Laurence Nicoletis

3-D modeling project; 3rd report

The two geologic models (overthrust and salt dome) are now finalized, the acquisition phases are defined, and DOE laboratories have started the computations. Simulation for phase A is expected to be completed during the first quarter of 1995.

Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications

An original method is presented that allows us to measure the local shear‐wave birefringence properties over any depth interval. It requires the acquisition of two shear‐wave vertical seismic profiles (VSPs), each with different initial polarizations of the shear wave. The method is based on the estimation of a two by two matrix (called the propagator matrix) that represents a linear operator between two states of polarization. No information is required about layering above the zone of interest (in particular, about the weathering zone). If these two states of polarization correspond to the direct downgoing shear wave at two different depths z1 and z2, the operator represents the transmission properties between the two depths. Under the previous hypothesis, this operator is independent of the source polarization and can be accurately estimated by a least‐squares method in the frequency domain. Physically, this operator is a multicomponent deconvolution, whose column vectors represent the state of polariz...

Regularization of illumination in angle domains—a key to true amplitude migration

The turn of the millennium has seen the long expected affordability of 3D prestack depth migration based on wave-equation, or better said, band-limited algorithms. The success of wave-equation PreSDM (prestack depth migration) comes from the fulfillment of two, and only two, promises: correct handling of geometrical spreading and correct handling of multipathing, in complex media. Even then, the migration velocity model needs to be accurate enough to ensure the full effectiveness of this expectedly correct handling of wave propagation. How to get a complex though correct velocity model is still an open issue and is beyond our scope. There are nevertheless capabilities of Kirchhoff migration that wave-equation PreSDM cannot emulate yet, though progress is being made. On the imaging side, Kirchhoff has the well-known capability of imaging steep dips. Kirchhoff migration can also handle velocity models with various types of anisotropy. On the amplitude side, Kirchhoff migration offers better handling of irregular acquisition, better amplitude control through the theory of Beylkin, and better understanding of all illumination and regularization issues. This understanding is needed because the regularization of illumination is the key to a reduction of classic migration artifacts, to an improvement of the image quality, and to the reliability of the migration amplitudes for AVA and 4D processing.

Hole geometry and anisotropic effects on tube-wave propagation: A quasi-static study

Tube-wave characteristics, namely velocity and polarization, are affected by borehole anomalies related to nonhydrostatic tectonic stress. The anomalies we consider are borehole ellipticity, azimuthal anisotropy as modeled by a rotated transversely isotropic medium, and borehole breakouts as modeled by local heterogeneities in elastic properties. The low-frequency tube-wave velocity is obtained by a variational approach to a plane-strain, static-equilbrium problem. We solve the problem with hole ellipticity analytically and the problem with azimuthal an-isotropy numerically by a finite-element method. The results show that weak ellipticity has a negligible effect on the tube-wave velocity: a relative variation of 10 percent in the main diameters of the hole produces a perturbation of only 0.5 percent in the velocity. However, localized damage to the hole can reduce tube-wave velocity significantly. Furthermore, for tube-wave polarization, it is unrealistic to obtain deviations from the radial direction greater than 15 degrees, which makes it difficult to obtain any valuable information on the stress directions from the tube wave.

Approximate ray tracing for qP-waves in inhomogeneous layered media with weak structural anisotropy

We present approximate equations for qP-wave ray tracing and paraxial ray tracing in inhomogeneous layered weakly transversely isotropic (TI) media. Inside layers, the symmetry axis direction of the TI medium is allowed to vary continuously. Approximate equations are based on perturbation theory in which deviations of anisotropy from isotropy are considered to be first-order quantities. For qP-waves propagating in a TI medium, the approximate ray-tracing and paraxial ray-tracing equations depend on three parameters and two angles defining the direction of the symmetry axis. We also present the boundary conditions at interfaces for first-order rays and paraxial rays and compute reflection/transmission coefficients to the first order. All the quantities required for evaluation of the Green’s function are calculated to the first order, except the traveltime that is calculated to the second order. The accuracy of the presented algorithm is verified on simple models with respect to exact ray-tracing results. F...

3-C Imaging of 3D Walk-away Data In Regard to Preprocessing

Summary We apply a 3D/3C true-amplitude ray-Born imaging algorithm to a 3D walk-away dataset after two different preprocessings: the first one consists only in a predictive and spiking deconvolution; the second one includes wave separation and shaping deconvolution based o n direct arrivals. Consistent results are obtained, showing the advantages and drawbacks of both techniques for imaging purposes.

High resolution interval velocity estimation in the depth domain

Summary Under the hypothesis of a locally 1D media and parabolic residual moveout variations with offset, a simple relationship can be established between residual moveout and the focalisation term. The new focalisation term can then be inverted to get a high resolution interval velocity profile. In that way, an interval velocity correction from residual moveout is obtained after depth migration. The method is tested on synthetic and real data. The synthetic data results show that an accurate velocity model is obtained and the common image gathers are correctly flattened. The synthetic results also show that the performance of the method depends basically on the resolution of the residual moveout estimation, which relies on the frequency content of the data and on the maximum offset.

Elastic migration in the angle-azimuth domain: application to a seabed node experiment

Summary While the theory of true amplitude migration in the double angle-azimut domain is well known, its implementation and use in order to obtain accurate depth reflectivity cube versus angle and azimut has not yet been shown. In this paper, we review and to some extent clarify the existing theory, propose practical solutions for implementation in standard Kirchhoff algorithms and demonstrate the validity of the methods using synthetic data. Application to a seabed node type data is also shown.

Low Frequency Propagation of Elastic Waves in a Fluid-Filled Borehole

A tube wave is the lowest order mode propagating in a fluid-filled borehole. It is the only one without a cut-off frequency and is similar to the Stoneley interface wave. It has been studied, for instance by WHITE [1] in the case of a circular cylinder.