Antoine Saucier

Influence of multifractal scaling of pore geometry on permeabilities of sedimentary rocks

Scanning electron microscope pictures of thin sections of sedimentary rocks have been digitized, and their pore space geometry analysed using multifractal statistics. It is observed that such analysis can lead to characterization of different sedimentological environments. In particular it is shown that the information dimension D(1) of the multifractal spectrum of the pore space is correlated to air permeability values measured from the corresponding core samples.

Effective permeability of multifractal porous media

We show how the real space renormalization group method can be used to calculate analytically the scaling exponents of the effective absolute permeability in multifractal porous media. The permeability fields considered are deterministic and random multifractals constructed with multiplicative processes. We discuss the implications of the results on the understanding of fluid flow in oil reservoirs.

Textural analysis of disordered materials with multifractals

We propose a systematic method to choose the scaling range for multifractal analysis, and we illustrate this method by examining the texture of paper formation and pore space of sedimentary chalks. To clarify the statistical meaning of a texture characterization based on the moments of a measure (such as multifractal analysis), we examine the connection between these moments and the multipoint correlations of the underlying signal.

Remarks on some properties of geometrical multifractals

In a porous medium the local density often exhibits spatial variations. These variations can be characterized by a multifractal spectrum, as long as suitable scaling characteristics are present. We derive some of the properties of geometrical multifractals, and show with examples how such objects can be constructed.

Application of generalized multifractal analysis for characterization of geological formations

We demonstrate how texture logs computed from multifractal analysis of dipmeter microresistivity signals can be used for characterizing geological formations (lithofacies) in combination with conventional well logs. In particular, we show that the generalized dimension D(1) (entropy dimension) can be considered as a heterogeneity index providing information on the spatial distribution (amounts of clustering) of heterogeneities in geological sediments. In addition, D(1) logs provide complementary information, compared to the conventional GR-log. This is illustrated by comparing core images of two intervals with similar GR responses and differing D(1) responses. Moreover, the method is equally valid if applied to the texture parameter D1(1) computed by generalized multifractal analysis. In this way, we propose a tool for extracting textural information from well logging signals, which provides valuable information suitable for integration with data obtained from conventional well logging tools.

USE OF MULTIFRACTAL ANALYSIS IN THE CHARACTERIZATION OF GEOLOGICAL FORMATIONS

We use multifractal analysis as a tool for the characterization of geological well log signals. The signals investigated come from dipmeter microresistivity log devices. It is suggested that the multifractal spectra computed from these signals could be used to distinguish geological formations and lithofacies containing different types of oil reservoir heterogeneities.

A new patchwork simulation method with control of the local-mean histogram

Abstract We present a new stochastic simulation method that builds two-dimensional images by assembling together square image pieces called blocks. The blocks are taken from a reference image. Our method, called patchwork simulation method (PSM), enforces pattern continuity in the image. Moreover, PSM allows to control the image local-mean histogram. This histogram bin-frequencies can be set to user-defined target values that may differ from the reference image local-mean histogram. This flexibility enhances the PSM generality by enlarging the set of all possible simulations. The local-mean histogram control is achieved by adjusting suitably the transition probabilities that associate a new block to an existing neighborhood in the partly simulated image. For several types of synthetic images and one polymer blend image, we show that PSM reproduces faithfully the reference image visual appearance (i.e. patterns are correctly shaped) and that simulated images are statistically compatible with the target local-mean histogram. Moreover, we show that our method has the ability to produce simulations that respect conditional hard data as well as a target local-mean histogram.

A fast and accurate frequency estimation method for canceling harmonic noise in geophysical records

The cancellation of harmonic noise from geophysical records can be achieved by subtracting an estimate of the harmonic noise. Estimating the harmonic noise consists of estimating the fundamental frequency and the amplitudes and phases of all harmonics. We propose a new frequency-estimation method that builds upon the estimator originally proposed by Nyman and Gaiser. This Nyman and Gaiser estimation (NGE) method exploits the fact that the noise fundamental frequency is known to be close to 60 Hz. The NGE method is based on solving a system of four equations that determine the amplitude, phase, and frequency of a given harmonic in the harmonic noise. Hence, NGE can produce frequency estimates for all harmonics. Our improved estimator uses a suitable linear combination of these NGE frequency estimates to produce a more accurate estimate of the fundamental frequency. Our method is more accurate than NGE, and its accuracy is comparable to least-squares estimation (LSE). The advantage of our method is that it is about two times faster than LSE. This speed gain can become valuable when processing large magnetotelluric (MT) data records. Applying our method to the restoration of MT data, we found that the harmonic noise amplitude in the periodogram is reduced by at least 60 dB to a level below that of MT data.

Getting Information from Modal Decomposition of Grain Size Distribution Curves

Soil samples may be difficult-to-identify mixtures of different layers. For environmental and groundwater projects, a detailed stratigraphy is needed because the coarse layers are highways for both water and dissolved contaminants. The paper proposes a method to decompose a grain size distribution curve (GSDC) into its 1, 2, or 3 log-normal components and their proportions. The proposed method can accurately decompose synthetic mixes of three lognormal modes, except when a mode contributes for less than about 2 %. In such a case, it is suggested to ignore this mode and describe the mix as a two mode mix. An example is given for an experimental site with many split-spoon soil samples. The suspected stratification was confirmed by the decomposition method, which found mixtures of only two soil components, fine sand and clayey silt, each of them with little variability. The large-scale permeability, as provided by a pumping test, corresponds to the horizontally composed permeability of the soil components: thus, it confirms the adequacy of the soil sample decomposition method.

Scaling properties of disordered multifractals

In turbulence, the simplest phenomenological models of the energy cascade are multiplicative processes constructed on a regular grid (in short, M.P.G.). They have been used mostly for their simplicity, allowing many of their properties to be derived analytically, and their capacity to reproduce the scale invariance properties of various geophysical fields. However, these M.P.G.s suffer from the drawback of lacking translation invariance in their spatial statistics (spatial homogeneity), and therefore they cannot be fully satisfactory models for geophysical fields. In this paper, we are interested in finding new construction methods for spatially homogeneous random multifractals. We investigate the scaling properties of a new family of gridless models of multifractals.