Statistics and Data Analysis in Geology

Keywords: Mecanique des sols ; Drainage ; Ecoulement souterrain Reference Record created on 2004-09-07, modified on 2016-08-08

Applications of soil physics.

A solution is presented for the change in water level in a well of finite diameter after a known volume of water is suddenly injected or withdrawn. A set of type curves computed from this solution permits a determination of the transmissibility of the aquifer.

Response of a finite-diameter well to an instantaneous charge of water. Paper No. H-21

An overview of permeable reactive barriers for in situ sustainable groundwater remediation.

SUMMARY

The surface conductivity of porous rocks has two contributions: the first is associated with the diffuse layer coating the grains and is frequency-independent as long as the diffuse layer is above a percolation threshold. The second contribution is associated with the Stern layer of weakly sorbed counterions on the mineral surface and is frequency-dependent if the Stern layer is discontinuous at the scale of the representative elementary volume. In the frequency range 1 mHz–100 Hz, this second contribution is also associated with the main polarization mechanism observed by the spectral induced polarization method in granular media (neglecting the contribution of other polarization processes like those associated with redox processes and membrane polarization). At the macroscale, we connect the Stern layer contribution to the complex conductivity and to the expectation of the probability distribution of the inverse of the grain size. This is done by performing a convolution between the probability distribution of the inverse of the grain size and the surface conductivity response obtained when all the grains have the same size. Surface conductivity at the macroscopic scale is also connected to an effective pore size used to characterize permeability. From these relationships, a new equation is derived connecting this effective pore size, the electrical formation factor, and the expected value of the probability distribution for the inverse of the grain size, which is in turn related to the distribution of the relaxation times. These new relationships are consistent with various formula derived in the literature in the limit where the grain size distribution is given by the delta function or a log normal distribution and agree fairly well with various experimental data showing also some limitations of the induced polarization method to infer permeability. One of these limitations is the difficulty to detect the relaxation, in the phase, associated with the smaller grains, as this polarization may be hidden by the Maxwell–Wagner polarization at relatively high frequencies (>100 Hz). Also, cemented aggregates of grains can behave as coarser grains.

https://hal-insu.archives-ouvertes.fr/insu-00565026/document

Determination of permeability from spectral induced polarization in granular media

In the framework of various studies to characterize the aquifer at the groundwater experimental field near Montalto Uffugo, Italy, the present work estimates the spatial distribution of hydraulic conductivity of the unconsolidated deposits that underlie the area, by applying the geostatistical technique of kriging with external drift to electrical-resistivity and hydraulic-conductivity data.

Application of kriging with external drift to estimate hydraulic conductivity from electrical-resistivity data in unconsolidated deposits near Montalto Uffugo, Italy

Experimental hydraulic heads and electrical (self-potential) signals associated with a pumping test were used in an inverse model to estimate the transmissivity distribution of a real aquifer Several works reported in the literature show that there is a relatively good linear relationship between the hydraulic heads in the aquifer and electrical signals measured at the ground surface In this experimental test field, first, the current coupling coefficient was determined by the best fit between experimental and modeled self-potential signals at the end of the pumping phase Soon afterward, with the hydraulic heads obtained from the self-potential signals, the transmissivity distribution of the aquifer was conditioned by means an inverse model based on the successive linear estimator (SLE) To further substantiate the estimated T field from the SLE analysis, we analyzed the drawdown rate, the derivative of the drawdown with respect to the ln(t), because the drawdown rate is highly sensitive to the variability in the transmissivity field In our opinion, these results show that self-potential signals allow the monitoring of subsurface flow in the course of pumping experiments, and that electrical potentials serve as a good complement to piezometric observations to condition and characterize the transmissivity distribution of an aquifer

An inverse procedure to estimate transmissivity from heads and SP signals.

Usage of infinitesimals in the Menger’s Sponge model of porosity

We analyzed the behavior of convergent flow tracer tests performed in a 3-D heterogeneous sandbox in presence of connected gravel channels under laboratory-controlled conditions. We focused on the evaluation of connectivity metrics based on characteristic times calculated from experimental breakthrough curves (BTCs), and the selection of upscaling model parameters related to connectivity. A conservative compound was injected from several piezometers in the box, and depth-integrated BTCs were measured at the central pumping well. Results show that transport was largely affected by the presence of gravel channels, which generate anomalous transport behavior such as BTC tailing and double peaks. Connectivity indicators based on BTC peak times provided better information about the presence of connected gravel channels in the box. One of these indicators, β, was defined as the relative temporal separation of the BTCs peaks from the BTCs centers of mass. The mathematical equivalence between β and the capacity coefficient adopted in mass transfer-based formulations suggests how connectivity metrics could be directly embedded in mass transfer formulations. This finding is in line with previous theoretical studies and was corroborated by reproducing a few representative experimental BTCs using a 1-D semianalytical bimodal solution embedding a mass transfer term. Model results show a good agreement with experimental BTCs when the capacity coefficient was constrained by measured β. Models that do not embed adequate connectivity metrics or do not adequately reproduce connectivity showed poor matching with observed BTCs.

/pdf/analysis-of-convergent-flow-tracer-tests-in-a-heterogeneous-3v138u9r2c.pdf

Carmine Fallico

Papers

Application of kriging with external drift to estimate hydraulic conductivity from electrical-resistivity data in unconsolidated deposits near Montalto Uffugo, Italy

An inverse procedure to estimate transmissivity from heads and SP signals.

Usage of infinitesimals in the Menger’s Sponge model of porosity

Analysis of convergent flow tracer tests in a heterogeneous sandy box with connected gravel channels

On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales