No abstract

Crosshole radar tomography is a useful tool in diverse investigations in geology, hydrogeology, and engineering. Conventional tomograms provided by standard ray-based techniques have limited resolution, primarily because only a fraction of the information contained in the radar data ͑i.e., the first-arrival times and maximum first-cycle amplitudes͒ is included in the inversion. To increase the resolution of radar tomograms, we have developed a versatile full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell's equations. This scheme largely accounts for the 3D nature of radar-wave propagation and includes an efficient method for extracting the source wavelet from the radar data. After demonstrating the potential of the new scheme on two realistic synthetic data sets, we apply it to two crosshole field data sets acquired in very different geologic/hydrogeologic environments. These are the first applications of full-waveform tomography to observed crosshole radar data. The resolution of all full-waveform tomograms is shown to be markedly superior to that of the associated ray tomograms. Small subsurface features a fraction of the dominant radar wavelength and boundaries between distinct geological/hydrological units are sharply imaged in the fullwaveform tomograms.

S U M M A R YSonic-log measurements provide detailed 1-D information on the distribution of elastic properties within the upper crystalline crust at scales from about one metre to several kilometres. 10 P-wave sonic logs from six upper-crustal drill sites in Europe and North America have been analysed for their second-order statistics. The penetrated lithological sequences comprise Archean volcanic sequences, Proterozoic mafic layered intrusions, and Precambrian to Phanerozoic gneisses and granites. Despite this variability in geological setting, tectonic history, and petrological composition, there are notable similarities between the various data sets: after removing a large-scale, deterministic component from the observed velocity-depth function, the residual velocity fluctuations of all data sets can be described by autocovariance functions corresponding to bandlimited self-affine stochastic processes with quasi-Gaussian probability density functions. Depending on the maximum spatial wavelength present in the stochastic part of the data, the deterministic trend can be approximated either by a low-order polynomial best fit or by a moving-average of the original sonic-log data. The choice of the trend has a significant impact on the correlation length and on the standard deviation of the residual stochastic component, but does not affect the Hurst number. For trends defined by low-order polynomial best fits, correlation lengths were found to range from 60 to 160m, whereas for trends defined by a moving average the correlation lengths are dominated by the upper cut-off wavenumber of the corresponding filter. Regardless of the trend removed, the autocovariance functions of all data sets are characterised by low Hurst numbers of around 0.1-0.2, or equivalently by power spectra decaying as -l/k. A possible explanation of this statistical uniformity is that sonic-log fluctuations are more sensitive to the physical state, in particular to the distribution of cracks, than to the petrological composition of the probed rocks.

The presence of stiffness contrasts at scales larger than the typical pore sizes but smaller than the predominant seismic wavelengths can produce seismic attenuation and velocity dispersion in fluid‐saturated porous rocks. This energy dissipation mechanism is caused by wave‐induced fluid pressure diffusion among the different components of the probed geological formations. In many cases, heterogeneities have elongated shapes and preferential orientations, which implies that the overall response of the medium is anisotropic. In this work, we propose a numerical upscaling procedure that permits to quantify seismic attenuation and phase velocity considering fluid pressure diffusion effects as well as generic anisotropy at the sample's scale. The methodology is based on a set of three relaxation tests performed on a 2‐D synthetic rock sample representative of the medium of interest. It provides a complex‐valued frequency‐dependent equivalent stiffness matrix through a least squares procedure. We also derive an approach for computing various poroelastic fields associated with the considered sample in response to the propagation of a seismic wave with arbitrary incidence angle. Using this approach, we provide an energy‐based estimation of seismic attenuation. A comprehensive numerical analysis indicates that the methodology is suitable for handling complex media and different levels of overall anisotropy. Comparisons with the energy‐based estimations demonstrate that the dynamic‐equivalent viscoelastic medium assumption made by the numerical upscaling procedure is reasonable even in the presence of high levels of overall anisotropy. This work also highlights the usefulness of poroelastic fields for the physical interpretation of seismic wave phenomena in strongly heterogeneous and complex media.