NMO Velocity Research Articles

Interactive attenuation of seismic multiples in the radial domain

In marine seismic surveys, reverberations in the water layer known as multiples obscure primary reflections from deeper geological boundaries. This is especially a problem in areas of the North West Shelf of Western Australia, where the geology of the area can produce very strong multiple events, often with similar NMO velocity to primary events. Because of this lack of velocity discrimination, conventional multiple attenuation methods often fail. An effective method of multiple attenuation using 1D Feedback Autoconvolution in the Radial Domain has been devised. This does not rely on a velocity discrimination between primary and multiple events, and can be applied interactively via a Motif X11 Graphical User Interface, and with minimal user input. A radial transform has been written that converts either CMP or shot record data, to make both simple water bottom and pegleg multiples from a horizontal sea floor, periodic on each trace, and is suitable for the application of autoconvolution. The extension of the radial transform to a dipping sea floor has been modelled using the mathematical modelling package MAPLE, and an approximate solution has been devised. The technique of successive autoconvolution on each seismic trace in a feedback loop, predicts surface related multiple events, at the correct time, reverse polarity, and theoretically correct amplitudes. In practice a scaling algorithm has been incorporated to match the predicted multiples to the original data. A program module to apply 1D Feedback autoconvolution on radial transformed data for both horizontal layer and dipping water bottom models has been developed, and applied successfully to both simple water bottom multiples and water bottom peg-legs.

ANISOTROPIC TRAVELTIME TOMOGRAPHY

AbstractVelocity estimation technique using seismic data is often based on time/distance equations which are independent of direction, and even though we now know that many rocks are quite anisotropic, useful results have been obtained over the years from these isotropic estimates. Nevertheless, if velocities are significantly direction‐dependent, then the isotropic assumption may lead to serious structural interpretation errors. Additionally, information on angle‐dependence may lead to a better understanding of the lithology of the rocks under measurement. VSP and cross‐well data may each lack the necessary aperture to estimate more than two velocity parameters for each wave type, and if the data straddle a symmetry axis, then these may be usefully chosen to be the direct velocities (from time‐and‐distance measurements along the axis) and NMO velocities (from differential time‐offset measurements). These sets of two parameters define ellipses, and provide intermediate models for the variation of velocity with angle which can later be assembled and translated into estimates of the elastic moduli of the rocks under scrutiny.If the aperture of the measurements is large enough e.g. we have access to both VSP and cross‐well data, we divide the procedure into two independent steps, first fitting best ellipses around one symmetry axis and then fitting another set around the orthogonal axis. These sets of four elliptical parameters are then combined into a new, double elliptical approximation. This approximation keeps the useful properties of elliptical anisotropy, in particular the simple relation between group and phase velocities which simplifies the route from the traveltimes measurements to the elastic constants of the medium.The inversion proposed in this paper is a simple extension of well‐known isotropic schemes and it is conceptually identical for all wave types. Examples are shown to illustrate the application of the technique to cross‐well synthetic and field P‐wave data. The examples demonstrate three important points: (a) When velocity anisotropy is estimated by iterative techniques such as conjugate gradients, early termination of the iterations may produce artificial anisotropy. (b) Different components of the velocity are subject to different type of artifacts because of differences in ray coverage, (c) Even though most rocks do not have elliptical dispersion relations, our elliptical schemes represent a useful intermediate step in the full characterization of the elastic properties.

Scaled physical modelling of anisotropic wave propagation: multioffset profiles over an orthorhombic medium

SUMMARY In this paper we report further results of scaled physical modelling experiments in the laboratory in which ultrasonic elastic waves are propagated through an anisotropic medium of orthorhombic symmetry. Whereas our earlier experiments consisted for the most part in sending and receiving on opposite faces of a small cube of phenolic laminate, these new results are from multioffset profiles run parallel and at 45 to principal directions on a larger slab of phenolic. The variation of NMO velocity with offset (or angle of incidence) has been determined for compressional and transverse shear waves along profiles in the two principal directions on the 3-face (parallel to laminations) of the slab. These observed group velocities differ from the exact theoretical values by a maximum of about 1 per cent or less and also compare favourably with the theoretical velocities calculated from Thomsen's first-order equations, with maximum differences of about 2 per cent. Differences between the observed and theoretical velocities are attributed to some combination of finite transducer size (geometrical or effective path length effects, array attenuation effects, or interference with the otherwise free surface), sample inhomogeneity and/or anelasticity, and experimental error. The transmission shot gathers acquired for propagation in symmetry planes, and for source-receiver pairs with the same polarization, are similar in form to records acquired over a transversely isotropic medium. The effect of the shear-wave window and the variation of the hyperbolic NMO parameter with offset are clearly seen. Transmission records were also acquired in off-symmetry planes, namely along profiles at 45 to principal directions. On these records, which include all nine possible pairs of source-receiver polarizations, we see clear shear-wave splitting at and near zero offset and more complicated wave effects with increasing offset, such as one or another wave phase dying out. This could be due to cusping of wave surfaces or rapid changes of amplitude and/or polarization with ray direction, possibly as consequences of nearby shear-wave singularities.

Anisotropic wave propagation and zero-offset migration

In reflection seismology, migration may be defined as the transformation of apparent reflector positions to their true positions. In practice this usually means that diffractions are collapsed and reflector dip angles are changed. When a medium is anisotropic, and the axes of velocity symmetry are tilted with respect to the horizontal, horizontal reflection events migrate laterally as well. The lateral migration of reflections from horizontal layers was studied by constructing an anisotropic scale model representing a medium in which the bedding is inclined to the surface. This situation may be classified as one of transverse isotropy with a tilted axis of symmetry. The elastic parameters of the anisotropic model were recovered by P- and SH-wave transmission measurements carried out to simulate a walk-away VSP. Numerical modelling of a P-wave CMP gather above a horizontal reflector in such a medium indicated that there would be an asymmetrical distribution of reflection points. The zero-offset reflection point was displaced laterally by a distance equal to more than 20% of the depth, and the spread of reflection points was 15% of the depth. The NMO velocity was found to be a function of offset. A zero-offset reflection survey was carried out on the model. The P-wave data were migrated with an anisotropic migration algorithm which may be applied to wavefronts of any shape. On the resulting section, the horizontal reflection features are moved laterally by a distance equal to 20% of the depth back to their correct positions. The lateral displacement of reflections from a horizontal reflector beneath a medium with tilted anisotropic velocity characteristics has significance for the selection of drill locations when such a situation is encountered in the field.

LIMITS OF STRUCTURAL INVERSION OF SEISMIC HORIZONS*

AbstractTime horizons can be depth‐migrated when interval velocities are known; on the other hand, the velocity distribution can be found when traveltimes and NMO velocities at zero offset are known (wavefront curvatures; Shah 1973).Using these concepts, exact recursive inversion formulae for the calculation of interval velocities are given. The assumption of rectilinear raypath propagation within each layer is made; interval velocities and curvatures of the interfaces between layers can be found if traveltimes together with their gradients and curvatures and very precise VNMO velocities at zero offset are known.However, the available stacking velocity is a numerical quantity which has no direct physical significance; its deviation from zero offset NMO velocity is examined in terms of horizon curvatures, cable length and lateral velocity inhomogeneities.A method has been derived to estimate the geological depth model by searching, iteratively, for the best solution that minimizes the difference between stacking velocities from the real data and from the structural model.Results show the limits and capabilities of the approach; perhaps, owing to the low resolution of conventional velocity analyses, a simplified version of the given formulae would be more robust.