Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a combination of the curvelet transform and a whitening filter along with procedure for noise variance estimation. The whitening filter is added to get the best performance of the curvelet transform under coherent and incoherent correlated noise cases, and furthermore, it simplifies the noise estimation method and makes it easy to use the standard threshold methodology without digging into the curvelet domain. The proposed method is tested on pseudo-synthetic data by adding noise to real noise-less data set of the Netherlands offshore F3 block and on the field data set from east Texas, USA, containing ground roll noise. Our experimental results show that the proposed algorithm can achieve the best results under all types of noises (incoherent or uncorrelated or random, and coherent noise)

The estimation of geoacoustic properties from broadband acoustic data, focusing on instantaneous frequency techniques

The compressional wave velocity and attenuation of marine sediments are fundamental to marine science. In order to obtain reliable estimates of these parameters it is necessary to examine in situ acoustic data, which is generally broadband. A variety of techniques for estimating the compressional wave velocity and attenuation from broadband acoustic data are reviewed. The application of Instantaneous Frequency (IF) techniques to data collected from a normal-incidence chirp profiler is examined. For the datasets examined the best estimates of IF are obtained by dividing the chirp profile into a series of sections, estimating the IF of each trace in the section using the first moments of the Wigner Ville distribution, and stacking the resulting IF to obtain a composite IF for the section. As the datasets examined cover both gassy and saturated sediments, this is likely to be the optimum technique for chirp datasets collected from all sediment environments

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

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

INVERSE ATTENUATION-FILTERING

When seismic waves propagate through the Earth, they are affected by numerous inelastic effects of the medium. These effects are usually characterized by the concept of the Q-factor and lead to variations of spectra of the signal and shapes of the waveforms, which further affect the results of reflection seismic imaging. Attenuation compensation, also often called the inverse Q filtering is a signal-processing procedure broadly used to compensate both of these effects of attenuation in reflection sections or volumes. The objective of this thesis is to present and investigate a new attenuation-compensation approach that is much more general than the conventional inverse Q filtering

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data