共查询到20条相似文献，搜索用时 15 毫秒
1.
An algorithm for determining the area of a spherical polygon of arbitrary shape is presented. The kernel of the problem is to compute the interior angle at each vertex of the spherical polygon; a well-known relationship between the area of a spherical polygon and the sum of its interior angles then may be exploited. The algorithm has been implemented as a FORTRAN subroutine and a listing is provided. Both algorithm and subroutine are general in their capabilities and can be used, for example, to determine the area of a spherical polygon containing one or more holes. 相似文献
2.
M. D. Sharma 《Journal of Earth System Science》2005,114(4):401-410
The three dimensional scattering of near-field, from a point source, is studied for acceleration in the time domain. The perturbation
method is applied to define the acceleration for the first order scattering from a weak inhomogeneity in a homogeneous surrounding.
A body force, arising from the interaction between the primary waves and the inhomogeneity, acts as the source generating
the scattered motion. The acceleration of scattered waves is related to the velocity and density fluctuations of the inhomogeneity.
No restrictions are placed on the inhomogeneity size or locations of the source and receiver. Decoupling of scattered motion
enables the identification of different phases. Integral expressions are derived for the scattering acceleration due to the
incidence of near-field wave (from an impulsive point force) at a radially inhomogeneous volume element. These integrals are
solved further for scattering from an inhomogeneous spherical shell. The accelerations for back scattering are obtained as
a special case. These accelerations are simple analytically solvable expressions in closed form.
Only spherical asymmetry ofP wave velocity inhomogeneity can affect the scatteredS acceleration. ScatteredP acceleration is affected by the gradient ofS wave velocity inhomogeneity. The back scattering of near-field from a spherical shell, is independent of radial inhomogeneity
ofP wave velocity. Inhomogeneity with smoothly perturbedS wave velocity does not back-scatter any acceleration. Accelerations are computed numerically for scattering from a part of
inhomogeneous spherical shell. Hypothetical models are considered to study the effects of the distances of spherical shell
from source, receiver, its thickness and its position relative to the direction of impulsive force. 相似文献
3.
M. D. Sharma 《Journal of Earth System Science》2001,110(3):205-213
Perturbations in elastic constants and density distinguish a volume inhomogeneity from its homogeneous surroundings. The equation
of motion for the first order scattering is studied in the perturbed medium. The scattered waves are generated by the interaction
between the primary waves and the inhomogeneity. First order scattering theory is modified to include the source term generating
the primary waves. The body force equivalent to the scattering source is presented in a convenient form involving the perturbations
in wave velocities and gradient of density perturbation.
A procedure is presented to study the scattering of a spherical pulse from a small inhomogeneity, in time domain. The size
of inhomogeneity is assumed small as compared to its distance from source and receiver. No restrictions are placed on the
positions of source, receiver and inhomogeneity. The dilatation and rotations are calculated for a pulse scattered from an
arbitrary point in a spherical volume. The aggregate of the scattered phases from all the points of the inhomogeneity, reaching
at a fixed receiver, gives the amount of scattering from the inhomogeneity. The interaction of bothP andS waves with inhomogeneity are considered. Dilatation and rotations for scattering are obtained as integral expressions over
the solid angle of inhomogeneity. These expressions are computed numerically, for hypothetical models. The effects of source
(unit force) orientations, velocity and density perturbations, and size of inhomogeneity, on the scattered phases, are discussed. 相似文献
4.
M. D. Sharma 《Journal of Earth System Science》2004,113(2):247-257
Three dimensional scattering of near-field is studied for dilatation and rotation in the time domain. The perturbation method
is applied to solve the equation of motion for the first order scattering from a weak inhomogeneity in an otherwise homogeneous
medium. The inhomogeneity is assumed close enough to the point source so that the near-field intermediate wave is dominating
over the far-field sphericalP andS pulses. The integral expressions are derived to relate dilatation and rotation of scattering to the radial fluctuations of
velocities and density in the inhomogeneity. These integrals are solved to calculate the strains of scattering from (a part
of) an inhomogeneous spherical shell of arbitrary curvature. Variable curvature may allow the shape of inhomogeneity volume
element to change uniformly from spherical to rectangular. Rotation of scattering from a spherical shell is independent ofP wave velocity inhomogeneity. Dilatation of scattering does not involveS wave velocity inhomogeneity but its gradient. The back scattering results are obtained as a special case. Strains are computed
numerically, for hypothetical models to study the effects of various parameters viz., velocity inhomogeneity, distance of
source from inhomogeneity and from receiver, and thickness of inhomogeneity. The curvature of the spherical shell is varied
to study the effects of the shape of inhomogeneous volume element on scattering. 相似文献
5.
Ross M. Renner 《Mathematical Geology》1995,27(4):485-497
If a geochemical compositional dataset
X (n×p)is a realization of a physical mixing process, then each of its sample (row) vectors will approximately be a convex combination (mixture) of a fixed set of (l×p)extreme compositions termed endmembers. The kpoints in p-space corresponding to a specified set of k (klinearly independent endmember estimates associated with a p-variate (n×p)compositional dataset
X,define the vertices of a (k–1)dimensional simplex
H.The nestimated mixtures
X (n×p)which together account for the systematic variation in the dataset
X,should each be convex combinations of the kfixed endmember estimates. Accordingly,the npoints in p-space which represent these mixtures should be interior points of the simplex
H.Otherwise, for each sample point which lies outside
H,at least one of the mixture coefficients (endmember contributions) will be negative. The purpose of this paper is to describe procedures for expanding
H
in the situation that its vertices are not a set of extreme points for the set which represents the mixtures. 相似文献
6.
The dynamic response due to a spherical source of radius a embedded in an elastic and viscoelastic full-space is investigated at a distance R from the source. Previous solutions to the elastic case are extended to incorporate realistic source pressure functions. The elastic solution is then cast in a scale independent form in order to generalize the application. The results show that the near-field of the spherical source may be defined by R/a < 5. For this region the particle velocity and displacement decrease as R?2, and the risetime decreases as R?1. However. in the far-field region (R/a > 5) the particle velocity and displacement decrease as R?1, and the risetime is independent of R. A non-constant Q model is developed to model viscoelastic attenuation and a complete analytical solution for wave propagation is obtained by cascading the separate mechanisms of geometric attenuation and viscoelastic attenuation. A comparison of our analytical model with the results of dynamic finite element modelling shows excellent agreement. This suggests that the method of cascading the separate transfer functions is a valid approach for wave propagation in viscoelastic media. 相似文献
7.
8.
The Feiran–Solaf metamorphic belt consists of low-P high-T amphibolite facies, partly migmatized gneisses, schists, amphibolites and minor calc-silicate rocks of metasedimentary origin. There are also thick concordant synkinematic sheets of diorite, tonalite and granodiorite orthogneiss and foliated granite and pegmatite dykelets. The gneissosity (or schistosity) is referred to as S1, and is almost everywhere parallel to lithological layering, S0. This parallelism is not due to transposition. The gneissosity formed during an extensional tectonic event (termed D1), before folding of S0. S1 formed by coaxial pure shear flattening strain (Z normal to S0, i.e. vertical; with X and Y both extensional and lying in S1). This strain also produced chocolate tablet boudinage of some layers and S1-concordant sills and veins. S1 has a strong stretching lineation L1 with rodding characteristics. Within-plane plastic anisotropy (lower ductility along Y compared to along X) resulted in L1-parallel extensional ductile shears and melt filled cracks. Continued shortening of these veins, and back-rotation of foliations on the shears produced intrafolial F1 folds with hinges parallel to the stretching lineation. F1 fold asymmetry variations do not support previous models involving macroscopic F1 folds or syn-gneissosity compressional tectonics. The sedimentary protoliths of the Feiran–Solaf gneisses were probably deposited in a pre-800 Ma actively extending intracratonic rift characterizing an early stage of the break-up of Rodinia. 相似文献
9.
Structural relaxation in silicate melts and non-Newtonian melt rheology in geologic processes 总被引：4，自引：0，他引：4
The timescale of structural relaxation in a silicate melt defines the transition from liquid (relaxed) to glassy (unrelaxed) behavior. Structural relaxation in silicate melts can be described by a relaxation time, , consistent with the observation that the timescales of both volume and shear relaxation are of the same order of magnitude. The onset of significantly unrelaxed behavior occurs 2 log10 units of time above . In the case of shear relaxation, the relaxation time can be quantified using the Maxwell relationship for a viscoelastic material; S = S/G
(where S is the shear relaxation time, G
is the shear modulus at infinite frequency and S is the zero frequency shear viscosity). The value of G
known for SiO2 and several other silicate glasses. The shear modulus, G
, and the bulk modulus, K
, are similar in magnitude for every glass, with both moduli being relatively insensitive to changes in temperature and composition. In contrast, the shear viscosity of silicate melts ranges over at least ten orders of magnitude, with composition at fixed temperature, and with temperature at fixed composition. Therefore, relative to S, G
may be considered a constant (independent of composition and temperature) and the value of S, the relaxation time, may be estimated directly for the large number of silicate melts for which the shear viscosity is known.For silicate melts, the relaxation times calculated from the Maxwell relationship agree well with available data for the onset of the frequency-dependence (dispersion) of acoustic velocities, the onset of non-Newtonian viscosities, the scan-rate dependence of the calorimetric glass transition, with the timescale of an oxygen diffusive jump and with the Si-O bond exchange frequency obtained from 29Si NMR studies. 相似文献
10.
Daniel Mikeš 《Mathematical Geosciences》2011,43(5):593-606
Natural flocs in an estuary grow with increasing time, salinity, suspended particulate matter concentration, and with decreasing
turbulence. Although various theoretical and empirical functions for floc growth have been proposed in the literature, they
are all complex. It is argued in this study that there should be a simple and general function of floc size D against time t, salinity S, suspended particulate matter concentration C, microscale η, and biochemical composition M. Theory and experiments seem to corroborate that average floc size responds systematically to its drivers. Moreover, the
response is partly similar to all drivers: a lower plateau followed by a rise, and partly different: an upper plateau for t, S and a fall for C, η. Assuming drivers are independent, each curve is normalized around its rise. The drivers are joined into one variable X that holds each normalized driver with equal weight. The result is a function that gives floc size against this composite
variable X. This composite variable in turn is a function of ambient conditions and the function predicts floc size for any set of ambient
conditions. The case is presented here using linear segments, but eventually the logistic growth function is proposed. 相似文献
11.
F. J. Bloore 《Mathematical Geology》1977,9(2):113-122
A theory of pebble erosion is presented, based on the assumption that the rate of erosion at a point on the surface is a function Vof the curvature there. It is proved that for physically reasonable functions V,the sphere is the only shape of pebble which can maintain its proportions as it wears away. An argument is given which leads
to a particular form for the function Vand a few qualitative consequences of this form are indicated. The surface of the pebble at time tmay be described using spherical polar coordinates θ, Φ by the radius function r (θ, Φ, t). This function is given by a highly nonlinear partial differential equation. However, in the case of the erosion
of a deformed sphere, when terms which are of second order or higher in the deformation are neglected, the equation becomes
linear and is a version of the diffusion equation. The stability of the spherical shape against deformations of the various
harmonic types is then easily analyzed. 相似文献
12.
Katsuhiro Tsukimura Hiromoto Nakazawa Tadashi Endo Osamu Fukunaga 《Physics and Chemistry of Minerals》1992,19(4):203-212
This paper describes the distribution of Fe and Ni between the octahedral and tetrahedral sites in pentlandite (Fe,Ni)9S8. The dependence of the distribution on pressure and temperature and the activation energy of the cation exchange reaction were determined through annealing experiments. Synthetic crystals were annealed at 433–723 K and pressures up to 4 GPa, and natural crystals were annealed at 423, 448 and 473 K in evacuated silica capillary tubes for various durations. The cation distributions in the synthetic crystals were determined with an X-ray powder method employing the anomalous dispersion effect of CuK. and FeK radiations, while those of natural crystals were calculated from the cell dimensions. The values of U, S and V for the Fe/Ni exchange reaction are –6818 J mol–1, 20.52 J K–1 mol–1, and 6.99 × 10–6 m3 mol–1, respectively. The dependence of the Fe/Ni distribution on pressure (Pa) and temperature (Kelvin) was determined as lnK = 2.47+8.20 × 102
T
–1+8.41 x 10–7
T
–1
P, where K = (Fe/Ni)octahedral /(Fe/Ni)tetrahedral. The activation energy of the cation exchange reaction was 185 kJ mol–1. 相似文献
13.
An eigenmethod for characterising the directional properties of convex polygons is described. Given a polygon, regular in the undeformed state, its image following a homogeneous strain transformation is an irregular polygon whose eigensolution (an ellipse) has the axis ratio and orientation of the strain ellipse. The eigenmethod can therefore be used for finite strain estimation using polygonal strain markers, and is compared with alternative methods recently proposed by Roder (1977) and Sanderson (1977). 相似文献
14.
Voronoi, or area-of-influence, polygons are convex, space-filling polygons constructed around a set of points (Voronoi centers) such that each polygon contains all points closer to its Voronoi center than to the center of any other polygon. The relationship of Voronoi centers to edges of Voronoi polygons is used to test whether any convex tessellation consists of Voronoi polygons. This test amounts to finding Voronoi centers that best fit the given tessellation. Voronoi centers are found by solving two systems of linear equations. These equations represent (1) conditions on the slope of polygon edges relative to the slope of lines through Voronoi centers, and (2) conditions on the distance from edges to Voronoi centers. Least squares and constrained least-squares solutions are used to solve the two systems. Different methods of solution can provide insight as to how a tessellation varies from Voronoi polygons. A goodness-of-fit statistic is derived and examined by testing randomly generated convex tessellations. Some polygonal ice cracks provide an example of naturally occurring polygons that are approximated closely by Voronoi polygons. 相似文献
15.
The occurrence of critical assemblages among antigorite, diopside, tremolite, forsterite, talc, calcite, dolomite and magnesite in progressively metamorphosed ophicarbonate rocks, together with experimental data, permits the construction of phase diagrams in terms of the variables P, T, and composition of a binary CO2-H2O fluid. Equilibrium constants are given for the 30 equilibria that describe all relations among the above phases. Ophicalcite, ophidolomite, and ophimagnesite assemblages occupy partially overlapping fields in the
diagram. The upper temperature limit of ophicalcite rocks lies below that of ophidolomite and ophimagnesite. The fluid phase in ophicarbonate rocks has
0.8$$
" align="middle" border="0">
, and there are indications that
during their progressive metamorphism is approximately equal to P
total. 相似文献
16.
Earth curvature effects on subduction morphology: Modeling subduction in a spherical setting 总被引：1，自引：0，他引：1
Gabriele Morra Philippe Chatelain Paul Tackley Petros Koumoutsakos 《Acta Geotechnica》2009,4(2):95-105
We present the first application in geodynamics of a (Fast Multipole) Accelerated Boundary Element Method (Accelerated-BEM)
for Stokes flow. The approach offers the advantages of a reduced number of computational elements and linear scaling with
the problem size. We show that this numerical method can be fruitfully applied for the simulation of several geodynamic systems
at the planetary scale in spherical coordinates, and we suggest a general approach for modeling combined mantle convection
and plate tectonics. The first part of the paper is devoted to the technical exposition of the new approach, while the second
part focuses on the effect played by Earth curvature on the subduction of a very wide oceanic lithosphere (W = 6,000 km and W = 9,000 km), comparing the effects of two different planetary radii (ER = 6,371 km, 2ER = 2 × 6,371 km), corresponding to
an "Earth-like" model (ER) and to a "flat Earth" one (2ER). The results show a distinct difference between the two models:
while the slab on a "flat Earth" shows a slight undulation, the same subducting plate on the "Earth-like" setting presents
a dual behavior characterized by concave curvature at the edges and by a folding with wavelength of the order of magnitude
of 1,000 km at the center of the slab. 相似文献
17.
The junctions of cracks in mudcrack, patterned ground, and columnar joint patterns can be categorized into Y, T,and Xtypes. The mean number of sides,
,to the polygonal areas in such nets is
= 2(2JT + 3JY + 4JX)/(JT + JY + 2JX)where JT, JY,and JX
are the proportions of T, Y,and Xjunctions, respectively. 相似文献
18.
Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests 
下载免费PDF全文
下载免费PDF全文 The strength parameter mi in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between mi and the physical characteristics of intact rock, this paper presents a systematic study of mi by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on mi. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on mi. The strength parameter mi increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter mi, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
G. D. Gwanmesia J. Liu G. Chen S. Kesson S. M. Rigden R. C. Liebermann 《Physics and Chemistry of Minerals》2000,27(7):445-452
Dense isotropic polycrystalline specimens of majorite-rich garnets (Py100, Py62Mj38, Py50Mj50, Py21Mj79 and Mj100) along the pyrope (Mg3Al2Si3O12 = Py100)-majorite (MgSiO3 = Mj100) join were fabricated in a 2000-ton uniaxial split-sphere anvil apparatus (USSA-2000) at pressures from 10 to 18.5 GPa and
temperatures from 1200 to 1850 °C, within their stability fields in runs of 2–4-h duration, using hot-pressing techniques
developed by Gwanmesia et al. (1993). These specimens are single-phased, fine-grained (≤5 mm), free of microcracks, and have
bulk densities greater than 99% of the corresponding single-crystal X-ray density. Elastic compressional (P) and shear (S) wave velocities were determined at room pressure and temperature for these polycrystalline garnet specimens by phase comparison
ultrasonic interferometry. For Mj100, the P and S wave velocities are within 1% of the Hashin-Shtrikman averages calculated from the single crystal elastic moduli measured
by Brillouin spectroscopy. Both the elastic bulk modulus (K) and the shear modulus (G) decrease continuously with increasing majorite content from pyrope garnet (Py100) to pure majorite garnet (Mj100). The compositional dependence of K and G are given by K = 172.3 (40) − 0.085X, and G = 91.6 (10) − 0.038X, where X = mol% majorite), respectively, indicating that substitution of Si for Mg and Al decreases both K and G by about 5% along the solid solution series.
Received: 25 March 1999 / Accepted: 12 July 1999 相似文献