorized into geometric attributes, azimuthal velocity anisotropy, amplitude variation with offset and azimuth, and diffraction imaging. These categories are complementary to each other and can provide overlapping information. The diversity of the assumptions under each category makes it challenging to bridge the gap for real world applications. Acquisition footprint overprints most seismic surveys and can mask or in some cases be misinterpreted as underlying faults and fractures. There are two modern trends in imaging the subsurface with high quality 3D seismic surveys. The first is to acquire new high density, high fold, wide azimuth surveys that exhibit less footprint. The second is to combine multiple legacy surveys into “megamerge” (or even “gigamerge” surveys) that exhibit multiple footprint patterns. To address this latter problem, I start my dissertation by introducing an adaptive 2D continuous wavelet transform (CWT) footprint suppression workflow whose design is based on artefacts seen on seismic attributes. Suboptimum seismic acquisition is one of the major causes of acquisition footprint. 5D interpolation (also called 5D regularization) is a modern seismic processing workflow that attempts to fill in the missing offsets and azimuths. I examine the effect of a commercial Fourier-based 5D interpolation on both footprint artefacts and geologic discontinuities measured using seismic attributes. I find that by accurately interpolating specular reflections, 5D interpolation suppresses acquisition footprint and improves the lateral continuity of prestack inversion images of P-impedances. Unfortunately, 5D Fourier-based interpolation incorrectly corrects diffraction events and therefore attenuates faults and karst edges seen in coherence. Whereas 5D interpolation attempts to enhance the specular component of seismic data, diffraction imaging attempts to enhance the non-specular or diffracted component of the seismic data necessary to image fractures. Although the lateral resolution of diffractions is better than that of specular reflections, closely spaced fractures forming a “fracture swarm” may appear to be a single, larger fracture, while more laterally extensive fracture swarms give rise to azimuthal and offset anisotropy. I investigate each technique’s ability to detect fractures using forward modeling and find that diffraction’s focusing sensitivity to velocity inaccuracies makes it an excellent candidate to highlight close-spaced fractures. I also find that cross-correlating images of diffractions from nearby experiments is useful in constructing an objective function that can be used to update the velocity due in the image domain. I demonstrate the efficiency of these findings using synthetic models with different complexity. Azimuthal and offset anisotropy signature for irregularly spaced fractures is complex and different from the constant fracture spacing approximated by effective medium theory particularly for reflection below the fractures. I find isotropic amplitude variation modeling give an indication if fractures are located at the bottom portion of the reservoir