Seismic multiples are a serious hindrance to hydrocarbon exploration in Australia. In particular, water bottom multiples can be very difficult to attenuate. This is because there often exists a strongly reflective sea floor which gives multiples large amplitudes when compared with the primary events they overlay, and secondly, because of a widely occurring velocity inversion, which seriously reduces the effectiveness of a very important class of multiple attenuation techniques.Multiple attenuation techniques can be classified according to the characteristic of the data which is used to discriminate against the multiples in conjunction with the operation behind the demultiple process. Common multiple attenuation processes include FK demultiple, Radon Demultiple, predictive deconvolution, wave equation based demultiple procedures and the family of techniques which come under the umbrella of Surface Multiple Attenuation (SMA). All of these techniques, given the right conditions, can be very effective. They also vary in price from very cheap (FK demultiple) through to expensive (wave equation based demultiple procedures).However, despite these procedures, and fifty odd years of research, there is no effective general solution to multiple problems off the coast of Western Australia and indeed in many regions around the world.Two new wavefield transformations, Multiple MoveOut (MMO) and IsoStretch Radial Trace (ISR), have been developed in this research to precondition data prior to the removal of surface related multiples by existing techniques. These form the basis of a new multiple attenuating procedure.MMO shifts the data so that the water bottom primary event is flattened and the simple water bottom multiples are also flat and periodic. Water bottom peg leg multiples are made approximately periodic.To solve the stretch problem introduced by the MMO transform, ISR ++ / interpolates oblique traces of constant stretch, which also map constant shot emergence angles. The water bottom primary and multiple events form a stationary time series after MMO and ISR. They are then amenable to removal by autoconvolution and predictive deconvolution.The results of the new procedure are demonstrated on two case studies from offshore Western Australia. It is shown to be more effective at removing both simple and peg leg water bottom multiples than traditional techniques. Finally, it is an inexpensive procedure, which does not require velocity analysis prior to its application.

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Incomplete data, unknown source-receiver signatures and free-surface reflectivity represent challenges for a successful prediction and subsequent removal of multiples. In this paper, a new method will be represented that tackles these challenges by combining what we know about wavefield (de-)focussing, by weighted convolutions/correlations, and recently developed curvelet-based recovery by sparsity-promoting inversion (CRSI). With this combination, we are able to leverage recent insights from wave physics towards a nonlinear formulation for the multiple-prediction problem that works for incomplete data and without detailed knowledge on the surface effects.

A method for acquiring and analyzing ultrasonic wavefields to characterize scattering from defects is described. A laser vibrometer and XY scanner are used to record high resolution wavefield data for angle-beam waves propagating in both a defect-free plate and a plate containing crack-like defects emanating from a through-hole. The properties of angle-beam wave propagation are first studied, which include wave generation mechanisms, propagation trajectories, and apparent phase velocities on the measurement surface. Scattering from a defect of interest is then analyzed by subtracting wavefields recorded before and after introduction of the defect. Wavefield subtraction is very sensitive to unavoidable spatial misalignment, which must be corrected prior to subtraction. Two methods for aligning wavefield data sets prior to subtraction are described and their performance is assessed. Several methods for characterizing scattering, including radial energy plots and scattering patterns, are described and used to quantify scattering from the introduced defects. Finally, efficacy of the scattering characterization methods is discussed and recommendations are made for future work.

In exploration seismology, seismic waves are emitted into the structurally complex Earth. Its response, consisting of a mixture of arrivals including primary reflections, conversions, multiples, and transmissions, is used to infer the internal structure and properties. Waves that interact multiple times with the inhomogeneities in the medium probe areas of the subsurface that are sometimes inaccessible to singly scattered waves. However, these contributions are notoriously difficult to use for imaging because multiple scattering turns out to be a highly nonlinear process. Conventionally, imaging algorithms assume singly scattered energy dominates data. Hence these require that energy that scatters more than once is attenuated. The principal focus of this thesis is to incorporate the effect of complex nonlinear scattering in the construction of subsurface elastic images. Reciprocity theory is used to establish an exact relation between the full recorded data and the local (zero-offset, zero-time) scattering response in the subsurface which constitutes our image. Fully nonlinear, elastic imaging conditions are shown to lead to better illumination, higher resolution and improved amplitudes in pure-mode imaging. Strikingly it is also observed that when multiple scattering is correctly handled, no converted-wave energy is mapped to any image point. I explain this result by noting that conversions require finite time and space to manifest. The construction of wavefield propagators (Green’s functions) that are used to extrapolate recorded data from the surface to points in the Earth’s interior is a crucial component of any imaging technique. Classical approaches are based on strong assumptions about the propagation direction of recorded data, and their polarization; preliminary steps of wavefield decomposition (directional and modal) are required to extract upward propagating waves at the recording surface and separate different wave modes. These algorithms also generally fail to explain the trajectories of multiply scattered and converted waves, representing a major problem when constructing nonlinear images as we do not know where such energy interacted with the scatterers to be imaged. A secondary aim of this thesis is to improve on the practice of wavefield extrapolation or redatuming by taking advantage of the different nature of multi-component data compared with single-mode acoustic data. Two-way representation theorems are used to define novel formulations in elastic media which allow both up- and downward propagating fields to be back-propagated correctly without ambiguity in the direction, and such that no cross-talk between wave modes is generated. As an application of directional extrapolation, the acoustic counterpart of the new approach is tested on an ocean-bottom cable field dataset acquired over the Volve field, North Sea. Interestingly, the process of redatuming sources to locations beneath a complex overburden by means of multi-dimensional deconvolution also requires preliminary wavefield separation to be successful: I propose to use the two-way convolution-type representation as a way to combine full pressure and particle velocity recordings. Accurate redatumed wavefields can then be obtained directly from multi-component data without separation. Another major challenge in seismic imaging is to construct detailed velocity models through which recorded data will be extrapolated. Nowadays the information contained in the extension of subsurface images along either the time or space axis is commonly exploited by velocity model building techniques acting in the image domain. Recent research has shown that when both extensions are taken into account, it is possible to estimate the data that would have been recorded if a small, local seismic survey was conducted around any image point in the subsurface. I elaborate on the use of nonlinear elastic imaging conditions to construct such so-called extended image gathers: missing events, incorrect amplitudes, and spurious energy generated from the use of only primary arrivals are shown to be mitigated when multiple scattering is included in the migration process. Finally, having access to virtual recordings in the subsurface is also very useful for target-oriented imaging applications. In the context of one-way representation, I apply the novel methodology of Marchenko redatuming to the Volve field dataset as a way to unravel propagation effects in the overburden structure. Constructed wavefields are then used to synthesize local, subsurface reflection responses that are only sensitive to local heterogeneities, and detailed images of target areas of the subsurface are ultimately produced. Overall the findings of this thesis demonstrate that, while incorporating multiply scattered waves as well as multi-component data in imaging may be not a trivial task, such information is vital for achieving high-resolution and true-amplitude seismic imaging.

Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models, to reproduce wave propagation phenomena in the Earth's subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, I generate effective isotropic inhomogeneous models that are capable of reproducing the first-arrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, I develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic one, is represented by a sixth order polynomial equation that includes the fastest solution corresponding to outgoing P-waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, which is done by explicitly solving the isotropic eikonal equation for the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. I extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.

Presented at Cyber-Enabled Discovery and Innovation: Knowledge Extraction as a success story lecture. See for more detail https://www.ipam.ucla.edu/programs/cdi2007/

An \emph {explicit} algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in {3-D}. By using ideas from ``\emph{compressed sensing}'', we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume{,} thereby reducing the size of the operators. According {to} compressed sensing theory, signals can successfully be recovered from an imcomplete set of measurements when the measurement basis is \emph{incoherent} with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain via a computationally cheaper operatoion. A proof of principle for the ``compressed sensing'' method is given for wavefield extrapolation in {2-D}. The results show that our method is stable and produces identical results compared to the direct application of the full extrapolation operator.

The objective of this thesis is to present analysis techniques that quantify the scattering of angle-beam ultrasonic waves from through-holes in plates. This topic is of interest because increased understanding of the scattering of ultrasonic waves by a defect is important for the development of many nondestructive evaluation (NDE) applications. Angle-beam techniques are commonly used in industry to detect and characterize defects, and many structures of concern have plate-like components. Scattering from through-holes is particularly important because cracks tend to form around fastener holes, which have high stress concentrations. In addition, varying boundary conditions within a fastener hole can change over the course of a structure’s lifetime and may have significant effects on NDE results. In this research, two signal processing techniques are developed to obtain scattering information from through-holes for a variety of fill conditions, including epoxy and complete and partial filling with metal inserts, using experimentally acquired wavefield measurements. Experimental procedures for acquiring wavefields, which measure the out of plane motion of ultrasonic waves on the surface of a specimen and allow for the visualization and characterization of propagating waves, are presented. Methods for obtaining radial and directional energy maps, which quantify scattering as a function of scattered angle and phase velocity, are described. In addition, baseline subtraction is used to obtain scattering patterns for both methods, which quantify scattering as a function of polar angle for each wave mode present in the wavefield. These techniques are applied to wavefield measurements from through-holes with various fill conditions to investigate the effects of boundary conditions on ultrasonic scattering. A comparison of the radial and directional energy mapping techniques, discussing the strengths and weaknesses of each approach, is provided, and recommendations are made for future work.

We discuss a systematic methodology that leads to the reconstruction of the material profile of either single, or assemblies of one-dimensional flexural components endowed with Timoshenko-theory assumptions. The probed structures are subjected to user-specified transient excitations: we use the complete waveforms, recorded directly in the time-domain at only a few measurement stations, to drive the profile reconstruction using a partial-differential-equation-constrained optimization approach. We discuss the solution of the ensuing state, adjoint, and control problems, and the alleviation of profile multiplicity by means of either Tikhonov or Total Variation regularization. We report on numerical experiments using synthetic data that show satisfactory reconstruction of a variety of profiles, including smoothly and sharply varying profiles, as well as profiles exhibiting localized discontinuities. The method is well suited for imaging structures for condition assessment purposes, and can handle either diffusive or localized damage without need for a reference undamaged state. / text