Upper-crustal seismic velocity heterogeneity as derived from a variety of P-wave sonic logs

Sonic-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 band-limited 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 160 m, 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 ∽ 1/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 rock

Seismic scattering in the upper crystalline crust based on evidence from sonic logs

Evidence from sonic logs indicates that velocity fluctuations in the upper crystalline crust are remarkably uniform. This motivates a generic approach to classifying upper-crustal seismic heterogeneity and to studying implications for seismic wave propagation. The resulting canonical model of upper-crustal seismic structure is characterized by a spatially isotropic von Kármán autocovariance function with a 100 m, ν ≈ 0.15, and σ ≈ 300 m s−1. Small-angle scattering theory is used to predict the transition from weak to strong scattering as well as phase fluctuations and scattering attenuation. Compared with ‘exponential' random media (ν = 0.50), the high fractal dimension (i.e. small values of ν) of upper-crustal heterogeneity causes smaller phase fluctuations, and transition from weak to strong scattering at lower frequencies and shorter path lengths. Acoustic finite-difference modelling shows that seismic reflections from deterministic features surrounded by heterogeneities are severely degraded when they fall into the strong scattering regime. Conversely, traveltime fluctuations of transmitted waves are found to be relatively insensitive to the transition from weak to strong scattering. Upper-crustal scattering Q is predicted to lie between 600 and 1500, which is one to two orders of magnitude higher than Q-values inferred from seismic data. This suggests that seismic attenuation in the upper crystalline crust is dominated by anelastic effects rather than by scatterin

A pseudospectral method for the simulation of 3-D ultrasonic and seismic waves in heterogeneous poroelastic borehole environments

We present a novel approach for the comprehensive, flexible and accurate simulation of poroelastic wave propagation in 3-D cylindrical coordinates. An important application of this method is the realistic modelling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, as of yet largely unresolved, problem in exploration geophysics. To this end, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the centre followed by the mudcake and/or casing, and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction and Fourier expansions in the vertical and azimuthal directions as well as a Runge–Kutta integration scheme for the time evolution. Trigonometric interpolation and a domain decomposition method based on the method of characteristics are used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces as well as to reduce the number of gridpoints in the innermost domain for computational efficiency. We apply this novel modelling approach to the particularly challenging scenario of near-surface borehole environments. To this end, we compare 3-D heterogeneous and corresponding rotationally invariant simulations, assess the sensitivity of Stoneley waves to formation permeability in the presence of a casing and evaluate the effects of an excavation damage zone behind a casing on sonic log recordings. Our results indicate that only first arrival times of fast modes are reasonably well described by rotationally invariant approximations of 3-D heterogenous media. We also find that Stoneley waves are indeed remarkably sensitive to the average permeability behind a perforated PVC casing, and that the presence of an excavation damage zone behind a casing tends to dominate the overall signature of recorded seismograms

Bayesian Markov-chain-Monte-Carlo inversion of time-lapse cross hole ground-penetrating radar data to characterize the vadose zone at the Arrenaes field site, Denmark

The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR traveltime data can allow for a significant reduction in uncertainty regarding subsurface van Genuchten-Mualem (VGM) parameters. Much of the previous work on the stochastic estimation of VGM parameters from crosshole GPR data has considered the case of steady-state infiltration conditions, which represent only a small fraction of practically relevant scenarios. We explored in detail the dynamic infiltration case, specifically examining to what extent time-lapse crosshole GPR traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify VGM parameters and their uncertainties in a layered medium, as well as the corresponding soil hydraulic properties. We used a Bayesian Markov-chain-Monte-Carlo inversion approach. We first explored the advantages and limitations of this approach with regard to a realistic synthetic example before applying it to field measurements. In our analysis, we also considered different degrees of prior information. Our findings indicate that the stochastic inversion of the time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics

Detection and characterization of hydraulically active fractures in a carbonate aquifer: results from self-potential, temperature and fluid electrical conductivity logging in the Combioula hydrothermal system in the southwestern Swiss Alps

A geophysical and geochemical study has been conducted in a fractured carbonate aquifer located at Combioula in the southwestern Swiss Alps with the objective to detect and characterize hydraulically active fractures along a 260-m-deep borehole. Hydrochemical analyses, borehole diameter, temperature and fluid electrical conductivity logging data were integrated in order to relate electrokinetic self-potential signals to groundwater flow inside the fracture network. The results show a generally good, albeit locally variable correlation of variations of the self-potential signals with variations in temperature, fluid electrical conductivity and borehole diameter. Together with the hydrochemical evidence, which was found to be critical for the interpretation of the self-potential data, these measurements not only made it possible to detect the hydraulically active fractures but also to characterize them as zones of fluid gain or fluid loss. The results complement the available information from the corresponding litholog and illustrate the potential of electrokinetic self-potential signals in conjunction with temperature, fluid electrical conductivity and hydrochemical analyses for the characterization of fractured aquifers, and thus may offer a perspective for an effective quantitative characterization of this increasingly important class of aquifers and geothermal reservoir

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered

Regional-scale integration of multi-scale hydrological and geophysical data using a two-step Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale for the purpose of improving predictions of groundwater flow and solute transport. However, extending corresponding approaches to the regional scale still represents one of the major challenges in the domain of hydrogeophysics. To address this problem, we have developed a regional-scale data integration methodology based on a two-step Bayesian sequential simulation approach. Our objective is to generate high-resolution stochastic realizations of the regional-scale hydraulic conductivity field in the common case where there exist spatially exhaustive but poorly resolved measurements of a related geophysical parameter, as well as highly resolved but spatially sparse collocated measurements of this geophysical parameter and the hydraulic conductivity. To integrate this multi-scale, multi-parameter database, we first link the low- and high-resolution geophysical data via a stochastic downscaling procedure. This is followed by relating the downscaled geophysical data to the high-resolution hydraulic conductivity distribution. After outlining the general methodology of the approach, we demonstrate its application to a realistic synthetic example where we consider as data high-resolution measurements of the hydraulic and electrical conductivities at a small number of borehole locations, as well as spatially exhaustive, low-resolution estimates of the electrical conductivity obtained from surface-based electrical resistivity tomography. The different stochastic realizations of the hydraulic conductivity field obtained using our procedure are validated by comparing their solute transport behaviour with that of the underlying ?true? hydraulic conductivity field. We find that, even in the presence of strong subsurface heterogeneity, our proposed procedure allows for the generation of faithful representations of the regional-scale hydraulic conductivity structure and reliable predictions of solute transport over long, regional-scale distances