Bilogarithmic Scale Research Articles

Identification of favourable geological formations for the determination of groundwater

Abstract in English Clean drinking water supply is a major concern to the population of the urban municipality of Boké, Republic of Guinea. This study is aimed to investigate the favourable geological structure for the accumulation of groundwater in Boké. Apparent resistivity data was collected by using the Schlumberger-type vertical electrical sounding technique. The apparent resistivity values were obtained on a bi-logarithmic scale in which the distances AB/2 were plotted on the abscissa and the resistivities are on the ordinate. It found the number of terrains and their characteristics (resistivity and thickness) in the area and the behaviour of the current in the soil through a curve. The results show that the structures favourable to the accumulation of groundwater were fractured dolerites, cracked shales and cracked or crushed sandstones. The sandstones were the most important in terms of the amount of water. They are located at a depth of more than 100 metres. It was also found that dolerites and shales are located at shallower depths (less than 100 m).

Imaging Analysis and Digital Restoration of the Holy Face of Manoppello—Part II

In this second work on the Holy Face of Manoppello, known also as the Veil, we have performed a spectral analysis of the transmitted image. Its thin linen threads are translucent, presumably because starched, allowing light to pass through them. As a result, the yellowish colour of the ancient linen and starch contribute substantially to the final hues of the Holy Face, especially when the Veil is lit from the backside with grazing light. Spectrophotometry measurements have allowed calculating how the fabric absorbs the various chromatic components. Through these quantitative evaluations, it has been possible to compensate the colours of the transmitted Holy Face image, by subtracting the contribution due to the yellowish coloration of the thin linen threads. Furthermore, the rotational spectrum of the image has been studied after digital restoration. The linear fit of the power spectrum in bi-logarithmic scale with a power law f P provided a slope parameter P = − 3.49 ± 0.03 . This is a surprising value because it is typical of photographs of human faces, not of portraits of human faces painted by artists, which instead have statistical properties of fractal type, with values of slopes P = − 2.0 .

A novel approach to the quantitative interpretation of petrophysical parameters using nano-CT: example of Paleozoic carbonates

The main goal was the analysis of parameters describing the structure of the pore space of carbonate rocks, based on tomographic images. The results of CT images interpretation, made for 17 samples of Paleozoic carbonate rocks were shown. The qualitative and quantitative analysis of a pore system was performed. Objects were clustered according to the pore size. Within the clusters, the geometry parameters were analysed. The following dependences were obtained for carbonate rocks, also for individual clusters (due to the volume): (1) a linear relationship (on a bilogarithmic scale) between the specific surface and the Feret diameter and (2) a strong linear relationship between specific surface area and Feret diameter and average diameter of the objects calculated for the sphere. The results were then combined with available results from standard laboratory tests, including NMR and MICP.

Seismic Dispersion and Attenuation in Saturated Porous Rock With Aligned Slit Cracks

AbstractWe estimate the seismic attenuation and velocity dispersion induced by fluid pressure diffusion in a saturated porous medium containing a sparse distribution of aligned slit fractures. This is done by solving the scattering problem for a single crack and using Waterman‐Truell scattering approximation for a distribution of cracks. This approach gives a numerical solution for the entire frequency range and analytical solutions for the low‐ and high‐frequency limits. Analysis of the results shows that the characteristics of the seismic dispersion and attenuation for the slit cracks are similar to known results for penny‐shaped crack. At high frequencies, the attenuation and dispersion are controlled by the crack density regardless of the crack geometry. At low frequencies, due to the different geometries of the slit and penny‐shaped cracks, the characteristics of seismic dispersion and attenuation are different. For both the slit and penny‐shaped crack case, the slope of the frequency dependence attenuation of factor (inverse quality factor) Q−1 tends to be 1. Yet the low‐frequency asymptotic solutions for these two cases are somewhat different. For penny‐shaped cracks, the Q−1(ω) on the bilogarithmic scale has a straight line asymptote with slope 1, so that the attenuation factor at low frequencies is proportional to the frequency ω. However, for slit cracks, the asymptotic low‐frequency solution contains a logarithmic function of ω, and no such asymptote exists. At the same time, similarly to the penny‐shaped crack case, the solution for compressional velocity in the low‐frequency limit is consistent with the anisotropic Gassmann theory.

Insight into bubble nucleation at high-pressure drop rate

This paper presents insight in bubble nucleation in polymer foaming with physical blowing agent using a batch foaming technique. In our experiments the bubble nucleation is triggered by a sudden pressure drop that causes the supersaturation in the polymer gas solution. In fact, the pressure drop rate is an important process variable since it plays a role in both bubble nucleation and growth. Herein, we investigated very high pressure drop rates, and confirmed the great importance of the pressure drop rate as foaming process variable. The results show that the number of nucleated bubbles increases of one order of magnitude and the foam density is reduced if the pressure drop rate is increased from 50 to 500 MPa/s. Interestingly, the number of nucleated bubble increases linearly in a bi-logarithmic scale as function of pressure drop rate at all the investigated temperatures. Moreover, in the current paper, it is discussed how talc used as nucleating agent plays a role in cooperation with pressure drop rate on bubble nucleation at different foaming temperatures.

Polystyrene Foaming at High Pressure Drop Rates

We studied the foaming of polystyrene with CO2 as the physical blowing agent at large pressure drop rates (PDRs) and at different foaming temperatures, with a novel batch foaming apparatus, capable of reaching PDRs as high as 500 MPa/s (in the underlying literature, the maximum so far achieved is 100 MPa/s). Results show that, at each foaming temperature, the number of nucleated bubbles per unit initial volume (N) linearly increases with PDR in a bilogarithmic scale, with slopes increasing with the temperature. The effect of talc as the nucleating agent was also investigated. Furthermore, a phenomenological model was developed and utilized to predict N at PDRs not experimentally accessible. The approach was validated and a good agreement with the experimental data was obtained.

A Positioning System Based on Low-Frequency Magnetic Fields

This paper describes the design and the realization of a low-frequency ac magnetic-field-based indoor positioning system (PS). The system operation is based on the principle of inductive coupling between wire loop antennas. Specifically, due to the characteristics of the ac artificially generated magnetic fields, the relation between the induced voltage and the distance is modeled with a linear behavior in a bilogarithmic scale when a configuration with coplanar, thus equally oriented, antennas is used. In this case, the distance between a transmitting antenna and a receiving one is estimated using measurements of the induced voltage in the latter. For a high operational range, the system makes use of resonant antennas tuned at the same nominal resonant frequency. The quality factors act as antenna gain increasing the amplitude of the induced voltage. The low-operating frequency is the key factor for improving robustness against nonline-of-sight (NLOS) conditions and environment influences with respect to other existing solutions. The realized prototype, which is implemented using off-the-shelf components, exhibits an average and maximum positioning error, respectively, lower than 0.3 and 0.9 m in an indoor environment over a large area of 15 m × 12 m in NLOS conditions. Similar performance is obtained in an outdoor environment over an area of 30 m × 14 m. Furthermore, the system does not require any type of synchronization between the nodes and can accommodate an arbitrary number of users without additional infrastructure.

Power Spectral Density Analysis of the Corrosion Potential Fluctuation of Stainless Steel 316L in Early Stages of Exposure to Caribbean Sea Water

Stainless Steel 316 L samples were exposed for one month to Caribbean sea water. The fluctuations of the free corrosion potential values (Ecorr at o.c.p.), considered as electrochemical noise (EN), were correlated with the stainless steel pitting corrosion in sea water. Ecorr fluctuation analysis was carried out using the power spectral density (PSD) vs frequency. Figure 1 presents the initially changes of Ecorr with time vs frequency in bilogarithmic scale. For the first three days, the PSD slopes present a negative β exponent (β > 1) at lower frequencies [0.002 – 0.05 Hz], indicating a release of spontaneous energy from the steel surface (corrosion). However, at major frequencies β tends to values close to zero (0.12 – 0.07). At later stages the PSD slopes show a unique value close to zero (0.02 – 0.06), in all range of frequencies [0.002 – 1 Hz]. The exponent β is associated with persistent processes (forces) in data series (216) over time. The calculated Hurst coefficient based on β values suggested that initially the localized corrosion process occurs with the contribution of fractional Brownian motion (fBm) and fractional Gaussian noise (fGn). After the first three days, the Ecorr fluctuations were only dominated by fGn (H≈0.5), which corresponds to the special case when the corrosion occurs at the border between anti-persistent (H<0.5) and persistent (H>0.5) processes. The Ecorr fluctuations were correlated with the data surfaces provided by SEM-EDS and XRD. Figure 1

High-cycle fatigue simulation for aluminium alloy using cohesive zone law

This article describes high-cycle fatigue simulation for 7050-T7451 aluminium alloy using cohesive zone law. A three-dimensional finite element model is developed for fatigue behaviour of aluminium alloy subjected to cyclic bending. A bilinear, cycle-dependent cohesive zone law is implemented with a help of experimental S-N (stress amplitude–number of cycles to failure) data. In the finite element model, a cycle jump strategy is used including stiffness degradation and reduction of fracture energy during cyclic loadings. Additionally, bending experiments are conducted with unnotched specimens and S-N curves are determined. Direct comparison of S-N curves between the simulation and the experiment is performed on bilogarithmic scale. Results show that the proposed method provides a good means of simulating high-cycle fatigue behaviour of aluminium alloys.

Peak particle velocity for rockbursts in underground coal mines and for shot-hole explosions in open-pit mines

The paper presents some results of in-situ seismological observations in hard-coal mines in the Ostrava-Karvina Coal Basin (OKCB) (Czech Republic) and in open-pit brown-coal and shale mines in Northwest and Central Bohemia, respectively. Trial measurements were aimed at investigating the peak particle velocity (PPV), which usually enables some criteria for the limitations of damage extent to be derived, e.g. of surface residential buildings, workings underground, failure and/or wall sliding. While rockbursts in hard-coal mines represent the source of recorded seismic waves, as opposed to that, shot-hole explosions for generating seismic waves in open-pit mines were used. Based on the regression analysis of the results of PPV experimental measurements vs. the square-root scaling factor for rockbursts and cube square factor for hole-shot explosion were applied, the slopes b of straight lines on the bilogarithmic scale were derived, i.e. b = −0.962 and b = −1.894, −1.843 and −2.256, respectively. On the other hand, PPV observed in the region of OKCB displayed values about 1–2 mm/s, while PPV at the sites in open-pit mines reached values roughly of 1–2 m/s due to a significantly smaller hypocentral distance, i.e. seismic source-velocity sensor distance.

Some parameters of rockbursts derived from underground seismological measurements

A total of 240 three-component recordings from 80 rockbursts, which occurred in various coal mines in the Ostrava-Karviná Coal Basin (Czech Republic) between 1993 and 2005, was used to examine the decrease in maximum particle velocities u i (m/s) with a scaled distance of d ⁎ = d/√E (m/√J) or d/ 3√E (m/ 3√J) and the rate of predominant frequencies of body waves. The energetic span of rockbursts was within the interval of E = 6.2 × 10 3 − 5.0 × 10 8 J, while calculated hypocentral distances d of four underground seismic stations varied from 0.6 to 7 km. The slopes b of regression straight lines for the maximum particle velocities u i (m/s) of P- and S-waves in the bilogarithmic scale correspond to the values of − 1.004, − 1.297, − 1.183 and − 1.527. The results of the linear regression are as follows: P max-waves u i = 1.184 × 10 − 4 × d ⁎ − 1.004 (m/s) (square root scaling) P max-waves u i = 3.055 × 10 − 3 × d ⁎ − 1.297 (m/s) (cube root scaling) S max-waves u i = 5.280 × 10 − 4 × d ⁎ − 1.183 (m/s) (square root scaling) S max-waves u i = 2.397 × 10 − 2 × d ⁎ − 1.527 (m/s) (cube root scaling). The evaluation of the abovementioned dynamic parameters was based on seismic events data gathered in the database of the regional seismic array, and calculations were carried out either by using special programs applied as part of the automated data processing in the computation center, or by usual linear regression approaches. The aim of the detailed analysis of the maximum particle velocity and predominant frequencies was a) to set up input data from underground seismological observations for laboratory experiments dealing with the comparison of rock mass behaviour under modeled laboratory conditions simulating manifestation of rockbursts, and b) to incorporate particle velocity into the design of support in order to control damage and evident devastation of workings by rockbursts. The investigation of peak particle velocities was based on the recognition that they are the best criterion to assess vibration damage to surface structures and in mines.

Partitioning of organic compounds in phases imitating the headgroup and core regions of phospholipid bilayers.

Solvation free energies of drugs, peptides, and other small molecules in the core and headgroup regions of phospholipid bilayers determine their conformations, accumulation, and transport properties. The transfer free energy includes the energy terms for the formation of a cavity for the solute, the interactions of the solute with phospholipids, electrostatic interactions of the solute with the membrane, and dipole potentials and entropy terms. The interaction energies with phospholipids can be estimated by correlating the partitioning in surrogate solvent systems and in the bilayer. As the headgroup surrogate, we use diacetylphosphatidylcholine (DAcPC), the acetylated headgroup of the most abundant mammalian phospholipid, phosphatidylcholine, which forms a homogeneous solution with acceptable viscosity when mixed with water in ratios similar to those in the fully hydrated bilayer. The two-phase system of n-hexadecane (C16) as the core surrogate and hydrated DAcPC was used to monitor partitioning of 16 nonionizable compounds. On the bilogarithmic scale, the C16/DAcPC partition coefficients correlate neither with those in the C16/water and 1-octanol/water systems nor with their difference, which is frequently used as a parameter of hydrogen bonding for prediction of the bilayer location of the solutes. The C16/DAcPC system provides a satisfactory emulation of the solvation properties of the bilayer regions, as reflected in correct predictions of the bilayer location for those of the studied chemicals, for which this information is available.

Novel method to quantify loss of heart rate variability in pediatric multiple organ failure.

To develop a power-law model for measurement of heart rate variability (HRV) and to compare this model with established methods for measuring HRV in a group of children with organ failure (OF). Prospective, observational study. Pediatric intensive care unit of a tertiary children's hospital. A total of 104 measurements were made on 50 patients (median age, 8 months; range, 2 days to 16 yrs) and categorized into three groups according to the number of simultaneous organs failing: 0-1 OF, 2 OF, and >/=3 OF. Heart rate was recorded over a 5-min period when patients were hemodynamically stable. The power-law model represents a power function relating frequency distribution to magnitude of effect (in this case, squared deviation from the mean heart rate). Plotting the data on a bi-logarithmic scale produces a regression line for each measurement, described in terms of r2, slope, and x-intercept. Comparison with other HRV measures included two time-domain measures (sd of the normal R-R intervals and the square root of the mean squared differences of successive normal R-R intervals), one frequency-domain method (power spectral analysis), and one nonlinear method (detrended fluctuation analysis). For the power-law model, patients exhibited a similar r2 of.87 (.09) (mean [sd]) and slope of -1.80 (0.29), regardless of the degree of OF. HRV could thus be described purely in terms of x-intercept, which demonstrated a left shift with increasing OF (p <.001). This was independent of age and heart rate. Loss of HRV with increasing OF was demonstrated by all methods; however, only the power-law model was able to discriminate between each OF group. Using the model, change in HRV in individual patients over successive days often concurred qualitatively with the change in OF status. The power-law model is an appropriate measure of HRV in pediatric patients, being neither age nor heart rate sensitive. Loss of HRV occurs with increasing OF; this effect was better demonstrated by the model compared with other measures of HRV.

Electrocardiography, heart rates, and heart weights of free-living birds.

To examine the waveforms of electrocardiograms, cardiac rhythm, heart rates at rest and during excitement, and the rate of increase of heart rate, electrocardiograms were recorded with standard bipolar limb leads from 79 free-living birds, including 19 species. The heart weights and heart-to-body weight ratios were obtained from an additional 96 free-living birds, including 20 species. In the majority of the electrocardiograms, lead I was of low amplitudes for all waves except the P wave, and leads II and II were very similar to each other with a predominant S wave and a very short or elevated ST segment. The P wave was often superimposed on the T wave when the heart rate increased to 330 beats/min. Four types of arrhythmia were observed in 50 of the 79 birds (63.3%): 48 sinus arrhythmias, four sinus arrests, two atrial premature contractions, and one ventricular premature contraction. The resting heart rate was negatively associated with the rate of increase, suggesting that a bird with a low resting rate might be able to maintain a greater capacity to increase its heart rate than one with a high resting rate. A negative correlation on a bilogarithmic scale was obtained between the heart weight and the resting heart rate, indicating that a bird with a high heart weight had lower resting heart rate than a bird with a low heart weight. When the heart-to-body weight ratios of free-living birds were compared according to their motility, the ratios of more active birds were greater than those of less active ones.

Electron Transfer through a Modified Electrode with a Fractal Structure: Cyclic Voltammetry and Chronoamperometry Responses

The problem of charge transfer by electron hopping through a volumic-modified electrode with a fractal structure was addressed, both in the case of chronoamperometry and linear sweep voltammetry. A behavior intermediate between that seen in classical diffusion and that of a thin layer was found. The currents in chronoamperometry and the peak currents in cyclic voltammetry both depend linearly on a bilogarithmic scale with, respectively, the time and the scan rate. The slopes of the curves in both cases depend on the fractal dimension, provided the spectral dimension remains constant. Plots are given in the case where the spectral dimension is equal to 4/3.

RAMET DYNAMICS FOR THE CLONAL SEAWEED PTEROCLADIELLA CAPILLACEA (RHODOPHYTA): A COMPARISON WITH CHONDRUS CRISPUS AND WITH MAZZAELLA CORNUCOPIAE (GIGARTINALES)

Little is known about the dynamics and the ecological interactions among ramets (fronds) from populations of clonal red seaweeds. Small ramets are very difficult to tag, so their growth cannot be monitored directly. The temporal variation of the relationship between stand biomass and ramet density offers information on ramet performance. We calculated this relationship for an intertidal population of Pterocladiella capillacea (Gmelin) Santelices et Hommersand (Gelidiales) from Baja California, Mexico. Biomass and density were positively correlated on an annual basis, indicating that biomass accumulated without involving self‐thinning among ramets. This contrasts with nonclonal seaweeds, for which self‐thinning among individuals occurs during growth, but agrees with other clonal red seaweeds, such as Chondrus crispus Stackhouse and Mazzaella cornucopiae (Postels et Ruprecht) Hommersand (both Gigartinales). The growth pattern for these members of the Gelidiales and of the Gigartinales holds despite differences in holdfast morphology and ramet branching degree and despite differences in the capacity of coalescence during early stages, known only for the Gigartinales. The positive slope for the dynamic biomass–density relationship, on a bilogarithmic scale, was statistically steeper for M. cornucopiae than for P. capillacea and for C. crispus. This suggests that the addition of new ramets during the growth season may be relatively more beneficial for biomass accumulation rates for M. cornucopiae. This would be expected for high‐intertidal species subjected to strong abiotic stress, for which ramet crowding constitutes a key protection. Pterocladiella capillacea occurs at the mid‐intertidal zone and C. crispus at the subtidal zone, so ramets would be relatively less important in that respect.

Geoelectric characterization of the hydraulic conductivity field and its spatial structure at variable scales

This paper describes how to begin with extensive geoelectric measurements of an aquifer along with a few hydraulic measurements and end with an estimate of the aquifer's hydraulic conductivity field and spectrum at variable scales. It is based on a preponderance of theoretical and empirical evidence indicating that electrical and hydraulic (eh) conductivities of aquifers are linearly correlated on a bilogarithmic scale. The steps required for a geoelectric characterization are scaling up, calibration, and spectrum estimation. Scaling up estimates electrical conductivity at variable scales from the apparent resistivity measurement. Calibration equilibrates coincident, equal‐scale eh conductivities using the theoretical eh conductivity correlation. Combined, scaling up and calibration provide a variable‐scale expression for the hydraulic conductivity field in terms of a geoelectric measurement. From this expression the hydraulic conductivity field spectrum is calculated. These steps are applied to borehole data collected at the Department of Energy Central Nevada Testing Area and the U.S. Geological Survey Cape Cod site. In each case a statistically significant eh conductivity correlation is observed. The paper ends by conjecturing that a horizontal exploitation of the eh conductivity correlation offers for the first time an inexpensive means of characterizing the hydraulic conductivity field at a high resolution and over a large area.

Implications of the sampling procedure used to estimate mean plant biomass for the analysis of plant self-thinning

In even-aged, crowded plant populations that are actively growing, intraspecific competition determines at some time that plant density decreases as total biomass increases, if interspecific competition and density-independent stresses do not occur. In a bilogarithmic scale, the temporal variation of the relationship between total stand biomass (expressed per unit area) and plant density during this stage is described by a straight line with negative slope, called the line'' (Weller 1987). For the study of self-thinning, two different questions may be of interest, although they are closely related to one another: (i) is self-thinning associated with an increase in total biomass for a given stand?, and (ii) do surviving plants grow in biomass during self thinning? To answer the first question, the temporal relationship between total stand biomass and plant density during selfthinning may be plotted. In a bilogarithmic scale, the straight lines obtained by regression for different stands of the same or different species growing under different conditions are used to compare their growth dynamics (Weller 1987). To answer the second question, one might simply note from the above analysis that surviving plants do grow in biomass as density decreases, because mean plant biomass is equal to total biomass (which increases) divided by number of plants (which decreases) for a given stand. A different way to answer this question might be to plot the temporal relationship between mean plant biomass and plant density in a bilogarithmic scale (Yoda et al. 1963 and other papers cited in Weller 1987) and test for the significance of the correlation between both variables. Then, regression lines might be hypothetically used to compare growth rates of plants during self-thinning among different stands, but the utility of this method is affected by some considerations that will be outlined below. Recently, it was stated (Petraitis 1995a) that the choice of either mean or total plant biomass for correlation studies against plant density depends solely on the research question and, thus, is not affected by other factors. I believe that such a conclusion is potentially misleading towards a correct utili-

The uses and abuses of the Archie equations, 1: The formation factor-porosity relationship

Model studies of the first Archie equation, which relates the formation resistivity factor and porosity specifically for effectively clean (shale-free) porous media, have quantified the changes to this relationship caused by latent shale effects. The scales of these departures correspond to the ranges reported by experimental investigators on the basis of empirical studies of supposedly clean formations, for which some of the experimental data would actually be physically untenable. Thus, many of the published versions of this equation do not, as is claimed, definitively relate porosity to an intrinsic formation factor but merely to an apparent formation factor, which shows an incidental relationship to porosity that is salinity-dependent and can even become inverted. The primary implication of departures from clean conditions, illustrated using field data from reservoirs with varying degrees of shaliness, is that the relationship between (apparent) formation factor and porosity can remain well defined even though the numerical form changes significantly with variations in salinity. The inadvertent use of such an arbitrary relationship to estimate formation factor from porosity can transmit errors of over 30 saturation units to be subsequent determination of water (and thence hydrocarbon) saturation. On this basis, the “standard” practice of determining the form of the first Archie equation from measurements of “formation factor” that use simulated formation water must be viewed with extreme caution. There is no guarantee that a well-defined linear trend on a bilogarithmic scale actually reflects effectively clean conditions. This is contrary to conventional thinking, which predicts a curvilinear trend where shale effects are manifest. Apart from the demonstrable effect on the determination of hydrocarbon saturation, these observations also have a direct bearing on the concept of reservoir zonation and on evaluation approaches that use the Archie exponent as an indicator of lithology, pore geometry, degree of induration, or permeability.

A MODIFIED GEOELECTRICAL PROCEDURE USING POLARDIPOLE ARRAYS—AN EXAMPLE OF APPLICATION TO DEEP EXPLORATION *

AbstractDipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar‐dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field.A special measurement technique is required since the dipole‐dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.