High-resolution mean sea surface computed with altimeter data of Ers-1 (geodetic mission) and topex-poseidon

The remote-sensing satellite ERS-1, launched in 1991 to study the Earth's environment, was placed on a geodetic (168-day repeat) orbit between 1994 April and 1995 March to map, through altimetric measurements, the gravity field over the whole oceanic domain with a resolution of 8 km at the equator in both along-track and cross-track directions. We have analysed the precise altimeter data of the geodetic mission, and, by also using one year of Topex-Poseidon altimeter data, we have computed a global high-resolution mean sea surface. The various steps involved in pre-processing the ERS-1 data consisted of correcting the data for environmental factors, editing, and reducing, through crossover analyses, the radial orbit error, which directly affects sea-surface height measurements. For this purpose, we adjusted sinusoids at 1 and 2 cycle rev⁻¹ along the ERS-1 profiles in order to minimize crossover differences between ERS-1 and yearly averaged Topex-Poseidon profiles. In effect, the orbit of Topex-Poseidon is very accurately determined (within 2–3 cm for the radial component), so Topex-Poseidon altimeter profiles can serve as a reference to reduce the ERS-1 radial orbit error. The ERS-1 residual orbit error was further reduced through a second crossover analysis between all ascending and descending profiles of the geodetic mission. The along-track ERS-1 and Topex-Poseidon data were then interpolated over the whole oceanic domain on a regular grid of 1/16°× 1/16° size. The mapping of the gridded sea-surface heights reveals the very fine structure of the marine geoid, up until now unknown at a global scale. This new data set will be most useful for marine geophysical and tectonic investigations.     

Fully normalized spherical cap harmonics: application to the analysis of sea-level data from TOPEX/POSEIDON and ERS-1

We introduce two sets of fully normalized harmonics for the spectral analysis of functions defined on a spherical cap. The harmonics are the products of Fourier functions and the fully normalized associated Legendre functions of non-integer degree. Using Sturm-Liouville theory for boundary-value problems, we present two convenient and stable formulae for computing the zeros of the associated Legendre functions that form two sets of orthogonal functions. Formulae for the stable numerical evaluation of the fully normalized associated Legendre functions of non-integer degree that avoid the gamma function are also derived. The result from the expansions of sea-level anomaly from altimetry into Set 2 fully normalized cap harmonics shows fast convergence of the series, and the degree variances decay rapidly without aliasing effects. The zero-degree coefficients (Set 2) of sea-level anomaly from TOPEX/ POSEIDON (T/P) and ERS-1 indicate an El Niño event during 1993 January-1993 July, and a La Niño event during 1993 November-1994 July, although the ERS-1 result is less obvious. Ocean circulations over the South China Sea and the Kuroshio area are clearly identified with the low-degree expansions of sea-surface topography (SST) from T/P and ERS-1. A cold-core eddy of 4° in diameter centred at 17.5°N, 118 E was detected with the expansion of SST from T/P cycle 47, and a property of the cap harmonics is used to compute this eddy's kinetic energy. The kinetic energy is at a low in winter and high in summer, and its variation seems to be periodic with an amplitude of 0.4 m² S^-2.     

Ice flow physical processes derived from the ERS-1 high-resolution map of the Antarctica and Greenland ice sheets

The ERS-1 satellite, launched in 1991, has provided altimetric observations of the Greenland Ice Sheet and 80 per cent of the Antarctica Ice Sheet north of 82°S. It was placed in a geodetic (168-day repeat) orbit between April 1994 and March 1995, yielding a 1.5  km across-track spacing at latitude 70° with a higher along-track sampling of 350  m. We have analysed the waveform altimetric data from this period to compute maps with a 1/30° grid size. Data processing consists of correcting for environmental factors and editing and retracking the waveforms. A further step consists of reducing the radial orbit error through crossover analysis and correcting the slope error to second order. The high-resolution topography of both ice sheets reveals numerous details. A kilometre-scale surface roughness running at 45° from the flow direction is the dominant topographic characteristic of both continents. Antarctica also exhibits many scars due to local flow anomalies. Several physical processes can be identified: abrupt transitions from deformation to sliding and vice versa, and impressive strike-slip phenomena, inducing en echelon folds.     

Moment tensor rate functions from waveforms with non-homogeneous variance

When discussing error estimates of the point-source mechanism and the source time function obtained by the two-step procedure by Šílený, Panza & Campus (1992), the authors insist that in the first step—inversion of seismograms (after Sipkin 1982) to get the moment tensor rate functions (MTRFs)—a homogeneous variance for all the data is needed to keep the advantageous symmetry of the normal equations. We show that this is too strong a requirement and can be dropped.     

Analysis of potential field data in the wavelet domain

Various Green's functions occurring in Poisson potential field theory can be used to construct non-orthogonal, non-compact, continuous wavelets. Such a construction leads to relations between the horizontal derivatives of geophysical field measurements at all heights, and the wavelet transform of the zero height field. The resulting theory lends itself to a number of applications in the processing of potential field data. Some simple, synthetic examples in two dimensions illustrate one inversion approach based upon the maxima of the wavelet transform (multiscale edges). These examples are presented to illustrate, by way of explicit demonstration, the information content of the multiscale edges. We do not suggest that the methods used in these examples be taken literally as a practical algorithm or inversion technique. Rather, we feel that the real thrust of the method is towards physically based, spatially local filtering of geophysical data images using Green's function wavelets, or compact approximations thereto. To illustrate our first steps in this direction, we present some preliminary results of a 3-D analysis of an aeromagnetic survey.     

Numerical aspects of a spline-based multiresolution recovery of the harmonic mass density out of gravity functionals

We show the numerical applicability of a multiresolution method based on harmonic splines on the 3-D ball which allows the regularized recovery of the harmonic part of the Earth's mass density distribution out of different types of gravity data, for example, different radial derivatives of the potential, at various positions which need not be located on a common sphere. This approximated harmonic density can be combined with its orthogonal anharmonic complement, for example, determined out of the splitting function of free oscillations, to an approximation of the whole mass density function. The applicability of the presented tool is demonstrated by several test calculations based on simulated gravity values derived from EGM96. The method yields a multiresolution in the sense that the localization of the constructed spline basis functions can be increased which yields in combination with more data a higher resolution of the resulting spline. Moreover, we show that a locally improved data situation allows a highly resolved recovery in this particular area in combination with a coarse approximation elsewhere which is an essential advantage of this method, for example, compared to polynomial approximation.     

Source ambiguity from an estimation of the scaling exponent of potential field power spectra

An analysis of the field scaling power spectrum yields useful information about the source distribution, but it is uncertain whether deterministic, random, fractal or mixed approaches have to be used for the interpretation. To this end, the scaling properties of potential field spectra are analysed for a number of different source models of geological interest. Besides the models of Naidu (purely random sources) and Spector and Grant (gross block statistical ensembles) we consider other types of density and magnetization distributions with spectral exponents in the fractal range, such as a single homogeneous body with a random white source distribution. Spectral slopes in the fractal range are obtained.
We also study the effects of important natural sources, such as salt domes and sedimentary basins, representing them with simple Gaussians or combinations of Gaussian signals. The same spectral slopes as for gravity signals generated by 3-D fractal source distributions are found for them. Hence the power law decay of the field is not a characteristic only of fractal source models.
If a 3-D fractal source distribution is assumed a priori , a way of verifying the goodness of the model is to examine the whitened field at source level. The probability that the whitened field derives from a random white population is estimated for synthetic and real anomalies by applying the usual statistical tests.