Leiv-J. Gelius

A generalized diffraction tomography algorithm

Available diffraction tomography algorithms are based on Fourier transform techniques and require either plane‐wave illumination in a uniform background medium or far‐field illumination combined with paraxial approximations. In this paper a generalized diffraction tomography algorithm is introduced that can handle both irregularly spaced measurement data, nonuniform background models, and general aquisition geometries. Using data from water tank experiments, the method’s ability to yield high‐quality reconstructions of geometry and velocity, as long as the weak‐scattering assumption is satisfied, is demonstrated.

Fresnel aperture prestack depth migration

We investigate possible improvements in seismic imaging. We discuss how the Fresnel zone relates to the migration aperture and introduce the concept of the Fresnel aperture, which is the direct time-domain equivalent, at the receivers’ surface, of the subsurface Fresnel zone. Through these concepts we propose a new and efficient method for optimal aperture selection and migration. For complex media, multipathing will occur and multiple Fresnel apertures can exist for a given image point. In practice, due to inaccuracies and smoothing of the background velocity macromodel, inaccuracies in the ray-tracing method used for Green’s function computations and possible noise corruption of the data, the true Fresnel apertures will, in many cases, be replaced by ‘false’ ones, with apparently new Fresnel apertures being added. Hence, contributions from these ‘false’ Fresnel apertures cause a noise-corrupted image of the subsurface. It is now assumed that the single scattered events are quite robust with respect to the above-mentioned distortions, and that their corresponding Fresnel apertures will remain essentially undistorted, with the strongest amplitudes. Based on this main assumption, we propose a method, analogous with velocity analysis, where the strong-amplitude Fresnel apertures can be picked interactively and at least semi-automatically. However, as in velocity analysis, a certain amount of user interaction has to be assumed. When this technique is combined with a prestack Kirchhoff-type depth-migration method, we call it Fresnel-aperture PSDM. This imaging method has been applied to data from both the Marmousi model and the North Sea. In both cases the improvements, when compared to conventional imaging, were considerable.

Time-reversal multiple signal classification in case of noise: A phase-coherent approach

The problem of locating point-like targets beyond the classical resolution limit is revisited. Although time-reversal MUltiple SIgnal Classification (MUSIC) is known for its super-resolution ability in localization of point scatterers, in the presence of noise this super-resolution property will easily break down. In this paper a phase-coherent version of time-reversal MUSIC is proposed, which can overcome this fundamental limit. The algorithm has been tested employing synthetic multiple scattering data based on the Foldy-Lax model, as well as experimental ultrasound data acquired in a water tank. Using a limited frequency band, it was demonstrated that the phase-coherent MUSIC algorithm has the potential of giving significantly better resolved scatterer locations than standard time-reversal MUSIC.

Ultrasonic Tomography of Biological Tissue

In this paper, quantitative tomographic reconstructions of biological tissue are presented. First, the experimental setup and a hybrid filtered backpropagation (FBP) technique are briefly described. Using this technique, which includes exact backpropagation of data prior to reconstruction by means of the classical FBP algorithm, quantitative velocity maps of relatively large biological objects can be obtained. Since the FBP algorithm is based on a first-order scattering approximation, the deteriorating effects of higher-order scattering in diffraction tomography are also discussed. The higher-order scattering limits the size of the biological object to a few centimeters.

Recovering diffractions in CRS stacked sections

The common reflection surface (CRS) method has been proposed as an alternative to the classical common midpoint method to further improve the signal-to-noise ratio, as well as to obtain additional kinematic parameters that are useful for a number of imaging purposes. In the CRS method, reflected events are enhanced by stacking along a generalized hyperbolic moveout, referred to as the CRS moveout. However, during the process of CRS stacking, diffractions are likely to be attenuated or even suppressed. Diffracted events are important since they carry high-resolution information about the subsurface structure. By the use of a modified version of the CRS technique, diffractions can be enhanced in the same way as reflections. This paper proposes a combined approach where the CRS stack is superimposed on the CRS diffraction-enhanced stack. In this way we can recover the diffractions in CRS stacked sections. The potential of the method has been demonstrated using marine seismic data acquired offshore Brazil.

Higher-Resolution Determination of Zero-Offset Common-Reflection-Surface Stack Parameters

We developed a higher resolution method for the estimation of the three travel-time parameters that are used in the 2D zero-offset, Common-Reflection-Surface stack method. The underlying principle in this method is to replace the coherency measure performed using semblance with that of MUSIC (multiple signal classification) pseudospectrum that utilizes the eigenstructure of the data covariance matrix. The performance of the two parameter estimation techniques (i.e., semblance and MUSIC) was investigated using both synthetic seismic diffraction and reflection data corrupted with white Gaussian noise, as well as a multioffset ground penetrating radar (GPR) field data set. The estimated parameters employing MUSIC were shown to be superior of those from semblance.

Migration-velocity building in time and depth from 3D (2D) Common-Reflection-Surface (CRS) stacking - theoretical framework

We demonstrate how the velocity concepts attached to conventional stacking assuming local smooth 1D type of Earth models, are modified within the setting of the Common Reflection Surface (CRS) method to handle lateral velocity variations. The corresponding matrix (scalar) normal moveout (NMO)- and Dix-velocities in 3D (2D) are now linked to a smooth velocity medium in depth sampled along the mapping or normal rays taking into account lateral velocities. This is rather different from the conventional 1D case where the link between the data-driven velocities and the smooth 1D velocity medium are represented by vertical mapping rays. Further and by analogy with the conventional 1D approach, where time-migration velocities are computed from NMO- or Dix-velocities after proper smoothing, its CRS counterpart is established. It is demonstrated that matrix (scalar) time-migration velocities to be used in ray-based 3D (2D) time-migration (TM) can be obtained by proper mapping of the corresponding CRS velocities. Relevant mapping equations valid for the 2D case have earlier been treated in the literature. However, to our knowledge, this is the first time such mapping equations have been derived for the 3D case. This mapping takes into account smooth lateral velocity variations, normally not properly accounted for in the initial model employed in conventional time-migration building based on NMO-velocities. Also, unlike the conventional approach, the use of the CRS method makes it feasible to build a smooth velocity field in depth beyond that of 1D. In this connection, we propose to use Normal Incidence Point (NIP) tomography (alternatively Image Incidence Point (IIP) tomography) to build a macro-velocity model upon which the time-to-depth mapping and the correction factors can be calculated. That step is then followed by construction of an updated smooth replacement medium, better able to capture local changes in velocity. The proposed approach can be used iteratively. Such depth velocities can be employed as an initial model for iterative depth migration. The main idea being that velocity-model building by using time-domain observables ensures more robustness.

2D common-offset traveltime based diffraction enhancement and imaging

The diffracted energy in a seismic recording contains key information about small-scale inhomogeneities or discontinuities of the subsurface. Diffractions can therefore lead to high-resolution imaging of subsurface structures associated with hydrocarbon traps. However, seismic diffracted signals are often much weaker than specular reflections and consequently require enhancement before they can be utilized. In this paper diffractions are enhanced relative to reflections based on two traveltime techniques, namely the modified common-reflection-surface approach, which uses the common-reflection-surface technique with some modification to tailor it for diffractions and the replacement-media approach derived here for the purpose of a simplified parametrization of diffraction traveltimes. Both approaches are implemented in the common-offset domain with the use of a finite-offset central ray unlike the zero- or small-offset diffraction enhancement techniques that use a zero-offset central ray. The validity of the two moveout expressions is tested using velocity data taken from a smooth isotropic Marmousi model. A feasibility test was also carried out with respect to the new replacement-media traveltime approximation addressing the various effects of signal-to-noise ratio, depth and lateral displacement of the diffractor location. Finally, diffraction enhancement and imaging was performed on 2D seismic data from the Jequitinhonha basin offshore Brazil. Diffractions were significantly enhanced and a high-resolution image of the discontinuities of the subsurface was obtained.

Limited‐view diffraction tomography in a nonuniform background

The main problems in geophysical diffraction tomography are (1) complicated media and (2) rather limited acquisition geometries. Existing algorithms solve the limited-view problem in an iterative manner, but are valid only for line sources and 2-D homogeneous background models. In this paper, the authors derive an iterative algorithm based on asymptotic wave theory that can compensate for a limited acquisition geometry. The method is valid for a 2-D nonuniform background model and point-source illumination (i.e., a 2.5-D geometry). Paraxial ray tracing is employed to model the arbitrary background wave response, and the general structure of the algorithm has a strong resemblance to the iterative ART-algorithm used in straight ray tomography. The authors method is shown to be stable in the presence of moderate white noise and gives reasonable results, both geometrically and quantitatively, when applied to synthetic crosshole data involving a nonhomogeneous background model and limited view.

Seismic Coherency Measures in Case of Interfering Events: A Focus on the Most Promising Candidates of Higher-Resolution Algorithms

In this article, the use of coherency measures in seismic signal processing is reviewed, along with the introduction of higher-resolution parameter estimation methods. The actual problem analyzed is that of separating diffractions from reflections and utilizing them to perform higher-resolution imaging of small-scale subsurface structures. The main idea is that diffracted waves can be described by a modified moveout equation normally employed by the common reflection surface (CRS) technique. A number of coherency measures have been proposed to assess how well a moveout (defined by some trial parameters) approximates a target signal. Traditional methods using semblance often fail in cases of interfering events. This fact has motivated the investigation of alternative coherency measures based on higher-resolution techniques like multiple signal classification (MUSIC), eigenvector (EV), and minimum variance (MV). Here, the various algorithms are tested employing controlled seismic data from the Marmousi model as well as field data acquired by a ground-penetrating radar (GPR). It is found that the MUSIC algorithm provides the best result slightly ahead of EV and with MV falling somewhere between these two techniques with the more standard approach based on semblance and time migration.