Vertical Inhomogeneity Research Articles

Hybrid Method for Love Wave Dispersion in Vertically Inhomogeneous Media

—Love wave dispersion in a vertically inhomogeneous multilayered medium is studied by a combination of analytical and numerical methods for arbitrary variation of rigidity and density with depth. The problem is reduced to a boundary value problem for a differential equation and solved numerically. The method compares favourably with other methods in use. Simple particular cases are considered and interesting results are exhibited graphically.

A Three-Dimensional Correlation/Spectral Model for Turbulent Velocities in a Convective Boundary Layer

A three-dimensional model for correlation functions and spectra in theatmospheric, convective boundary layer (CBL) is presented. The modelincludes vertical inhomogeneities introduced by eddy-blocking at the ground.By assuming the disturbance to the turbulent flow resulting from the groundblocking is irrotational, an equation is developed which allows one to writethe inhomogeneous, two-dimensional (2D) cross spectra for the blocked flowin terms of the 2D cross spectra for a homogeneous flow. VonKarman's energy spectrum then is used to determine thehomogeneous, 2D cross spectra. Although there are only two adjustableparameters in the model, the variance and a length scale, the model is shownto agree quite well with a diversity of previous results for the CBL.

Evidence of anisotropic structures of free-standing porous silicon films

Optical and secondary electron beam images of free-standing porous silicon films reveal a pronounced layered structure. Films tend to split into sheets parallel to the 〈111〉 plane of the initial substrate and form steps and terraces at the broken edge of the film. We have investigated these layers by scanning and transmission electron as well as optical microscopy. We have not observed any significant differences in the microstructure of each layer. Film layering in the cross-section view, caused by these terraces, has a periodicity of about 1 μm. The origin of this effect is discussed and could arise from the electrochemical etching regime used, vertical inhomogeneities in the starting material or mechanical stress-related effect arising from electrolyte evaporation. © 1997 Elsevier Science S.A.

ExTra: A FORTRAN program to calculate resistivity departure curves with a quasi-exponential transition zone

In borehole geophysics it is important to determine accurately the physical parameters of the formation. For electrical methods in oil exploration one of the most important being the true resistivity of the formation. This information helps to assess the recoverability of the oil and the economic viability of the oil field. An interactive computer program ExTra is presented in the paper. The source code is written in standard FORTRAN 77. ExTra computes the forward model response for borehole resistivity sounding for two electrode (normal) configuration. The earth model consists of three cylindrical layers of infinite extent, which is an ideal setup for response computation in one-dimension (1-D). These layers consist of borehole mud, the innermost layer, the flushed zone, and invaded zone. The outermost layer is of infinite radial extent and termed an uncontaminated zone. The dc (direct current) boundary value problem is solved analytically. Resistivity values in the different zones are considered to be uniform except in the invaded zone where the value changes radially. Analytical derivation has been cited for a quasi-exponential transition in resistivity in the invaded zone. Gauss quadrature is used for numerical evaluation of the infinite integral. To achieve higher efficiency, 1-D spline interpolation is introduced for computation of the kernel function at desired values of the integration variable. All the results are expressed as dimensionless quantities. Apparent resistivity response for other known arrays (electrode configurations) can be computed using this program with minor and necessary changes in the code. Solution for infinite bed thickness is shown which can be extended for finite bed thickness where the effect from the vertical inhomogeneity is negligible. The invasion profile presented here is realistic from the point of the actual borehole environment and physical model studies.

Apparent soil thermal diffusivity, a case study: HAPEX-Sahel experiment

In this paper, we determine the apparent soil thermal diffusivity of a dense sandy soil of the HAPEX-Sahel experiment. Several current methods are compared. Two temperature data sets are chosen. In the first, the assumption of steady periodicity is fulfilled and in the second, it is not. In both cases, we compare methods which assume a vertical homogeneity of the soil thermal properties with the NHS method which is based on the vertical inhomogeneity of the thermal diffusivity. Results obtained with both sets of data show that thermal properties are not homogeneous vertically. It is shown that the NHS method is not applicable when the steady periodicity assumption is not valid. In this case, when abrupt change in the temperature wave pattern occurs, as frequently happens in the Sahel just before or just after a rain, a method based on the Lapalce Transform with a corrective factor for the non uniformity of the initial temperature profile (CLTM) must be used. When the steady periodicity assumption is fulfilled, both the Harmonic (HM) and the CUM methods lead to somewhat greater values of the thermal diffusivity than the NHS method.

A line‐by‐line investigation of solar radiative effects in vertically inhomogeneous low clouds

AbstractUsing a detailed line‐by‐line, multiple‐scattering solar radiative‐transfer model, the influences due to cloud internal inhomogeneity in the vertical upon the solar radiative transfer are investigated. In particular, the consequences due to non‐uniform vertical profiles of liquid water and droplet sizes within low clouds are explored in a systematic manner. The fine structure of the spectral overlap between the water droplet and water vapour optical properties, and its effects upon the radiation absorbed within the cloud layer and that reflected at the top of the cloud, are discussed. Without consideration of the in‐cloud water vapour, a vertically inhomogeneous cloud with properties resembling those observed absorbs more solar radiation than an equivalent homogeneous cloud. However, consideration of the effects of the in‐cloud vapour, while still leading to a slightly greater absorption for the inhomogeneous case, partly offsets the difference introduced by the vertical distribution of the drop microphysics. The vertical distribution of cloud heating rate is changed substantially because of the inhomogeneity in the microphysics, with the heating rate in the top region of the cloud nearly 50% more than that due to an equivalent vertically homogeneous cloud. Vertical inhomogeneity of cloud microphysics has little influence on the broadband solar albedo, but can cause significant decreases of the cloud reflectance at specific near‐infrared wavelengths i.e. wavelengths greater than 1 μm, (equivalently, wave numbers less than 10000 cm−1).

Transformation to zero offset in transversely isotropic media

Nearly all dip‐moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero‐offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale’s v(z) ray‐tracing‐based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray‐tracing procedure crafted for anisotropic media, I modify some aspects of their DMO so that it can work for v(z) anisotropic media. DMO impulse responses in typical transversely isotropic (TI) models (such as those associated with shales) deviate substantially from the familiar elliptical shape associated with responses in homogeneous isotropic media (to the extent that triplications arise even where the medium is homogeneous). Such deviations can exceed those caused by vertical inhomogeneity, thus emphasizing the importance of taking anisotropy into account in DMO processing. For isotropic or elliptically anisotropic media, the impulse response is an ellipse; but as the key anisotropy parameter η varies, the shape of the response differs substantially from elliptical. For typical η > 0, the impulse response in TI media tends to broaden compared to the response in an isotropic homogeneous medium, a behavior opposite to that encountered in typical v(z) isotropic media, where the response tends to be squeezed. Furthermore, the amplitude distribution along the DMO operator differs significantly from that for isotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common‐midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale‐induced anisotropy.

Scaling behaviour of vertical magnetic susceptibility and its fractal characterization: an example from the German continental deep drilling project (KTB)

The variations of rock magnetism reflect the geological inhomogeneities of the earth's crust, i.e. its petrological-mineralogical and structural organization. The present state of the crust bears meaningful information of its past dynamic processes and evolution. We analysed magnetic susceptibility data series from the boreholes of the German Continental Deep Drilling Project (KTB). By means of spectral and rescaled-range (R/S) analyses we could detect a scaling behaviour of magnetic data series and quantify it in fractal terms. In particular, the R/S method yields more precise results than the Fourier analysis and leads to Hurst coefficients H > 0.5, which means that the magnetic variations exhibit some persistence with depth. Because of the relation between rock magnetism and crustal features, we suggest that the magnetic vertical inhomogeneities in the KTB area can be described by a self-affine model with H ≌ 0.8, corresponding to a fractal dimension D ≌ 1.2.

ELF-VLF atmospheric waveforms under night-time ionospheric conditions

Abstract. Tweek atmospherics generated by lightning discharges and propagated in the night-time Earth-ionosphere waveguide, have often very pronounced dispersive features near the first few waveguide cut-off frequencies ( fcm~m\\dot{s} fc1, fc 1~1.6–1.9 kHz, m=1, 2, . . . , ), being very extended in time, and have rather large amplitudes of oscillations with periods corresponding to the narrow vicinity of the cut-off frequencies. In this paper an analytical approach is developed to describe the waveform of distant tweeks. It is based on the solving of the Maxwell equations in two qualitatively different regions, whose changes are related in the first instance to the changes in the relative magnitudes of the displacement current and components of the conduction currents, and the following asymptotic matching of the solutions in the transitional region. The analytical night-time waveguide model accounts for both anisotropy and vertical inhomogeneity of the low ionosphere. The model is valid for upper ELF – lower VLF range and is well suitable for the analysis of the QTEm modes in the cut-off frequency regions, which determine the most important part of the tweek spectra and tweek amplitudes. The influence of the different ionospheric heights on the tweek characteristics is determined. The efficiency of the tweek generation by cloud-to-cloud discharge is also evaluated.

Validation of Satellite Retrievals of Cloud Microphysics and Liquid Water Path Using Observations from FIRE

Cloud effective radii (re) and cloud liquid water path (LWP) are derived from ISCCP spatially sampled satellite data and validated with ground-based pyranometer and microwave radiometer measurements taken on San Nicolas Island during the 1987 FIRE IFO. Values of re derived from the ISCCP data are also compared to values retrieved by a hybrid method that uses the combination of LWP derived from microwave measurement and optical thickness derived from GOES data. The results show that there is significant variability in cloud properties over a 100 km×80 km area and that the values at San Nicolas Island are not necessarily representative of the surrounding cloud field. On the other hand, even though there were large spatial variations in optical depth, the re values remained relatively constant (with σ≤2–3 µm in most cases) in the marine stratocumulus. Furthermore, values of re derived from the upper portion of the cloud generally are representative of the entire stratiform cloud. When LWP values are less than 100 g m−2 then LWP values derived from ISCCP data agree well with those values estimated from ground-based microwave measurements. In most cases LWP differences were less than 20 g m−2. However, when LWP values become large (e.g., ≥200 g m−2), then relative differences may be as large as 50%–100%. There are two reasons for this discrepancy in the large LWP clouds: 1) larger vertical inhomogeneities in precipitating clouds and 2) sampling errors on days of high spatial variability of cloud optical thicknesses. Variations of re in stratiform clouds may indicate drizzle: clouds with droplet sizes larger than 15 µm appear to be associated with drizzling, while those less than 10 µm are indicative of nonprecipitating clouds. Differences in re values between the GOES and ISCCP datasets are found to be 0.16±0.98 µm.

Stratification and wind mixing in the Southern Kattegat

Abstract Changes in salt stratification were investigated by using temperature and fluorescence measurements as tracers. By doing this, information on the short term history of the water column was revealed. Further the dominant processes in mixing and stratification of the upper metres of the water column in the southern Kattegat were identified. Due to the salt content, density increased with depth over most of the water column during the period of measurement., A 50 km intrusion of warm, phytoplankton-rich water from the Great Belt outlet was identified. The density increase was maintained due to the buoyancy input given by the combined effect of a horizontal density gradient and vertical shear. Hence the vertical temperature inhomogeneities lasted for 3–7 days and were not mixed even under an event of strong wing mixing. In this period the nutrient and salt transport are uncoupled, since most of the mixing energy is used to redistribute salt within the nutrient-poor surface layer. A reduction of the horizontal density gradient reduced the buoyancy input and allowed for the homogenization of the upper 15 metres within a few hours. One sharp interface was created. After the formation of the sharp interface salt and nutrient transport can be calculated by using the same entrainment function for both salt and nutrient transport. Only during approximately 5 % of the time there was a direct entrainment of bottom water and only 30% of the available mixing energy could be used to give this entrainment.

The effects of atmospheric circulation on line‐of‐sight microwave links

This paper presents an investigation of a lake‐land breeze atmospheric circulation responsible for strong horizontal and vertical inhomogeneities of moisture distribution which affected the refractivity in the neighborhood of a microwave line‐of‐sight link, as observed during a multi‐instrument radiometeorological experiment carried out in São Paulo, Brazil. A boundary layer and mesoscale atmospheric model was used to simulate the local circulation within the link region and to compute the time evolution of the vertical structure of the atmospheric refractive index. A ray‐tracing model was also used to calculate the intensity of the received signals from the measured refractive index vertical profiles. The integrated simulation results were then compared with the measurements. The good agreement obtained between the measured and the simulated characteristics of the temperature and moisture advection, as well as between the measured and the calculated received signal levels, indicates that the lake‐land breeze circulation mechanism is a likely source of the propagation phenomena observed in the microwave link.

Rain-rate duration statistics over a five-year period: a tool for assessing slant path fade durations

A rain gauge network of 10 tipping bucket rain gauges on the Mid-Atlantic coast of the United States has been in continuous operation since June 1, 1986. Rain-rate distributions and estimated slant path fade distributions at 20 and 30 GHz covering the first five-year period have been derived from the gauge network measurements and published data of Goldhirsh, Krichevsky and Gebo (see ibid., vol.40, no.11, p.1408, 1992). In this article, we present rain-rate time duration statistics. The conversion of rain-rate duration statistics derived from in situ measurements to slant path fade duration statistics is complicated because of the vertical and lateral inhomogeneity of the rain. A benchmark set of fade duration statistics at 20 and 30 GHz for a vertical path is derived from the rain-rate duration statistics employing Crane's (1980) global model. These results may be used by investigators for comparison with and/or conversion to slant path fade duration statistics. Such statistics are important for better assessing optimal coding procedures over defined bandwidths. >

The Picard iterative approximation to the solution of the integral equation of radiative transfer—part I. The plane-parallel case

The present Picard Iterative (PI) approach is designed to be a compromise between the generality of Monto Carlo techniques and the numerical efficiency of the existing analytical approaches. The PI method, like the Successive Orders of Scattering approach, begins with the integral equation form of the radiative transfer equation (RTE). Starting with an approximate radiance field, the PI performs a fixed-point iteration. The solution converges in approx. 10 iterations for C1 water cloud phase functions and in approx. 20 iterations for highly peaked cirrus-type phase functions. The PI iteration (1) is unaffected by a vertical inhomogeneities; (2) converges even for highly peaked phase functions; and (3) can be extended to 3-D geometries. However, it is less efficient for (1) optically thick, but homogeneous, media; and (2) media with a weakly peaked scattering phase function.

On determination of Th concentration in specimens by means of gamma rays and alpha particles

Experiments on improving the track technique for the determination of Th content in natural samples have been performed. For Th concentration measurements, γ-rays with energies of 18 and 20 MeV were used. For γ-rays in the energy range 6–23.5 MeV, the ratio of fission fragment track densities N U/ N Th of these elements for thick targets has been obtained. The ratio ranges from 1.7 to 3.2 with the maximum at a γ-ray energy of 15 MeV. The determined Th concentrations in the calibrated Th standards and iron manganese nodules agree, within experimental error, with the known values. For 9.1 MeV/n α-particles, the track density ratio N Th/ N U has been found to be equal to (1.06 ± 0.07), but the Th content was lowered, possibly due to the vertical inhomogeneity of the α-particle beam and also due to partial thermal fading of the tracks in mica. The investigation was performed at the Laboratory of Nuclear Reactions, JINR.

Vertical inhomogeneity of the magnetization reversal in antiferromagnetically coupled Co/Cu multilayers at the first maximum

Magnetization behavior in antiferromagnetically (AFM) coupled multilayer systems was calculated by using an atomic layer model. Comparisons with the experimental results obtained on sputtered Co/Cu multilayers reveal remarkable differences in the magnetization reversal and in the field dependence of the magnetoresistance. Kerr loops measured from both sides of the stack display strong vertical differences. At the lower side near the Fe seed layer the magnetization reversal is in good agreement with that of our calculations whereas near the surface in large portions of the stack the AFM coupling is destroyed or varied. These effects are presumably caused by magnetic short circuits at defects in the multilayer structure. Cross-section transmission electron microscopy reveals growth defects which seem to be responsible for the deviations from the calculated ideal behavior.

Solar Radiative Transfer in Clouds with Vertical Internal Inhomogeneity

Abstract To investigate the photon transport in inhomogeneous clouds, a Monte Carlo cloud model with internal variation of optical properties is developed. The data for cloud vertical internal inhomogeneity are chosen from published observations. Parameterization of the solar radiative properties of clouds is used in the form of the liquid water content and the effective radius of cloud droplet. The Monte Carlo simulations show that for overcast stratocumulus clouds, the differences in reflectance between the vertical inhomogeneous clouds and their planeparallel counterpart are very small (only about 1%). These differences can be enhanced up to 10% for large solar zenith angles, when the overcast clouds are separated into broken cloud fields. If the cloud coverage is large, the vertical inhomogeneity of clouds can cause about 7% increase in cloud absorption, which may help to explain the cloud absorption anomaly. Also, the parameterization of effective cloud amount for cloud absorption is discussed.

An example of lateral-inhomogeneity effects on seismic traveltimes in a zero-offset VSP experiment

SUMMARY 2-D random media with ellipsoidal autocorrelation functions are used to point out the effects of lateral inhomogeneities on zero-offset VSP data. The ellipsoidal autocorrelation functions allow the characterization of lateral and vertical inhomogeneities by two independent scaling factors a and b in the two Cartesian directions; a for lateral inhomogeneities and b for vertical inhomogeneities. Thus we can describe 2-D media by taking non-zero finite values of a and b, or 1-D media by extending to infinity one of the two scaling factors. Here we consider two models: (i) a 2-D model where a and b are finite and non-zero, and (ii) a 1-D model with the same vertical realization of inhomogeneities (i.e. the same value for b) but with a tending to infinity. By comparing zero-offset VSP synthetic seismograms obtained from these two models, we observe that the seismic pulse through the 2-D model arrives earlier than the pulse through the 1-D model. The time difference between these two arrivals increases linearly with the depth of receivers. We have reported time difference up to 10 ms per 1000 m. This time difference is also directly related to the scale of lateral inhomogeneities a.

Microwave radiative transfer through horizontally inhomogeneous precipitating clouds

Recent advances in cloud microphysical models have led to realistic three‐dimensional distributions of cloud constituents. Radiative transfer schemes can make use of this detailed knowledge in order to study the effects of horizontal as well as vertical inhomogeneities within clouds. This study looks specifically at the differences between three‐dimensional radiative transfer results and those obtained by plane parallel, independent pixel approximations in the microwave spectrum. A three‐dimensional discrete ordinates method as well as a backward Monte Carlo method are used to calculate realistic radiances emerging from the cloud. Analyses between these models and independent pixel approximations reveal that plane parallel approximations introduce two distinct types of errors. The first error is physical in nature and is related to the fact that plane parallel approximations do not allow energy to leak out of dense areas into surrounding areas. In general, it was found that these errors are quite small for emission‐dominated frequencies (37 GHz and lower) and that physical errors are highly pronounced only at scattering frequencies (85 GHz) where large deviations and biases up to 8 K averaged over the entire cloud were found. The second error is more geometric in nature and is related to the fact that plane parallel approximations cannot accommodate physical boundaries in the horizontal dimension for off‐nadir viewing angles. The geometric errors were comparable in magnitude for all frequencies. Their magnitude, however, depends on a number of factors including the scheme used to deal with the edge, the nature of the surface, and the viewing angle.

Rapid Thermal Oxidation for Passivation of Porous Silicon

ABSTRACTChemical and mechanical stability of porous silicon layers (PSL) is the prerequisite of any active (luminescent) or passive (e.g. porous substrate) integrated applications. In this work X-ray diffraction (XRD) was used to analyze quantitatively the strain distribution obtained in different morphology PSL that were prepared on (100) p and p+Si substrates. Tetragonal lattice constant distortion can be as high as 1.4% in highly porous “as-prepared” samples. Incoherent optical heating RTO is governed by the absorption in the oxidized specimen. PSL show vertical inhomogeneity according to interpretation of spectroscopic ellipsometry (SE) data. Oxygen incorporation during RTO is controlled by specific surface (in p+ proportional, in p inversely proportional with porosity), while the developing compressive stress depends on pore size, and decreases with porosity in both morphologies.