A simple method of interpreting dipole resistivity soundings

Geophysics ◽  
1987 ◽  
Vol 52 (10) ◽  
pp. 1412-1417 ◽  
Author(s):  
Sri Niwas ◽  
M. Israil
Keyword(s):  
Apparent Resistivity ◽  
Forward Modeling ◽  
Computational Method ◽  
Matrix Operator ◽  
Earth Model ◽  
Simple Method ◽  
One Dimensional ◽  
Automatic Interpretation ◽  
Earth Models ◽  
Electrical Sounding

A computational method has been developed based on a linear relationship between apparent resistivity and the kernel function through a matrix operator. Forward modeling of dipole apparent resistivity values over a one‐dimensional layered earth model as well as the inversion of electrical sounding data can be easily accomplished using this matrix operator. For a few two‐layer, three‐layer, and four‐layer earth models, the apparent resistivity values can be calculated quickly and accurately. It is shown that the technique is adaptable to automatic interpretation in both the resistivity and the kernel domains.

Validity of Resolving the 785 km Discontinuity in the Lower Mantle with P′P′ Precursors?

2020 ◽  
Vol 91 (6) ◽  
pp. 3278-3285
Author(s):  
Baolong Zhang ◽  
Xiangfang Zeng ◽  
Jun Xie ◽  
Vernon F. Cormier
Keyword(s):  
Lower Mantle ◽  
Forward Modeling ◽  
Earth Model ◽  
Frequency Content ◽  
Waveform Data ◽  
Mantle Discontinuities ◽  
The Earth ◽  
Earth Models ◽  
Beamforming Technique ◽  
Ray Paths

Abstract P ′ P ′ precursors have been used to detect discontinuities in the lower mantle of the Earth, but some seismic phases propagating along asymmetric ray paths or scattered waves could be misinterpreted as reflections from mantle discontinuities. By forward modeling in standard 1D Earth models, we demonstrate that the frequency content, slowness, and decay with distance of precursors about 180 s before P′P′ arrival are consistent with those of the PKPPdiff phase (or PdiffPKP) at epicentral distances around 78° rather than a reflection from a lower mantle interface. Furthermore, a beamforming technique applied to waveform data recorded at the USArray demonstrates that PKPPdiff can be commonly observed from numerous earthquakes. Hence, a reference 1D Earth model without lower mantle discontinuities can explain many of the observed P′P′ precursors signals if they are interpreted as PKPPdiff, instead of P′785P′. However, this study does not exclude the possibility of 785 km interface beneath the Africa. If this interface indeed exists, P′P′ precursors at distances around 78° would better not be used for its detection to avoid interference from PKPPdiff. Indeed, it could be detected with P′P′ precursors at epicentral distances less than 76° or with other seismic phases such as backscattered PKP·PKP waves.

scholarly journals Magnetic dipole source TEM all-time apparent resistivity one-dimensional forward modeling and optimization calculation

2020 ◽  
Vol 194 ◽  
pp. 05054
Author(s):  
Zhongyuan Sun ◽  
Qingxin Meng
Keyword(s):  
Time Domain ◽  
Apparent Resistivity ◽  
Forward Modeling ◽  
Full Time ◽  
One Dimensional ◽  
Halley’S Method ◽  
Transient Electromagnetic ◽  
Optimization Calculation ◽  
Halley's Method ◽  
The Moment

Carrying out the forward modeling and one-dimensional apparent resistivity optimization calculation of TEM(transient electromagnetic method), theoretically verifies the the possibility that obtains the apparent resistivity in the full time domain under the condition of multiple offsets. By calculating the second derivative, Halley’s method can accelerate the iteration and make the function converge. The moment, offset and apparent resistivity are controlled by variable method. Halley’s method is used to iterate the moment, offset and apparent resistivity for completing the optimization calculation. In this paper, a conclusion will be finally drawn that the multi-offset TEM can get the apparent resistivity in the full time domain.

A convenient formulation of Sadowsky's model for elastic ribbons

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Sébastien Neukirch ◽  
Basile Audoly
Keyword(s):  
Differential Equations ◽  
Constitutive Relation ◽  
Classical Problem ◽  
Constitutive Law ◽  
System Of Differential Equations ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Aspect Ratios ◽  
Nonlinear Constitutive Relation

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

Effective Shear Area in One Dimensional Ship Hull Finite Element Models to Predict Natural Frequencies of Vibration

2013 ◽  
Author(s):  
Osvaldo Pinheiro de Souza e Silva ◽  
Severino Fonseca da Silva Neto ◽  
Ilson Paranhos Pasqualino ◽  
Antonio Carlos Ramos Troyman
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Numerical Results ◽  
Computational Method ◽  
Scale Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Shear Area

This work discusses procedures used to determine effective shear area of ship sections. Five types of ships have been studied. Initially, the vertical natural frequencies of an acrylic scale model 3m in length in a laboratory at university are obtained from experimental tests and from a three dimensional numerical model, and are compared to those calculated from a one dimensional model which the effective shear area was calculated by a practical computational method based on thin-walled section Shear Flow Theory. The second studied ship was a ship employed in midshipmen training. Two models were made to complement some studies and vibration measurements made for those ships in the end of 1980 decade when some vibration problems in them were solved as a result of that effort. Comparisons were made between natural frequencies obtained experimentally, numerically from a three dimensional finite element model and from a one dimensional model in which effective shear area is considered. The third and fourth were, respectively, a tanker ship and an AHTS (Anchor Handling Tug Supply) boat, both with comparison between three and one dimensional models results out of water. Experimental tests had been performed in these two ships and their results were used in other comparison made after the inclusion of another important effect that acts simultaneously: the added mass. Finally, natural frequencies experimental and numerical results of a barge are presented. The natural frequencies numerical results of vertical hull vibration obtained from these approximations of effective shear areas for the five ships are finally discussed.

scholarly journals Viscous Effects in the Solid Earth Response to Modern Antarctic Ice Mass Flux: Implications for Geodetic Studies of WAIS Stability in a Warming World

2020 ◽  
Vol 33 (2) ◽  
pp. 443-459 ◽  
Author(s):  
E. Powell ◽  
N. Gomez ◽  
C. Hay ◽  
K. Latychev ◽  
J. X. Mitrovica
Keyword(s):  
Mass Flux ◽  
Crustal Deformation ◽  
Earth Model ◽  
Elastic Model ◽  
West Antarctica ◽  
Viscous Effects ◽  
Quarter Century ◽  
Viscosity Models ◽  
Earth Models ◽  
Warming World

AbstractThe West Antarctic Ice Sheet (WAIS) overlies a thin, variable-thickness lithosphere and a shallow upper-mantle region of laterally varying and, in some regions, very low (~1018 Pa s) viscosity. We explore the extent to which viscous effects may affect predictions of present-day geoid and crustal deformation rates resulting from Antarctic ice mass flux over the last quarter century and project these calculations into the next half century, using viscoelastic Earth models of varying complexity. Peak deformation rates at the end of a 25-yr simulation predicted with an elastic model underestimate analogous predictions that are based on a 3D viscoelastic Earth model (with minimum viscosity below West Antarctica of 1018 Pa s) by ~15 and ~3 mm yr−1 in the vertical and horizontal directions, respectively, at sites overlying low-viscosity mantle and close to high rates of ice mass flux. The discrepancy in uplift rate can be reduced by adopting 1D Earth models tuned to the regional average viscosity profile beneath West Antarctica. In the case of horizontal crustal rates, adopting 1D regional viscosity models is no more accurate in recovering predictions that are based on 3D viscosity models than calculations that assume a purely elastic Earth. The magnitude and relative contribution of viscous relaxation to crustal deformation rates will likely increase significantly in the next several decades, and the adoption of 3D viscoelastic Earth models in analyses of geodetic datasets [e.g., Global Navigation Satellite System (GNSS); Gravity Recovery and Climate Experiment (GRACE)] will be required to accurately estimate the magnitude of Antarctic modern ice mass flux in the progressively warming world.

scholarly journals Predicting one-dimensional compression of tire derived aggregate using a simple method

2019 ◽  
Vol 59 (5) ◽  
pp. 1292-1301
Author(s):  
Yaolin Yi ◽  
Chao Kang ◽  
Alireza Bayat
Keyword(s):  
Simple Method ◽  
One Dimensional ◽  
Tire Derived Aggregate

scholarly journals A Simple Method to Determine Critical Coagulation Concentration from Electrophoretic Mobility

2020 ◽  
Vol 4 (2) ◽  
pp. 20 ◽  
Author(s):  
Marco Galli ◽  
Szilárd Sáringer ◽  
István Szilágyi ◽  
Gregor Trefalt
Keyword(s):  
Electrophoretic Mobility ◽  
Dlvo Theory ◽  
Computational Method ◽  
Particle Aggregation ◽  
Critical Coagulation Concentration ◽  
Simple Method ◽  
Interparticle Forces ◽  
Mobility Data ◽  
Key Parameter ◽  
Multivalent Electrolytes

Critical coagulation concentration (CCC) is a key parameter of particle dispersions, since it provides the threshold limit of electrolyte concentrations, above which the dispersions are destabilized due to rapid particle aggregation. A computational method is proposed to predict CCC values using solely electrophoretic mobility data without the need to measure aggregation rates of the particles. The model relies on the DLVO theory; contributions from repulsive double-layer forces and attractive van der Waals forces are included. Comparison between the calculated and previously reported experimental CCC data for the same particles shows that the method performs well in the presence of mono and multivalent electrolytes provided DLVO interparticle forces are dominant. The method is validated for particles of various compositions, shapes, and sizes.

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