On: “Inversion of gravity profiles by use of a Backus‐Gilbert approach” by William R. Green (GEOPHYSICS, October 1975, p. 763–772).

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 777-777
Author(s):  
Ramesh Chander
Keyword(s):  
Gravity Anomaly ◽  
Total Mass ◽  
Gravity Data ◽  
Unit Length ◽  
Three Dimensional ◽  
Density Model ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Mass Excess ◽  
Seminal Paper

An important possible constraint on a density model obtained from inversion of gravity data has been overlooked in the seminal paper by Green. The computed density model should be such that the corresponding total mass excess or deficit per unit length in a two‐dimensional case, or total mass excess or deficit in a three‐dimensional case, should be comparable to the value obtained by applying Gauss’s theorem to the observed gravity anomaly data (Grant and West, 1965, p. 227–28 and p. 232).

scholarly journals Identification of local sesars of tejakula buleleng bali with anomaly gravity data using second vertical derivative method

2020 ◽  
Vol 3 (1) ◽  
pp. 18-25
Author(s):  
Komang Ngurah Suarbawa ◽  
I Gusti Agung Putra Adnyana ◽  
Elvin Riyono
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Three Dimensional ◽  
Fault Model ◽  
Two Dimensional ◽  
Upward Trend ◽  
Gravity Method ◽  
Vertical Derivative ◽  
Subsurface Structures ◽  
Derivative Method

Research has been carried out related to subsurface structures in the Tejakula Buleleng Bali area and its surroundings using the gravity method. This study aims to identify the local Tejakula fault. The data used in this study is gravity anomaly data obtained from observations of Geodetic Satellite (GEOSAT). The method used in interpreting the type of disturbance uses the Second Vertical Derivative method, which then produces two-dimensional (2D) and three-dimensional (3D) fault model interpretations. Based on the results obtained in the study, the condition of the bouguer gravity anomaly value in the Tejakula area and its surroundings at the research location is in the range of 65 mGal to 185 mGal. Meanwhile, based on the Second Vertical Derivative method in determining the type of fault, the Tejakula Fault can be categorized as a mandatory fault with an upward trend.

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

scholarly journals Basin Depth Mapping Beneath Wellington City Based on Residual Gravity Anomalies

2021 ◽  
Author(s):  
◽  
Alistair Stronach
Keyword(s):  
Gravity Anomaly ◽  
Sedimentary Basin ◽  
Gravity Data ◽  
Three Dimensional ◽  
Maximum Amplitude ◽  
Central Business District ◽  
Gravity Anomalies ◽  
Depth Map ◽  
Capital City ◽  
Detailed Knowledge

<p><b>New Zealand’s capital city of Wellington lies in an area of high seismic risk, which is further increased by the sedimentary basin beneath the Central Business District (CBD). Ground motion data and damage patterns from the 2013 Cook Strait and 2016 Kaikōura earthquakes indicate that two- and three-dimensional amplification effects due to the Wellington sedimentary basin may be significant. These effects are not currently accounted for in the New Zealand Building Code. In order for this to be done, three-dimensional simulations of earthquake shaking need to be undertaken, which requires detailed knowledge of basin geometry. This is currently lacking, primarily because of a dearth of deep boreholes in the CBD area, particularly in Thorndon and Pipitea where sediment depths are estimated to be greatest.</b></p> <p>A new basin depth map for the Wellington CBD has been created by conducting a gravity survey using a modern Scintrex CG-6 gravity meter. Across the study area, 519 new high precision gravity measurements were made and a residual anomaly map created, showing a maximum amplitude anomaly of -6.2 mGal with uncertainties better than ±0.1 mGal. Thirteen two-dimensional geological profiles were modelled to fit the anomalies, then combined with existing borehole constraints to construct the basin depth map. </p> <p>Results indicate on average greater depths than in existing models, particularly in Pipitea where depths are interpreted to be as great as 450 m, a difference of 250 m. Within 1 km of shore depths are interpreted to increase further, to 600 m. The recently discovered basin bounding Aotea Fault is resolved in the gravity data, where the basement is offset by up to 13 m, gravity anomaly gradients up to 8 mGal/km are observed, and possible multiple fault strands identified. A secondary strand of the Wellington Fault is also identified in the north of Pipitea, where gravity anomaly gradients up to 18 mGal/km are observed.</p>

On the Hydrodynamic Interaction Between Ship and Free-Surface Motions on Vessels With Moonpools

2019 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Linear Potential ◽  
Two Dimensional ◽  
Sloshing Mode ◽  
Vessel Motion

Abstract Coupling between moonpool resonance and vessel motion is investigated in two-dimensional and quasi three-dimensional settings, where the models are studied in forced heave and in freely floating conditions. The two-dimensional setups are with a recess, while the quasi three-dimensional setups are without recess. One configuration with recess is presented for the two-dimensional case, while three different moonpool sizes (without recess) are tested for the quasi three-dimensional setup. A large number of forcing periods, and three wave steepnesses are tested. Boundary Element Method (BEM) and Viscous BEM (VBEM) time-domain codes based on linear potential flow theory, and a Navier–Stokes solver with linear free-surface and body-boundary conditions, are implemented to investigate resonant motion of the free-surface and the model. Damping due to flow separation from the sharp corners of the moonpool inlets is shown to matter for both vessel motions and moonpool response around the piston mode. In general, the CFD simulations compare well with the experimental results. BEM over-predicts the response significantly at resonance. VBEM provides improved results compared to the BEM, but still over-predicts the response. In the two-dimensional study there are significant coupling effects between heave, pitch and moonpool responses. In the quasi three-dimensional tests, the coupling effect is reduced significantly as the moonpool dimensions relative to the displaced volume of the ship is reduced. The first sloshing mode is investigated in the two-dimensional case. The studies show that damping due to flow separation is dominant. The vessel motions are unaffected by the moonpool response around the first sloshing mode.

Pipe Response Under Concentrated Lateral Loads and External Pressure

2005 ◽  
Author(s):  
Spyros A. Karamanos ◽  
Charis Eleftheriadis
Keyword(s):  
Three Dimensional ◽  
External Pressure ◽  
Absorption Capacity ◽  
Pressure Effects ◽  
Analytical Models ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Lateral Loads ◽  
Offshore Pipelines ◽  
Different Levels

The present paper examines the denting deformation of offshore pipelines and tubular members (D/t≤50) subjected to lateral (transverse) quasi-static loading in the presence of uniform external pressure. Particular emphasis is given on pressure effects on the ultimate lateral load of tubes and on their energy absorption capacity. Pipe segments are modeled with shell finite elements, accounting for geometric and material nonlinearities, and give very good predictions compared with test data from non-pressurized pipes. Lateral loading between two rigid plates, a two-dimensional case, is examined first. Three-dimensional case, are also analyzed, where the load is applied either through a pair of opposite wedge-shaped denting tools or a single spherical denting tool. Load-deflection curves for different levels of external pressure are presented, which indicate that pressure has significant influence on pipe response and strength. Finally, simplified analytical models are proposed for the two-dimensional and three-dimensional load configurations, which yield closed-form expressions, compare fairly well with the finite element results and illustrate some important features of pipeline response in a clear and elegant manner.

Optimum profiles in two-dimensional Stokes flow

1995 ◽  
Vol 450 (1940) ◽  
pp. 603-622 ◽  
Keyword(s):  
Circular Cylinder ◽  
Cross Section ◽  
Stokes Flow ◽  
Unit Length ◽  
Three Dimensional ◽  
Variational Formula ◽  
Effective Radius ◽  
Two Dimensional ◽  
Equivalent Radius ◽  
Optimum Profile

We consider the problem of designing the section of a cylinder to minimize the drag per unit length it experiences when placed perpendicular to a uniform stream at low Reynolds number; we suppose the area of the cross-section to be given, and the flow to be two-dimensional. The relevant properties of a cylinder of general cross-section in a particular orientation can conveniently be expressed in terms of its equivalent radius; when the drag and flow at infinity are parallel, this equivalent radius is the radius of the circular cylinder giving rise to the same drag per unit length. We obtain a variational formula for this equivalent radius when the surface of the cylinder is perturbed; this shows that the optimum profile we seek must be such that the flow past it has a vorticity of constant magnitude at its surface, and this fact enables the optimum to be determined analytically. The efficacy of a particular section may be measured by its effective radius, this being the equivalent radius when the length scale is chosen to give the section an area π ; thus a circular cylinder has an effective radius of 1. The minimum possible effective radius, achieved by the optimum profile, is 0.88876. To illustrate some of the arguments we exploit in a more familiar setting, we also obtain a variational formula for the drag on a three-dimensional body in Stokes flow when its surface is perturbed.

Three-dimensional ray tracing and the method of principal curvature for geometric spreading

1983 ◽  
Vol 73 (3) ◽  
pp. 765-780
Author(s):  
Jia-Ju Lee ◽  
Charles A. Langston
Keyword(s):  
Principal Curvature ◽  
Three Dimensional ◽  
Seismic Energy ◽  
Front Surface ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Ray Method ◽  
P Waves ◽  
Curved Boundaries ◽  
Wave Source

abstract A three-dimensional ray method is used to compute three components of ground motion for complex structures involving curved boundaries. The method of principal curvature is developed to compute geometrical spreading of rays. This method, commonly used in electromagnetic wave propagation problems, employs phase matching at model interfaces and analysis of the wave front surface metric as the ray propagates throughout the model. It is an elegant way to examine the characteristics of three-dimensional caustics. Results computed for a two-dimensional canonical basin model with a plane SH-wave source are compared and are found to be in good agreement with those previously obtained by other independent numerical methods. Relaxing the restriction that the incident wave be perpendicular to the basin symmetry axis gives rise to large amplitude vertical and radial motions for incident SH waves and large tangential motions for incident P waves. As in the two-dimensional case, seismic energy is geometrically focused in the central region of the basin but strong later arrivals from the curved boundaries are not well developed in the three-dimensional case. The method is of direct use in analyzing three-dimensional crustal structure from off-azimuth P to S and S to P conversions.

FINDING SIMPLICES CONTAINING THE ORIGIN IN TWO AND THREE DIMENSIONS

2011 ◽  
Vol 21 (05) ◽  
pp. 495-506 ◽  
Author(s):  
KHALED ELBASSIONI ◽  
AMR ELMASRY ◽  
KAZUHISA MAKINO
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Line Segments

We show that finding the simplices containing a fixed given point among those defined on a set of n points can be done in O(n + k) time for the two-dimensional case, and in O(n2 + k) time for the three-dimensional case, where k is the number of these simplices. As a byproduct, we give an alternative (to the algorithm in Ref. 4) O(n log r) algorithm that finds the red-blue boundary for n bichromatic points on the line, where r is the size of this boundary. Another byproduct is an O(n2 + t) algorithm that finds the intersections of line segments having two red endpoints with those having two blue endpoints defined on a set of n bichromatic points in the plane, where t is the number of these intersections.

Release of a viscous power-law fluid over an inviscid ocean

2012 ◽  
Vol 700 ◽  
pp. 63-76 ◽  
Author(s):  
Samuel S. Pegler ◽  
John R. Lister ◽  
M. Grae Worster
Keyword(s):  
Power Law ◽  
Large Time ◽  
Three Dimensional ◽  
Shear Thinning ◽  
Capillary Forces ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Initial Shape ◽  
Algebraic Decay

AbstractWe consider the two- and three-dimensional spreading of a finite volume of viscous power-law fluid released over a denser inviscid fluid and subject to gravitational and capillary forces. In the case of gravity-driven spreading, with a power-law fluid having strain rate proportional to stress to the power $n$, there are similarity solutions with the extent of the current being proportional to ${t}^{1/ n} $ in the two-dimensional case and ${t}^{1/ 2n} $ in the three-dimensional case. Perturbations from these asymptotic states are shown to retain their initial shape but to decay relatively as ${t}^{\ensuremath{-} 1} $ in the two-dimensional case and ${t}^{\ensuremath{-} 3/ (n+ 3)} $ in the three-dimensional case. The former is independent of $n$, whereas the latter gives a slower rate of relative decay for fluids that are more shear-thinning. In cases where the layer is subject to a constraining surface tension, we determine the evolution of the layer towards a static state of uniform thickness in which the gravitational and capillary forces balance. The asymptotic form of this convergence is shown to depend strongly on $n$, with rapid finite-time algebraic decay in shear-thickening cases, large-time exponential decay in the Newtonian case and slow large-time algebraic decay in shear-thinning cases.

Sign in / Sign up

Export Citation Format

Share Document