Frequency‐domain methods are well suited to the imaging of wide‐aperture cross‐hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source‐receiver geometries, are overcome by applying inverse techniques that operate in the frequency‐space domain. In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency‐domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite‐difference equations to be factored in‐place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions. Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non‐linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non‐linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time‐lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.

A series of experiments to determine the elastic properties of a sequence of saturated sedimentary rocks over as wide a frequency range as possible was carried out at the Imperial College borehole test site. These experiments fall into four categories: vertical seismic profiles (VSPs) within the frequency range 30–280 Hz, crosshole surveys (0.2–2.3 kHz), sonic logging (8–24 kHz), and laboratory measurements (300–900 kHz). The intrinsic attenuation and velocity of compressional and shear waves were measured whenever possible. Velocity dispersion is observed for both compressional and shear waves. The intrinsic attenuation of compressional waves is frequency dependent with a peak in the attenuation in the sonic frequency band. The data were modeled assuming the attenuation is caused by local fluid flow in pores of small aspect ratio. The modeling indicates that the intrinsic attenuation may be dominated by cracks with aspect ratios of around [Formula: see text] to [Formula: see text].

Several factors limit the resolution obtained in ray tomography. Of these the least thoroughly discussed in the geophysical literature is the effect of the ray approximation itself; scattering is ignored and the information contained in a seismic trace is reduced to one traveltime pick. Frequency domain comparisons of ray tomography with diffraction tomography have suggested that the minimum feature size resolvable by ray tomography is of the order of the width of the first Fresnel zone. We investigate resolution in the spacetime domain with a numerical experiment. Four synthetic data sets were generated with a finite‐difference program corresponding to crosshole tomographic surveys at two hole separations and two frequencies. The scale of resolution achieved in tomograms derived from these is then assessed by calculating their semblance to filtered versions of the original model and reconstructions from data sets obtained by tracing rays through the original models. The results broadly confirm the relation of resolution to Fresnel zones. It is therefore possible that such limits on resolution may be at least as significant as those due to other factors such as experimental geometry.

A B S T R A C TLaboratory estimates of the normal (B n ) and shear (B t ) compliance of artificial fractures in samples of Jurassic and Carboniferous limestone under wet and dry conditions are presented. The experiments were performed over a range of confining pressures (from 5 MPa up to 60 MPa), at ultrasonic frequencies in a Triaxial Hoek cell, using the pulse-echo reflection technique. The results of this study confirm that the B n /B t ratio of a fracture is dependent on the fluid fill. A value of B n / B t of less than 0.05 was obtained for our wet (honey saturated) sample which is consistent with the prediction that this ratio should be close to zero for fluid saturated fractures. Values of B n /B t for the dry sample are significantly higher and increase with confining pressure from 0.2 to 0.5. It is suggested that a Bn/Bt ratio of 0.5 is probably a more representative value to use in modelling studies of gas filled fractures than the common assumption that Bn ≈ Bt. I N T R O D U C T I O NWe present laboratory estimates of the normal (B n ) and shear (B t ) compliance of artificial fractures in samples of Jurassic and Carboniferous limestone under wet and dry conditions for a range of applied confining pressures. The main aim of the study was to determine the ratio of normal to shear compliance (Bn/Bt). There is increasing interest in the numerical modelling of seismic wave propagation through fractured media in which the fractures cannot be assumed to be small relative to the seismic wavelength. Vlastos et al. (2006) have modelled seismic wave propagation in a fractured network including the effects of changes in pore pressure, which is relevant to the interpretation of time-lapse data. Other recent modelling studies include Willis et al. (2006), Will, Archer and Dershowitz (2005), Daley et al. (2002) and Zhu and Sneider (2002). For models of gas filled fractures, it is usually assumed that Bn = Bt, principally based on theoretical arguments since experimental data are very sparse.Liu, Hudson and Pointer (2000) have shown that if a dry (gas filled) fracture is modelled as a planar distribution of small *

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