In situ measurements of petrophysical properties of the upper crust from wire‐line logs provide a direct means of assessing fluctuations in these properties with depth, and thus allow for the statistical characterization of crustal heterogeneity. Wire‐line logs from a cluster of nine boreholes (1000–1500 m deep) have been analysed using four different techniques: autocorrelation, semi‐variogram, rescaled range and power spectra. Six of the boreholes are vertical, the remainder inclined. All penetrate clastic and pyroclastic rock. The analysis techniques have been tested on synthetic data, for which we have precise control on the scaling, in order to assess their robustness. The results, for the borehole data, show broad‐band fractal scaling with a fractal dimension of 1.62 to 1.97 (autocorrelation), 1.59 to 1.79 (rescaled range) and 1.61 to 2.0 (power spectra). The use of different techniques to estimate the fractal dimension provides an excellent constraint on the results. Furthermore, it allows us to determine which model for crustal heterogeneity best describes the data: a ‘band‐limited’ von Kármán function or ‘unbounded’ fractal scaling. In order to test the possible anisotropy in the scaling parameters, the horizontal scaling properties for this area have been calculated by correlation‐spectra analysis of neighbouring wells. This suggests that upper‐crustal correlation lengths are of the order of kilometres and anisotropic, being over four times greater in the horizontal direction. The origins of the observed power‐law scaling are complex. Analysis of long‐term correlations between logs and televiewer data points towards the influence of fracture porosity within the pyroclastics. But a fractal distribution of pore spaces within the clastics also controls the log fluctuations. Separating the logs into clastic and pyroclastic subsets reveals slight differences in fractal scaling, as determined by autocorrelation and semi‐variogram. These differences are attributed to the dominance of either primary or fracture porosity within each geological unit.

Abstract.Well-logging provides a direct means of assessing fluctuations in petrophysical properties with depth, and thus allows for the statistical characterisation of crustal heterogeneity. Using records from three

The measured geophysical response of sand–shale sequences is an average over multiple layers when the tool resolution (seismic or well log) is coarser than the scale of sand–shale mixing. Shale can be found within sand–shale sequences as laminations, dispersed in sand pores, as well as load bearing clasts. We present a rock physics framework to model seismic/sonic properties of sub‐resolution interbedded shaly sands using the so‐called solid and mineral substitution models. This modelling approach stays consistent with the conceptual model of the Thomas–Stieber approach for estimating volumetric properties of shaly sands; thus, this work connects established well log data‐based petrophysical workflows with quantitative interpretation of seismic data for modelling hydrocarbon signature in sand–shale sequences. We present applications of the new model to infer thickness of sand–shale lamination (i.e., net to gross) and other volumetric properties using seismic data. Another application of the new approach is fluid substitution in sub‐resolution interbedded sand–shale sequences that operate directly at the measurement scale without the need to downscale; such a procedure has many practical advantages over the approach of “first‐downscale‐and‐then‐upscale” as it is not very sensitive to errors in estimated sand fraction and end member sand/shale properties and remains stable at small sand/shale fractions.

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We have developed a new technique of mineral substitution that accurately predicts the change in rock stiffness upon changes in the elastic properties of the rock mineral frame, assuming no changes in the microstructure or mineral volume fraction. The method is rigorous, the results are realizable, and the predictions are always within bounds. We have applied mineral substitution to separate the effects of composition (mineralogy and pore fill) on the rock stiffness from the effects of microstructure, i.e., porosity and pore shape. Application of mineral substitution on laboratory measured data sets of effective moduli (sandstones, limestones, and dolomites) revealed that if the original minerals making up the frame of sandstones (predominantly quartz) were replaced (or substituted) with calcite mineral properties, the newly predicted P- ([Formula: see text]) and S-wave velocity ([Formula: see text]) trends for the modified sandstones were very similar to the previously observed quadratic [Formula: see text]-[Formula: see text] empirical trends for limestones. Similarly, the [Formula: see text]-[Formula: see text] trends for modified limestones, with original minerals replaced by quartz mineral properties, were very similar to the observed linear [Formula: see text]-[Formula: see text] empirical trends for sandstones. The remaining minor differences between the modified and previously observed [Formula: see text]-[Formula: see text] trends might be attributed to the differences in rock microstructure. These findings are striking and suggest that [Formula: see text]-[Formula: see text] trends of natural rocks are dominated by mineralogy and the effects of microstructure are minor. We also found new [Formula: see text]-[Formula: see text] trends for rocks composed of various minerals, including zeolite, feldspar, pyrite, alpha-cristobalite, and halite.