ALBERT

Notes: Measurements of minority-carrier lifetime have been carried out on slices of n-type CdxHg1−xTe (0.2〈x〈0.3) prepared by both normal Bridgman and accelerated crucible rotation (ACRT) Bridgman techniques. Some of these crystals were deliberately doped with a high level of a single impurity. A study of aging effects has been concluded. Lifetime variations with temperature are explained using a combination of band-to-band and Shockley–Read recombination processes. Frequently, a single level 10–30 meV below the conduction-band edge was assumed, but for ACRT crystals it was necessary to postulate a second level. Attempts to identify the origin of the centers, by measurements on doped crystals, were only successful in the case of iron since it acts as a recombination center without providing conduction electrons in CdxHg1−xTe.

Notes: Modern wide-angle surveys are often multi-fold and multi-channel, with densely sampled source and receiver spacings. Such closely spaced data are potentially amenable to multi-channel techniques involving wavefield propagation methods, such as those commonly used in reflection data processing. However, the wide-angle configuration requires techniques capable of handling very general wave types, including those not commonly used in reflection seismology. This is a situation analogous to that faced in cross-borehole seismics, where similar wave types are also recorded. In a real cross-borehole example, we compare pre-stack migration, traveltime tomography and wavefield inversion. We find that wavefield inversion produces images that are quantitative in velocity (as are the tomograms) but are of significantly higher resolution; the wavefield inversion results have a resolution comparable to that of the (qualitative) pre-stack migration images. We seek to extend this novel development to the larger-scale problem of crustal imaging.An essential element of the approach we adopt is its formulation entirely within the temporal frequency domain. This has three principal advantages: (1) we can choose to ‘decimate’ the data, by selecting only a limited number of frequency components to invert, thus making inversion of data from large numbers of source positions feasible; (2) we can mitigate the notorious non-linearity of the seismic inverse problem by progressing from low-frequency components in the data to high-frequency components; and (3) we can include in the model any arbitrary frequency dependence of inelastic attenuation factors, Q(ω), and indeed solve for the spatial distribution of Q.An initial synthetic test with an anomaly located within the middle crust yields a velocity image with the correct structural features of the anomaly and the correct magnitude of velocity anomaly. This is related to the fact that the reconstruction is obtained from forward-scattered waves. Under these conditions, the method thus behaves much like tomography. A second test with a deeper, more extensive anomaly yields an image with the correct velocity polarity and the correct location, but with a deficiency in low and high wavenumbers. In this case, this is because the reconstruction is obtained from backscattered waves; under these conditions the method behaves not like tomography, but like migration.A more extensive test, based on a large wide-angle survey in south-eastern California and western Arizona, demonstrates a real potential for high-resolution imaging of crustal structures. Although our results are limited by the acoustic approximation and by the relatively low frequencies that we can model today, the images are sufficiently encouraging to warrant future research. The problem of local minima in the objective function is the most significant practical problem with our method, but we propose that appropriate ‘layer’ stripping methods can handle this problem.

Notes: In principle, crosshole, traveltime tomography is ideal for directly detecting and measuring seismic anisotropy. The traveltimes of multiple rays with wide angular coverage will be sensitive both to inhomogeneities and to anisotropy. In practice, the traveltimes will depend only on a limited number of the anisotropic velocity parameters, and the data may not be adequate even to determine these parameters uniquely. In addition, trade-offs may exist between anisotropy and inhomogeneities. In this paper, we use the linear perturbation theory for traveltimes in general, weakly anisotropic media to discuss the dependence of traveltimes in 2-D crosshole tomographic experiments on the anisotropic parameters. In a companion paper, we apply the results to synthetic and real data examples. We show that when measurements are restricted to a 2-D plane, the qP and qS traveltimes depend on subsets of the complete set of 21 anisotropic velocity parameters. Formulae are developed for the differential coefficients of the traveltimes with respect to these parameters in piecewise homogeneous and in linearly interpolated models. It is shown how in a generally oriented model element, the local parameters are related to the same parameters in the global model. The parameters that can be determined from 2-D tomographic data do not in general determine the full nature of the anisotropy. Rather, these parameters serve only to describe the intersection of the slowness sheet with the 2-D plane. Since many models may fit this description, additional information on symmetry properties and orientations is required. For example, if a priori information suggests that the anisotropy is transversely isotropic (TI), then we can determine some of the TI parameters and some information on the orientation of the axis of symmetry. Formulae are given relating the general parameters to those of a TI system with general orientation of the symmetry axis. The general formulae for qS traveltimes are intrinsically more complicated than those for qP. In the qS case, the traveltime perturbation depends on the polarization, which in turn depends on the perturbation. This makes the general problem non-linear even for small perturbations. However, the mean qS traveltime and the traveltime dependence on various subsets of parameters are linear. Although linear perturbation theory is invalid for qS rays, degenerate perturbation theory is valid for the calculation of the traveltimes and could be used in a non-linear inversion scheme.

Notes: Cross-borehole seismic data have traditionally been analysed by inverting the arrival times for velocity structure (traveltime tomography). The presence of anisotropy requires that tomographic methods be generalized to account for anisotropy. This generalization allows geological structure to be correctly imaged and allows the anisotropy to be evaluated. In a companion paper we developed linear systems for 2-D traveltime tomography in anisotropic media. In this paper we analyse the properties of the linear system for quasi-compressional waves and invert both synthetic and real data. Solutions to the linear systems consist of estimates of the spatial distributions of five parameters, each corresponding to a linear combination of a small subset of the 21 elastic, anisotropic velocity parameters. The parameters describe the arrival times in the presence of weak anisotropy with arbitrary symmetries. However, these parameters do not, in general, describe the full nature of the anisotropy. The parameters must be further interpreted using additional information on the symmetry system. In the examples in this paper we assume transverse isotropy (TI) in order to interpret our inversions, but it should be noted that this final interpretation could be reformulated in more general terms.The singular value decomposition of the linear system for traveltime tomography in anisotropic media reveals the (expected) ill-conditioning of these systems. As in isotropic tomography, ill-conditioning arises due to the limited directional coverage that can be achieved when sources and receivers are located in vertical boreholes. In contrast to isotropic tomography, the scalelength of the parametrization controls the nature of the parameter space eigenvectors: with a coarse grid all five parameters are required to model the data; with a fine grid some of the parameters appear only in the null space.The linear systems must be regularized using external, a priori information. An important regularization is the expectation that the elastic properties vary smoothly (an ad hoc recognition of the insensitivity of the arrival times to the fine-grained properties of the medium). The expectation of smoothness is incorporated by using a regularization matrix that penalizes rough solutions using finite difference penalty terms. The roughness penalty sufficiently constrains the solutions to allow the smooth eigenvectors in the null space of the unconstrained problem to contribute to the solutions. Hence, the spatial distribution of all five parameters is recovered. The level of regularization required is difficult to estimate; we advocate the analysis of a suite of solutions. Plots of the solution roughness against the data residuals can be used to find ‘knee points’, but for the fine tuning of the regularization one has little recourse but to examine a suite of images and use geological plausibility as an additional criterion.The application of the regularized numerical scheme to the synthetic data reveals that the roughness penalty should include terms that penalize high gradients addition to penalizing high second derivatives. Only when this constraint was included were the features of the original model recovered. The inversions of the field data yield good images of the expected stratigraphy and confirm previous estimates of the magnitude of the anisotropy and the orientation of the symmetry axis. The solutions further indicate an increase in anisotropy from the top to the bottom of the survey region that was not previously detected.

Notes: Abstract —Seismic amplitude data are used to invert for the geometry of reflection interfaces of multi-layered structures, in which the reflection interface is parameterised by a set of Fourier series with different wavenumbers. Two main difficulties arise in amplitude inversion: a high wavenumber oscillation artificially generated by inversion on shallow interfaces, and a failure to recover the long wavelength components of deep, curved interfaces. To overcome these difficulties, the capabilities of two inversion algorithms, a damped subspace method and a multi-scale scheme are investigated. Based on those two schemes, we develop a multi-stage damped subspace method to abate the instability of high wavenumber components and, simultaneously, to enhance the resolution of the low wavenumber components of the subsurface reflectors from seismic amplitude inversion.