AMBIGUITY IN GRAVITY INTERPRETATION

Geophysics ◽  
1947 ◽  
Vol 12 (1) ◽  
pp. 43-56 ◽  
Author(s):  
D. C. Skeels
Keyword(s):  
Gravity Data ◽  
Magnetic Data ◽  
Second Derivative ◽  
Two Dimensional ◽  
Wide Range ◽  
Geometrical Shapes ◽  
Unique Interpretation ◽  
Analytical Proof ◽  
Minimum Depth ◽  
Gravity Interpretation

It is shown that contrary to what is stated and implied in much of the literature, gravity data cannot, of themselves, be interpreted uniquely. It is shown by means of a two‐dimensional example that for a given anomaly and a given density contrast a wide range of possible interpretations can be made, at various depths, and that whereas there is a maximum depth for the solution the minimum depth is zero. Other examples are given to show that depth rules based upon the assumption of geometrical shapes may give results very much in error when applied to actual anomalies. Nor does the method of interpretation by vertical gradients allow us to make an unique interpretation, or to distinguish deep from shallow anomalies as has been claimed. It is shown that we do not escape the ambiguity by using second derivative quantities such as gradient and curvature, and that, in fact, gravity and its derivatives are related by a corollary of Green’s theorem. This theorem provides an analytical proof of ambiguity not only for the case of gravity data but for magnetic data as well.

A method to minimize edge effects in two‐dimensional discrete Fourier transforms

Geophysics ◽  
1988 ◽  
Vol 53 (8) ◽  
pp. 1113-1117 ◽  
Author(s):  
Yanick Ricard ◽  
Richard J. Blakely
Keyword(s):  
Fourier Transforms ◽  
Earth Science ◽  
Gravity Data ◽  
Power Spectra ◽  
Magnetic Data ◽  
Moho Depth ◽  
Two Dimensional ◽  
Science Data ◽  
Discrete Fourier Transforms ◽  
Earth Science Data

Fourier transforms are widely used in analysis of two‐dimensional (2-D) earth‐science data, such as gravity and magnetic surveys, topographic models, and remote‐sensing images. For example, manipulations of gridded magnetic or gravity data, such as upward and downward continuation, reduction to the pole, wavelength filters, pseudogravity transformation, and vertical derivatives (Hildenbrand, 1983), are greatly simplified with Fourier transforms, as are certain forward and inverse calculations (Parker, 1973; Parker and Huestis, 1974). Power spectra computed from 2-D Fourier transforms are used to estimate depth to the top and bottom of magnetic sources from gridded magnetic data (Spector and Grant, 1970; Connard et al., 1983) and to estimate lithospheric strength and Moho depth from gridded gravity data (Dorman and Lewis, 1970; Louden and Forsyth, 1982; McNutt, 1983).

NOTE ON THE EFFECT OF RANDOM ERRORS IN GRAVITY SECOND DERIVATIVE VALUES

Geophysics ◽  
1953 ◽  
Vol 18 (3) ◽  
pp. 720-724
Author(s):  
G. Ramaswamy
Keyword(s):  
Gravity Data ◽  
Prima Facie ◽  
Resolving Power ◽  
Magnetic Data ◽  
Second Derivative ◽  
Random Component ◽  
Random Errors ◽  
Prima Facie Case ◽  
Interesting Paper ◽  
Second Derivative Method

In an interesting paper “The Effect of Random Errors in Gravity Data on Second Derivative Values,” Thomas A. Elkins (1952) points out the need for eliminating the random component of gravity data before proceeding to interpret them with the aid of second derivative maps. There is a prima facie case for the elimination of random errors, if only to ensure reliability in results. The need, however, becomes more apparent if it is remembered: a. that the Second Derivative method of interpreting gravity (or magnetic) data is one of high resolving power, and b. that, therefore, errors creeping into those data may considerably vitiate the interpretation of those data.

A CONTRIBUTION TO THE COMPUTATION OF THE “SECOND DERIVATIVE” FROM GRAVITY DATA

Geophysics ◽  
1953 ◽  
Vol 18 (4) ◽  
pp. 894-907 ◽  
Author(s):  
Otto Rosenbach
Keyword(s):  
Gravity Data ◽  
Second Derivative ◽  
Practical Application ◽  
Arithmetic Means ◽  
Interesting Paper ◽  
Approximation Formulas ◽  
Series Development ◽  
Concentric Circles ◽  
Gravity Interpretation ◽  
Second Derivative Method

The theory and practical application of the second derivative method of gravity interpretation have been discussed by Elkins (1951) in a very interesting paper based partly on an earlier paper by Peters (1949). In this paper, Elkins shows how the second derivative may be computed at the center of a series of concentric circles using the arithmetic means of the gravity values, assumed to be continuous, around each circle. A method is here proposed which does not use a continuum of gravity values but instead requires only a series development. The approximation formulas needed for the routine calculations can be derived by a method different from that of Elkins and the least squares adjustments he used can be dispensed with. Two hypothetical examples using the formulas derived by the series method are given and the results are compared with those computed by Elkins’ formula.

Aromatic Volatile Composition of Celery and Celeriac Cultivars

HortScience ◽  
1990 ◽  
Vol 25 (5) ◽  
pp. 556-559 ◽  
Author(s):  
Fredy Van Wassenhove ◽  
Patrick Dirinck ◽  
Georges Vulsteke ◽  
Niceas Schamp
Keyword(s):  
Volatile Compounds ◽  
Chromatographic Method ◽  
Apium Graveolens ◽  
Volatile Components ◽  
Two Dimensional ◽  
Qualitative Composition ◽  
Volatile Composition ◽  
Wide Range ◽  
Gas Chromatographic Method ◽  
Identification And Quantification

A two-dimensional capillary gas chromatographic method was developed to separate and quantify aromatic volatiles of celery in one analysis. The isolation, identification, and quantification of the volatile compounds of four cultivars of blanching celery (Apium graveolens L. var. dulce) and six cultivars of celeriac (Apium graveolens L. var. rapaceum) are described. The qualitative composition of Likens-Nickerson extracts of both cultivars is similar. The concentration of terpenes and phthalides, the key volatile components, found in various cultivars of both celery and celeriac varied over a wide range.

scholarly journals Prediction of Wide Range Two-Dimensional Refractivity Using an IDW Interpolation Method from High-Altitude Refractivity Data of Multiple Meteorological Observatories

2021 ◽  
Vol 11 (4) ◽  
pp. 1431
Author(s):  
Sungsik Wang ◽  
Tae Heung Lim ◽  
Kyoungsoo Oh ◽  
Chulhun Seo ◽  
Hosung Choo
Keyword(s):  
High Altitude ◽  
Korean Peninsula ◽  
Interpolation Method ◽  
Atmospheric Condition ◽  
Propagation Path ◽  
Two Dimensional ◽  
Data Set ◽  
Wide Range ◽  
Atmospheric Data ◽  
Terrain Surface

This article proposes a method for the prediction of wide range two-dimensional refractivity for synthetic aperture radar (SAR) applications, using an inverse distance weighted (IDW) interpolation of high-altitude radio refractivity data from multiple meteorological observatories. The radio refractivity is extracted from an atmospheric data set of twenty meteorological observatories around the Korean Peninsula along a given altitude. Then, from the sparse refractive data, the two-dimensional regional radio refractivity of the entire Korean Peninsula is derived using the IDW interpolation, in consideration of the curvature of the Earth. The refractivities of the four seasons in 2019 are derived at the locations of seven meteorological observatories within the Korean Peninsula, using the refractivity data from the other nineteen observatories. The atmospheric refractivities on 15 February 2019 are then evaluated across the entire Korean Peninsula, using the atmospheric data collected from the twenty meteorological observatories. We found that the proposed IDW interpolation has the lowest average, the lowest average root-mean-square error (RMSE) of ∇M (gradient of M), and more continuous results than other methods. To compare the resulting IDW refractivity interpolation for airborne SAR applications, all the propagation path losses across Pohang and Heuksando are obtained using the standard atmospheric condition of ∇M = 118 and the observation-based interpolated atmospheric conditions on 15 February 2019. On the terrain surface ranging from 90 km to 190 km, the average path losses in the standard and derived conditions are 179.7 dB and 182.1 dB, respectively. Finally, based on the air-to-ground scenario in the SAR application, two-dimensional illuminated field intensities on the terrain surface are illustrated.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

scholarly journals Robust anomalous metallic states and vestiges of self-duality in two-dimensional granular In-InOx composites

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Xinyang Zhang ◽  
Bar Hen ◽  
Alexander Palevski ◽  
Aharon Kapitulnik
Keyword(s):  
Magnetic Field ◽  
Metallic Phase ◽  
Broadband Noise ◽  
Two Dimensional ◽  
Conventional Theory ◽  
Logarithmic Divergence ◽  
Self Duality ◽  
Low Field ◽  
Wide Range ◽  
Low Temperature Resistance

AbstractMany experiments investigating magnetic-field tuned superconductor-insulator transition (H-SIT) often exhibit low-temperature resistance saturation, which is interpreted as an anomalous metallic phase emerging from a ‘failed superconductor’, thus challenging conventional theory. Here we study a random granular array of indium islands grown on a gateable layer of indium-oxide. By tuning the intergrain couplings, we reveal a wide range of magnetic fields where resistance saturation is observed, under conditions of careful electromagnetic filtering and within a wide range of linear response. Exposure to external broadband noise or microwave radiation is shown to strengthen the tendency of superconductivity, where at low field a global superconducting phase is restored. Increasing magnetic field unveils an ‘avoided H-SIT’ that exhibits granularity-induced logarithmic divergence of the resistance/conductance above/below that transition, pointing to possible vestiges of the original emergent duality observed in a true H-SIT. We conclude that anomalous metallic phase is intimately associated with inherent inhomogeneities, exhibiting robust behavior at attainable temperatures for strongly granular two-dimensional systems.

scholarly journals Energetics of mesoscale cell turbulence in two-dimensional monolayers

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Shao-Zhen Lin ◽  
Wu-Yang Zhang ◽  
Dapeng Bi ◽  
Bo Li ◽  
Xi-Qiao Feng
Keyword(s):  
Kinetic Energy ◽  
Tumor Metastasis ◽  
Cell Types ◽  
Boltzmann Distribution ◽  
Scaling Exponent ◽  
Biological Processes ◽  
Two Dimensional ◽  
Cell Monolayers ◽  
Wide Range ◽  
Epithelial Cell Monolayers

AbstractInvestigation of energy mechanisms at the collective cell scale is a challenge for understanding various biological processes, such as embryonic development and tumor metastasis. Here we investigate the energetics of self-sustained mesoscale turbulence in confluent two-dimensional (2D) cell monolayers. We find that the kinetic energy and enstrophy of collective cell flows in both epithelial and non-epithelial cell monolayers collapse to a family of probability density functions, which follow the q-Gaussian distribution rather than the Maxwell–Boltzmann distribution. The enstrophy scales linearly with the kinetic energy as the monolayer matures. The energy spectra exhibit a power-decaying law at large wavenumbers, with a scaling exponent markedly different from that in the classical 2D Kolmogorov–Kraichnan turbulence. These energetic features are demonstrated to be common for all cell types on various substrates with a wide range of stiffness. This study provides unique clues to understand active natures of cell population and tissues.

Heat and Mass Transfer in an Incompressible Turbulent Boundary Layer

1972 ◽  
Vol 94 (1) ◽  
pp. 23-28 ◽  
Author(s):  
E. Brundrett ◽  
W. B. Nicoll ◽  
A. B. Strong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Plate ◽  
Mixing Length ◽  
Two Dimensional ◽  
Transfer Data ◽  
Incompressible Turbulent Boundary Layer ◽  
Wide Range ◽  
Incompressible Boundary

The van Driest damped mixing length has been extended to account for the effects of mass transfer through a porous plate into a turbulent, two-dimensional incompressible boundary layer. The present mixing length is continuous from the wall through to the inner-law region of the flow, and although empirical, has been shown to predict wall shear stress and heat transfer data for a wide range of blowing rates.

scholarly journals Universal behavior of the bosonic metallic ground state in a two-dimensional superconductor

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Zhuoyu Chen ◽  
Bai Yang Wang ◽  
Adrian G. Swartz ◽  
Hyeok Yoon ◽  
Yasuyuki Hikita ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Quantum Phase Transitions ◽  
Metallic State ◽  
Two Dimensional ◽  
Metallic Behavior ◽  
Universal Behavior ◽  
Hall Resistivity ◽  
Wide Range ◽  
Metal State

AbstractAnomalous metallic behavior, marked by a saturating finite resistivity much lower than the Drude estimate, has been observed in a wide range of two-dimensional superconductors. Utilizing the electrostatically gated LaAlO3/SrTiO3 interface as a versatile platform for superconductor-metal quantum phase transitions, we probe variations in the gate, magnetic field, and temperature to construct a phase diagram crossing from superconductor, anomalous metal, vortex liquid, to the Drude metal state, combining longitudinal and Hall resistivity measurements. We find that the anomalous metal phases induced by gating and magnetic field, although differing in symmetry, are connected in the phase diagram and exhibit similar magnetic field response approaching zero temperature. Namely, within a finite regime of the anomalous metal state, the longitudinal resistivity linearly depends on the field while the Hall resistivity diminishes, indicating an emergent particle-hole symmetry. The universal behavior highlights the uniqueness of the quantum bosonic metallic state, distinct from bosonic insulators and vortex liquids.

Sign in / Sign up

Export Citation Format

Share Document