Zdeněk Martinec

Higher-degree reference field in the generalized Stokes-Helmert scheme for geoid computation

In this paper we formulate two corrections that have to be applied to the higher-degree reference spheroid if one wants to use it in conjunction with the Stokes-Helmert scheme for geoid determination. We show that in a precise geoid determination one has to apply the correction for the residual topographical potential and the correction for the earth ellipticity. Both these corrections may reach several decimetres; we show how their magnitudes vary within Canada and we give their global ranges.

Is the long‐wavelength geoid sensitive to the presence of postperovskite above the core‐mantle boundary?

[1] The analysis of seismic data represents today the primary tool in the search for the presence of postperovskite in the lowermost mantle (D 00 ). This work aims at testing whether the inversion of gravitational data can also contribute to the detection of postperovskite in D 00 .W e assume that the transition from perovskite to postperovskite is accompanied by a reduction in viscosity and test the effects of such viscosity change on the prediction of the dynamic geoid with a numerical model of subducted lithosphere. Our results show that the long-wavelength component of the geoid is very sensitive to the presence of postperovskite areas in D 00 , especially if their viscosity is significantly lower than the viscosity of the surrounding perovskite and if these areas are located close to density � � � � � � � � � � � � � � � � � � � � � ��

Glacial-isostatic Adjustment and the Viscosity Structure Underlying the Vatnajökull Ice Cap, Iceland

We examine the dependence of glacial-isostatic adjustment (GIA) due to changes in the Vatnajokull Ice Cap, Iceland, on the underlying viscosity structure. Iceland offers a unique case study for GIA research, with a thinner elastic lithosphere underlain by a low-viscosity zone or asthenosphere, as opposed to regions such as Fennoscandia or North America described by a thicker lithosphere, while not necessarily featuring an asthenosphere.

Expansion of geoid heights over a triaxial earth's ellipsoid into a spherical harmonic series

РезюмеВыво¶rt;umся aлорumм ¶rt;ля вычuсленuяaрмонuческuх коэффuцuенmов в рaзложенuu рa¶rt;uус-векmорaеоu¶rt;a в ря¶rt; nо сферuческuм функцuям nуmем лuнеŭноо обрaщенuяaрмонuческоо ря¶rt;a ¶rt;ляеоnоmенцuaлa. Ощuбкa uз-зa лuнеaрuзaцuu nоря¶rt;кa кубa сжamuя Землu.

Program to calculate the spectral harmonic expansion coefficients of the two scalar fields product

Abstract A program to compute the spectral harmonic expansion coefficients of the product of two triangular truncated scalar fields is presented. The calculations are performed by a transform method which is more computer efficient relative to the traditional interaction coefficient approach or finite-difference method.

The Phobos Gravitational Field Modeled on the Basis of its Topography

The parameters of the best-fitting ellipsoid have been derived using the latest spherical harmonics of the Phobos topography (Duxbury, 1989) by solution of non-linear overdetermined inverse problem. The lengths of the equatorial axes of the ellipsoid have been determined (a = 12.9 km, b = 11.4 km). They are nearly the same as established by Duxbury (ibid.) on the basis of the linearized relationship between the squared lengths of ellipsoidal axes and the topography coefficients C20 and C22. The length of the polar axis (c = 9.1 km) differs of about 20% from Duxburys value. Supposing mass homogeneity of Phobos, the Stokes parameters of the external gravitational field have been derived up to those of the sixth degree and order. The large irregularities in the Phobos figure cause the values of the Duxburys potential coefficients be fairly inaccurate except the harmonics C20, C32, S43 and S51, i.e. linearized relationship between gravity and topography cannot be applied for Phobos. Finally, positions of the centre of figure and the directions of the principal axes of inertia have been established.

A model of compensation of topographic masses

The compilation of new global Mohorovičić (‘Moho’) topographic data enables the density contrast between the crust and mantle to be estimated. Assuming that this contrast is constant, the minimization of the external gravitational potential induced by the Earths topographic masses and the Moho discontinuity yields the value of 0.28 g/cm3 for the density jump at the Moho. Moreover, it is shown that the Airy Heiskanen model of compensation only partly compensates the surface topographic masses. To fit the external gravitational potential, induced by the surface topography, the Pratt-Hayford concept of compensation has to be considered. Employing the dynamical flattening of the Earth, the minimum depth of compensation has been estimated at 100–150 km. This means that the topographic masses are compensated throughout the Earths lithosphere at least.

Spectral variational approach to the non-Newtonian stokes problem in a spherical shell

Abstract A hybrid-variational formulation of the Stokes equation for incompressible non-Newtonian flow is suggested. A spherical harmonic technique is adopted to discretize the problem. In the case of non-Newtonian rheology, the energy functional becomes non-quadratic. To minimize it on the set of admissible stress-functions, the gradient method is used and the convergence of the method is demonstrated.

Program to calculate the least-squares estimates of the spherical harmonic expansion coefficients of an equally angular-gridded scalar field

Abstract The program SPHAN estimates the spherical harmonic coefficients of a scalar field by least-square fitting of data values measured on an equal angular grid on a globe.

Matrix approach to the solution of electromagnetic induction in a spherically layered earth

РезюмеВыве¶rt;ены мамрuчные формулы ¶rt;ля наnряженносмu nолеŭ магнuмного u элекмрuческого мuna. С nомощью эмuх формул nре¶rt;смаавлены: кажущееся соnромuвленuе, функцuя омклuка u макже часмомное уравненuе, оnре¶rt;еляющее часмомы собсмвенных колебанuŭ соомвемсмвующuх волн. Пре¶rt;ложен бысмрыŭ aлгорuмм ¶rt;ля чuсленного расчема функцuŭ омклuка u кажущегося соnромuвленuя.SummaryMatrix formulae for the intensities of the M- and E-fields have been derived. They have been applied to express the apparent resistivity, the transfer function, as well as the frequency equation determining the frequencies of free motion of the M- and E-waves. A fast algorithm for computing the transfer function and the apparent resistivity has been suggested.