Travel time curves for complex inhomogeneous slightly anisotropic media

Summary The linearization approach is used to compute the travel times in inhomogeneous slightly anisotropic media. The basic formulae are outlined and their accuracy demonstrated in comparison with the exact solution based on the zero-order ray theory and the Backus formula (1965). The linearization is extended also to complex media with curved interfaces. The computer program for calculating travel times in 2D, inhomogeneous, slightly anisotropic, complex media is briefly described. The numerical results obtained for a realistic situation and various types of waves are presented to enable the effects of anisotropy and the effects of inhomogeneity on the resulting travel times to be compared.

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Measurements of gradients of gravity in mines

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Approximate spectral analysis by least-squares fit

An approximate method of spectral analysis called successive spectral analysis based upon the mean-quadratic approximation of an empirical function by generalised trigonometric polynomial with both unknown frequencies and coefficients is developed. A few quotations describing some properties of the method as well as one of the possible methods for numerical solution are given.     

A radar-based verification of precipitation forecast for local convective storms

Local flash flood storms with a rapid hydrological response are a real challenge for quantitative precipitation forecasting (QPF). It is relevant to assess space domains, to which the QPF approaches are applicable. In this paper an attempt is made to evaluate the forecasting capability of a high-resolution numerical weather prediction (NWP) model by means of area-related QPF verification. The results presented concern two local convective events, which occurred in the Czech Republic (CR) on 13 and 15 July 2002 and caused local flash floods. We used the LM COSMO model (Lokall Model of the COSMO consortium) adapted to the horizontal resolution of 2.8 km over a model domain covering the CR. The 18 h forecast of convective precipitation was verified by using radar rainfall totals adjusted to the measured rain gauge data. The grid point-related root mean square error (RMSE) value was calculated over a square around the grid point under the assumption that rainfall values were randomly distributed within the square. The forecast accuracy was characterized by the mean RMSE over the whole verification domain. We attempt to show a dependence of both the RMSE field and the mean RMSE on the square size. The importance of a suitable merger between the radar and rain gauge datasets is demonstrated by a comparison between the verification results obtained with and without the gauge adjustment. The application of verification procedure demonstrates uncertainties in the precipitation forecasts. The model was integrated with initial conditions shifted by 0.5° distances. The four verifications, corresponding to the shifts in the four directions, show differences in the resulting QPF, which depend on the size of verification area and on the direction of the shift.     

Tensor structure and the least squares

It is shown that for linear parametric adjustment models all the least-squares equations can be obtained from a commutative diagram, where the observation and parameter spaces are regarded as covariant. Their contravariant counterparts are defined through the metric property of the covariance matrix of the observations.     

Electromagnetic induction in a spherical earth with a circular bulge in the upper mantle

Summary Results of computing the anomalies of the variable magnetic field, generated by a harmonically variable field of the H_1,0-type in the model of a spherical Earth with an expressive bulge in the well-conducting part of the mantle, are presented. It was found that not only the radial, but also the tangential component of the magnetic field is disturbed above the bulge. The largest amplitudes of these changes can be observed over the area of the largest slope of the conductivity boundary if the exciting magnetic field is perpendicular to the surface of the interface.     

Détection des cavités à l'aide de mesures électriques et du géoradar dans une galerie d'amenée d'eau

Old water-delivery tunnels can become leaky and produce water losses of some economic importance. The detection of solution cavities behind the concrete lining was the purpose of an investigation in a 2 km long part of a water-delivery tunnel in Switzerland. A gypsum zone of about 700 m length was considered to be especially critical. Two geophysical methods were used at the same time: resistivity profiling with three different array lengths, and ground-penetrating radar. The cavities were characterized by higher electrical resistivity, principally for the short array (AB = 3 m). Detailed measurements with a pole-dipole array were made for a better depth interpretation of anomalies in some critical zones. The GPR investigations were made with an antenna of 500 MHz. Some transverse profiles were carried out with GPR in order to better delineate the discovered cavernous or weathered zones. GPR located cavities up to a few meters in length, at depths between 0 and 4 m behind the lining. Anomalies found by one investigation method were often confirmed by the other one. Their complementarity thus allowed a more reliable interpretation of the gathered data. Verifying drillholes have mostly confirmed the good correlation between geophysical interpretation and drilling results. Endoscopic investigations in the drillholes enabled us to have a real vision of discovered cavities.Although GPR-profiling has the advantage of a continuous underground imaging and of greater efficiency during data acquisition (investigation speed) we consider the combination of both methods in the present study as a good example of an integrated geophysical survey, which enables a more reliable interpretation of the gathered data.

Résumé

Les galeries d'amenée d'eau d'un certain âge peuvent poser des problèmes à cause de pertes d'eau parfois importantes. L'objectif de cette étude a été la mise en évidence et le positionnement de cavités derrière le revêtement d'une galerie en Suisse, sur une longueur de 2 km. Une zone de gypse longue de 700 m était considérée comme particulièrement critique. Deux méthodes géophysiques ont été conjointement utilisées: le traîné électrique multiple avec trois longueurs de ligne d'envoi de courant et le géoradar. Les cavités, caractérisées par des résistivités élevées, ont surtout été mises en évidence par le dispositif le plus court (AB = 3 m). Des mesures de détail ont été réalisées dans les zones critiques avec un dispositif pôle-dipôle en vue d'une meilleure interprétation des anomalies en profondeur. Les mesures de géoradar ont été exécutées avec une antenne de 500 MHz. Quelques profils transversaux ont été effectués pour vérifier l'extension des zones d'altérations ou des cavités. Le géoradar a pu localiser des cavités mesurant jusqu'à plusieurs mètres en longueur à des profondeurs variant entre 0 et 4 m derrière le revêtement de la galerie. Les anomalies décelées par une méthode ont souvent pu être confirmées par l'autre et leur complémentarité a permis une interprétation plus sûre. Des forages carottés ont montré une bonne corrélation entre les anomalies géophysiques et la réalité. Des mesures de fibroscopie dans les forages nous ont permis de déterminer la géométrie des cavités.Le géoradar possède des avantages certains: imagerie continue du massif rocheux et grande rapidité dans l'acquisition des données. Néanmoins, nous considérons la combinaison des deux méthodes utilisées dans cette étude comme le bon exemple d'une investigation géophysique combinée permettant une interprétation optimale de tous les résultats.