Vertical Line Source Research Articles

Numerical modeling of borehole-to-surface logging technology based on incomplete Cholesky conjugate gradient

For vertical line source, the total potential is divided into normal potential and abnormal one to eliminate singularity in this paper. Normal potential produced in homogeneous half-space is calculated by analytic method. While for abnormal potential produced by underground anomalous body, the finite difference method is used based on differential equation of abnormal potential. Further, the total potential is calculated and the forward is realized. Accordingly, incomplete Cholesky conjugate gradient that is introduced in this paper gives the analytical solution of equation, it converges more quickly while requiring less memory. It is an initiation to introduce a dipping bed model to indicate potential distribution produced by underground anomalous body.

Tephra Fallout Models: The Effect of Different Source Shapes on Isomass Maps

Numerous tephra dispersion and sedimentation models rely on some abstraction of the volcanic plume to simplify forecasts of tephra accumulation as a function of the distance from the volcano. Here we present solutions to the commonly used advection-dispersion equation using a variety of source shapes: a point, horizontal and vertical lines, and a circular disk. These may be related to some volcanic plume structure, such as a strong plume (vertical line), umbrella cloud (circular disk), or co-ignimbrite plume (horizontal line), or can be used to build a more complex plume structure such as a series of circular disks to represent a buoyant weak plume. Basing parameters upon eruption data, we find that depositions for the horizontal source shapes are very similar but differ from the vertical line source deposition. We also compare the deposition from a series of stacked circular disk sources of increasing radius above the volcanic vent with that from a vertical line source.

2D and 3D Turbulent Fluctuations in Open Channel Flow with Re τ = 590 Studied by Large Eddy Simulation

Well-resolved 3D Large Eddy Simulations (LES) are presented for open channel flow at a Reynolds number Reτ = 590 based on friction velocity uτ and water depth h. The results are depth-averaged and thereby information is obtained on the 2D horizontal fluctuations in the channel. The total turbulence is decomposed into 2D and 3D fluctuations and the energy content of these as well as their spectral distribution is studied. It is found that only 15% of the fluctuating energy is contained in the 2D fluctuations and that these are mostly of scales larger than the water depth while the 3D fluctuations are restricted by the limited vertical extent of the water body and have scales smaller than the water depth. Information is obtained on the dispersion terms arising from the depth-averaging procedure, and scalar transport due to a vertical line source of tracer is studied thereby investigating the contribution of the 2D and 3D fluctuations to the transverse mixing of the scalar.

傾斜版列を前面壁とする遊水室型杭式防波堤の港湾域における効果について

We have proposed a new type breakwater supported by piles, which consists of three major parts, i. e., an inclined plate array as a front wall, a vertical rear wall and a submerged plate at the bottom. It has been confirmed by the two dimensional study of vertical plane that the breakwater enables to reduce both reflected and transmitted waves for comparatively wide range of wave frequency, and also to generate mean current by wave actions in the offshore direction. In this study, we have examined the performance of this type of breakwater in the three dimensional wave fields, such as a harbor model basin. For the comparisons, conventional breakwaters, such as a curtain-walled breakwater and also a vertical impermeable breakwater, were also used as a harbor breakwater model. For the theoretical prediction of wave height distributions around the harbor, applicability of the numerical analysis based on the vertical line source Green's function method was extensively examined.

Analysis of Interference Tests With Horizontal Wells

Summary One of the common assumptions in horizontal-well interference-test analysis is to ignore fluid flow in and out of the horizontal observation well and represent it by a point. In some cases, the active well is also approximated by a vertical line source. Using a semianalytical model, this paper answers three fundamental questions: What is the critical distance between the wells to represent the horizontal observation well by an observation point? Where should the observation point be placed along the horizontal well? Under what conditions may the active well be approximated by a vertical line source and the exponential integral solution be used to analyze observation-well responses? Two correlations are presented to simplify the analysis of horizontal-well interference tests. Example applications are presented, and error bounds are documented.

A model for the numerical simulation of tephra fall deposits

A simple semianalytical model to simulate ash dispersion and deposition produced by sustained Plinian and sub-Plinian eruption columns based on the 2D advection–dispersion equation was applied. The eruption column acts as a vertical line source with a given mass distribution and neglects the complex dynamics within the eruption column. Thus, the use of the model is limited to areas far from the vent where the dynamics of the eruption column play a minor role. Vertical wind and diffusion components are considered negligible with respect to the horizontal ones. The dispersion and deposition of particles in the model is only governed by gravitational settling, horizontal eddy diffusion, and wind advection. The model accounts for different types and size classes of a user-defined number of particle classes and changing settling velocity with altitude. In as much as wind profiles are considered constant on the entire domain, the model validity is limited to medium-range distances (about 30–200 km away from the source). The model was used to reconstruct the tephra fall deposit from the documented Plinian eruption of Mt. Vesuvius, Italy, in 79 A.D. In this case, the model was able to broadly reproduce the characteristic medium-range tephra deposit. The results support the validity of the model, which has the advantage of being simple and fast to compute. It has the potential to serve as a simple tool for predicting the distribution of ash fall of hypothetical or real eruptions of a given magnitude and a given wind profile. Using a statistical set of frequent wind profiles, it also was used to construct air fall hazard maps of the most likely affected areas around active volcanoes where a large eruption is expected to occur.

Propagation of auroral hiss at high altitudes

Using multicomponent wave measurements of the Polar spacecraft, we provide direct evidence of the propagation pattern of funnel‐shaped auroral hiss at a radial distance of 5 Earth radii. The waves propagate upward and the Poynting flux is directed toward higher latitudes in the high‐latitude part of the emission and to lower latitudes in the low‐latitude part. The wave vectors are found to be close to the whistler mode resonance angle. Consistent with the theory, the latitudinal component of the wave vector is opposite compared to that of the Poynting flux in the low‐latitude and high‐latitude parts of the funnel‐shaped emission. In the central part of the emission we observe a very broad distribution of the wave energy with respect to the azimuth angle. The waves thus simultaneously come from different directions with different wave vectors. This leads us to the conclusion that hiss is more likely generated in an extended sheet source rather than in a vertical line source or a point source. In this case the observed propagation pattern suggests that the sheet source is oriented roughly in the longitudinal direction, consistent with the region where we can expect presence of upgoing or counterstreaming electron beams.

APPLICABILTY OF VLG METHOD TO THE ESTIMATION OF WAVE HEIGHT DISTRIBUTUION AROUND A CIRCULAR SHOAL

For a circular shoal bathymetry, the conventional wave ray method is comparatively hard to estimate wave height distributions. In order to avoid the difficulty, combined analysis of the vertical line source Green's function method and the regional division method was adopted. Applicability of the method to a circular shoal bathymetry was examined by the comparison between the experimental and computed results. As an extensive case study, a circular shoal bathymetry with a vertical circular caisson at the top was used to know the effect of wave diffraction on the wave refraction by the shoal.

INFLUENCE OF TRANSMISSION AND REFLECTION PROPERTIES OF MARITIME STRUCTURES WITH WAVE PERIOD ON A HARBOR TRANQUILITY

Recently, it has become known that multi directional and irregular natures of incident waves are important for estimating wave sheltering effects by maritime structures, such as wave diffraction effects about a harbor entrance gap. In this study, concerning with variations of wave reflections and transmissions about harbor breakwaters with wave period, the harbor tranquility for the incidence of multi-directional and irregular waves was examined extensively. The vertical line source Green's function method was basically used for the numerical computations. Extension of the method to the permeable boundary conditions was briefly introduced.

Effects of source cavity shape on steady, three‐dimensional flow of soil gases

For a point or a spherical source in infinite space the steady state potential is simply a constant over the distance from the source. Flow of soil gases was studied by comparing results for other cavity shapes for sources (or sinks) to the spherical solution. Cavity shapes included a vertical line source of finite length, a prolate spheroid with a vertical axis of rotation, and a vertical well also of finite length and radius. Questions addressed include the distance over which the differences between a sphere and the alternatives become negligible and what radius of spherical source at a given pressure results in the same flow rate as from the other shapes. For a vertical line source the pressure is within 5% of the pressure for the spherical source at a distance of 2.5 times the vertical line and within 1% beyond 6 times the vertical line. Similar results were expressed for the other shapes relative to a spherical source. Travel times are presented in a generalized relationship illustrated for spherical and finite line sources. The results are relevant to other potential problems as well, for example, steady water flow in saturated porous media, steady water flow in unsaturated porous media without gravity, heat conduction, diffusion, and electrostatics.

Crustal deformation in the mid-May 1991 crisis preceding the extrusion of a dacite lava dome at Unzen volcano, Japan

Tilt observations at FG1 station located about 680 m west of the central crater of Unzen volcano, southwestern Japan, revealed details about the process of magma ascent during the mid-May 1991 crisis, just before the appearance of a lava dome. Crustal deformations measured during this period can be interpreted by a combination of upward growth of a buried magma column and lateral intrusion of a dike, modeled by a vertical line source and a planer tensile dislocation in an elastic half space. Marked change in tilt was observed at first in the EW direction at FG1 during May 11–14, suggesting the ascent of a magma column with a diameter of about 40 m from about 300 m to 160 m in depth beneath the central crater. After the interruption of the rise of the magma column, magma began to intrude laterally as a dike on May 15 toward approximately the N80°W direction. This resulted in a large tilt change essentially in the NS component at FG1. The horizontal extent of the dike might have exceeded 400 m in a few days with a thickness of about 6 m. On May 17, the magma column started to rise again, probably because the impediment to magma ascent was fractured by the growth of the dike. The top of the magma column finally reached to the crater bottom probably on May 19, and a new lava dome was actually observed on May 20. After which, the remarkable upward tilt to the south at FG1 due to the dike intrusion decreased rapidly. The deformation after May 20 can be interpreted by a gradual increase in the thickness of the dike up to 13 m by the end of May 1991. Although large errors are inevitable in estimated values because of a lack of sufficient data, the present results confirm the importance of making continuous observations of crustal deformation near the summit areas of active volcanoes in order to clarify the underground processes of magma movement leading to eruptions.

Estimation of shape factor and depth from gravity anomalies due to some simple sources

The gravity anomalies over some simple geometry sources have been inverted to compute the shape factor and depth using a hybrid algorithm involving simulated annealing followed by non-linear curve fitting. The shape factors for a point, an infinite horizontal line and a semi-infinite vertical line source are 1.5, 1.0 and 0.5, respectively. A procedure to determine the depth and the horizontal or vertical extent of a line source has been developed. A ribbon of finite vertical extent is characterized by a shape factor varying between 0. 1 and 1.0. A symmetrical syncline can be distinguished from an anticline on the basis of the shape factor, as this assumes values greater than 1.0 for a syncline and less than 1.0 for an anticline. Interpretation schemes are presented to compute the depth to the horizontal base and its radius for models of a 2D dome and a 2D depression. The efficiency and potential of the proposed technique has been evaluated by applying it to three published field examples: a chromite anomaly in Cuba, the Mobrun orebody and the Louga anomaly.

A NUMERICAL COMPUTATION METHOD ON WAVE HEIGHT DISTRIBUTION IN A HARBOR WITH PERMEABLE BREAKWATERS

An approximate method for solving wave boundary-value problems about a harbor consisting of impermeable and permeable boundaries, such as rubble mound breakwaters and vertical breakwaters, is developed. The vertical line source Green's function method was basically used for efficient computations. Extensions of the method to the permeable boundary conditions were examined precisely. It was confirmed that the approximate method developed here is very effective for estimating wave height distributions in a harbor with permeable breakwaters.

Efficient computation of apparent resistivity curves for depth profiling of a layered earth

The problem of computing the electrical potential as a result of a direct current electric source in a layered earth is reformulated to avoid instability in the numerical computation that may occur with the standard propagator matrix formalism described in a number of textbooks. The present spectral formalism involves constituents that contain only exponential functions with nonpositive arguments. The vertical spectral input admittances at the interface levels up to the source level are calculated recursively, starting at the uppermost and lowermost interfaces of the layered earth. These admittances at the source level are then used to compute the electrical voltage at the source level. With the known voltage and the admittances at the source level, the spectral amplitudes at the source level are known. Computation of the amplitudes at the other interfaces is, progressively, carried out by expressing the amplitudes at any interface above the source level in terms of the amplitude on the interface just below it and expressing the amplitudes at any interface below the source level in terms of the amplitude on the interface just above it. This results in an efficient scheme for computing electrical potential in any arbitrary depth levels (required for imaging subsurface conductivity). We simulate single‐borehole and hole‐to‐hole experiments. Neglecting the influence of the boreholes, we consider a plane layered earth model in which point electrodes along a vertical line (source line) inject and extract a stationary electric current, and point electrodes either along the source line or along another vertical line (receiver line) measure a potential difference. From the potential measurements, apparent resistivities are computed along the vertical lines.

A Fredholm integral equation method for propagation predictions over small terrain irregularities

Two-dimensional propagation of vertical line source fields over lossy, irregular terrain is considered using the magnetic field integral equation. The terrain is characterized by its elevation profile and the local surface impedance, both of which may vary with distance. For treatment via the Fredholm integral equation, the domain under consideration is made finite by enclosing the terrain irregularity and the source within an arbitrary outer boundary. Absorbing boundary conditions are imposed on the outer boundary to reduce unwanted reflections from it. The integral equation is solved by the boundary element method with quadratic elements. Substantial comparison is made with specific canonical problems, with previously published results of other workers, and with measurements to validate the method. >

Mapping hydraulic fractures using a borehole-to-surface electrical resistivity method

A series of shallow-depth hydraulic fracturing experiments was carried out in the summer of 1988 at the Elda landfill near Cincinatti, Ohio and mise-à-la-masse (MLM) borehole-to-surface resistivity measurements were obtained in an attempt to detect the fracturing. The well casing of an injection borehole was energized and potentials were measured at various points on the surface near the borehole before and after hydraulic fracturing was performed with a conductive fluid. Forward and inverse modeling algorithms based on the DC alpha center method were developed and tested with synthetic data to create a tool for interpretation of the experimental data. The alpha center forward algorithm incorporates a vertical line source of current to model an energized steel well casing. The advantages of the alpha center method are its speed and simplicity, and its ability to handle 3D geometry and indicate positions of conductive inhomogeneities. The forward solution is incorporated into an iterative least-squares inversion algorithm, with constraints applied to the alpha center parameters to facilitate modeling of fractures.

Two‐dimensional source potentials in a two‐fluid medium for the modified Helmholtz′s equation

Velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodally along its length. The technique of deriving the potentials here is an extension of the technique used for the case of only time harmonic vertical line source. The present case is concerned with the two‐dimensional modified Helmholtz′s equation while the previous is concerned with the two‐dimensional Laplace′s equation.

A laboratory experiment on lateral diffusion of scalar quantities in the stratified surface layer

Buoyancy effects on the lateral and vertical diffusion of scalar quantities in the atmospheric surface layer or in the wall region were investigated by a laboratory experiment. Fully developed density stratification was attained in the turbulent flow between horizontal parallel plates kept at different temperatures. Lateral eddy diffusivity coefficients in the horizontal planes K Dy were obtained from measurements of diffusion of ethane from a specially designed vertical line source. Based on a local gradient concept and vertical eddy diffusivity coefficient K Dz presented in a previous paper (Fukui etal., 1983), buoyancy effects were evaluated at the same nondimensional vertical distance from the wall z + ( = zu ∗/v; u ∗ and v being the friction velocity and kinematic viscosity, respectively). The results indicated that the ratio of the vertical diffusion coefficient under diabatic conditions to its value in neutral conditions, expressed by a shear function, agreed well with observations by Businger etal. (1971). Although the ratio K Dy K Dz in the neutral condition was found to be 1.5–2.0 in the fully turbulent region, increasing to a value more than 10 in the vicinity of the wall, this ratio in the stratified conditions, when normalized by the neutral value, could be correlated by only ξ( = z/ L; L being the Monin-Obukhov length); it increased with ξ in the stable condition, while in the unstable condition it remained almost unity. However, in extremely unstable conditions it decreased rapidly.

A new transient vertical hot-wire thermal conductivity instrument for fluids utilising a ramp power input

A knowledge of accurate data on thermal conductivity of liquids and gases is essential for optimal design of many engineering units. Only a few compounds have been studied and the investigations have been limited to temperatures below the normal boiling points. This paper discusses an improved transient hot-wire technique based on the perturbation of an ideal vertical line source with a ramp in power which signifies: (i) minimal free convection, radiation and Knudsen contributions to the apparent thermal conductivity, (ii) enhanced sensitivity to greater utilisation of the overall resistance change of the wire, and (iii) decreased capital cost relative to previous instruments due to use of a microcomputer. Based on a detailed mathematical model of this technique, an instrument has been designed and constructed. Thermal conductivity measurements on liquid toluene, a proposed standard, have proved the viability of the proposed technique. Results are in excellent agreement with the measurements of other investigators. The precision and accuracy of the results are estimated to be better than 0.8 and 1.1% respectively.

A model for the estimation of the concentrations and spatial extent of suspended sediment plumes

A simple model is presented for the spatial structure of suspended sediment plumes produced by over-board pipeline disposal of dredge spoil in shallow waters. The model is based on a solution to the advection-diffusion equation for a continuous vertical line source. It provides information on the variation of both centerline concentration and the second moment of the lateral distribution with distance from the source. The structure of the plume is described by only two parameters: one proportional to the settling velocity of the suspended material and the other equal to the ratio of a diffusion velocity to the advective velocity of the ambient flow. The model has been applied to represent the structure of observed suspended sediment plumes at three separate shallow water sites.