Studia Geophysica et Geodaetica最新文献

The marine gravity field is vital for mapping various submarine geological and tectonic structures, also for computation of high-resolution gravimetric geoid. This study aims to evaluate the accuracy of two latest high-resolution marine gravity models derived from satellite altimetry (DTU17 and SSv27.1) using shipborne gravity data and to pruduce high-precision gravity field over the Gulf of Guinea. The gross-errors affecting the shipborne gravity data have been removed by cross-validation technique to ensure better evaluation of gravity field models. The standard deviation σ of the differences between the measured and model gravity data drops from 9.96 mGal before the cross-validation to 6.28 mGal after this process. The comparison between the DTU17 and SSv27.1 gravity field models has been done in order to detect significant differences between them. The differences between the two models are quite small with a mean of 1.73 mGal and σ of 6.55 mGal. The discrepancies between them are found around coastal areas and along islands. This shows the poor accuracy of satellite altimetry near coastal areas. Afterwards, the accuracy of each marine gravity field models was evaluated using shipborne gravity data free of gross-errors. The SSv27.1 model fits better to the shipborne gravity data with a mean of −4.88 mGal and σ of 7.18 mGal. Hence, the SSv27.1 model has a better performance than the DTU17 model on the Gulf of Guinea. Finally, we used the least-squares collocation technique associated to the Markov model of second-order covariance to combine the SSv27.1 model with the shipborne gravity data. We produced here a marine gravity field of good accuracy around the Gulf of Guinea with no data gaps. The precision of this combined gravity field is estimated to be 5.54 mGal with a spatial resolution of 1 arc-minute.

The stiffness matrix of a viscoelastic medium is symmetric in the low—frequency and high—frequency limits, but not for finite frequencies. We thus consider a non—symmetric stiffness matrix in this paper. We determine the general form of a rotationally invariant non—symmetric stiffness matrix of a viscoelastic medium. It is described by three additional complex—valued parameters in comparison with a rotationally invariant symmetric stiffness matrix of a transversely isotropic (uniaxial) viscoelastic medium with a symmetric stiffness matrix. As a consequence, we find that the stiffness matrix of an isotropic viscoelastic medium is always symmetric.

Recent research has shown that the floodplains of the Sanaga river catchment contain significant resources of minerals suitable for industry. However, these studies were carried out in large grids, and do not allow for detailed specification of the geometry of the identified resources. The aim of this study is to minimize the uncertainties observed in the characterization of these deposits using two techniques: geoelectric imaging and manual drilling. The geoelectrical results associated with the lithological sections show, from surface to depth, three main units: semi-resistive (66–500 Ωm) corresponding to clayey sands; conductive (42–100 Ωm) associated with sandy clays/silt clays, and resistive (<1000 Ωm) corresponding to sands and gravels. The data show good correlation between resistivity and clay content, and resistivity and sand content. Similarly, good correlation exists between the thickness determined by geoelectrical method and the actual thickness. The average thickness of these layers on the banks of the Sanaga river, suitable for exploitation, is 4 m over an area of about 100 m². Our results show that the combination of geoelectric technique and manual drilling allows a good assessment of the volume of deposits of useful resources and can better constrain their exploitation in the field of civil engineering.

The gravity field is a signature of the mass distribution and interior structure of the Earth, in addition to all its geodetic applications especially geoid determination and vertical datum unification. Determination of a regional gravity field model is an important subject and needs to be investigated and developed. Here, the spherical radial basis functions (SBFs) are applied in two scenarios for this purpose: interpolating the gravity anomalies and solving the fundamental equation of physical geodesy for geoid or disturbing potential determination, which has the possibility of being verified by the Global Navigation Satellite Systems (GNSS)/levelling data. Proper selections of the number of SBFs and optimal location of the applied SBFs are important factors to increase the accuracy of estimation. In this study, the gravity anomaly interpolation based on the SBFs is performed by Gauss-Newton optimisation with truncated singular value decomposition, and a Quasi-Newton method based on line search to solve the minimisation problems with a small number of iterations is developed. In order to solve the fundamental equation of physical geodesy by the SBFs, the truncated Newton optimisation is applied as the Hessian matrix of the objective function is not always positive definite. These two scenarios are applied on the terrestrial free-air gravity anomalies over the topographically rough area of Auvergne. The obtained accuracy for the interpolated gravity anomaly model is 1.7 mGal with the number of point-masses about 30% of the number of observations, and 1.5 mGal in the second scenario where the number of used kernels is also 30%. These accuracies are root mean square errors (RMSE) of the differences between predicted and observed gravity anomalies at check points. Moreover, utilising the optimal constructed model from the second scenario, the RMSE of 9 cm is achieved for the differences between the gravimetric height anomalies derived from the model and the geometric height anomalies from GNSS/levelling points.

Datong Window is at the junction of Datong Basin and Liulengshan Range in the northern part of Shanxi Graben, China. It is important to analyze the relationship between the frequency of small earthquakes and the deep velocity structure in this region since the earthquake swarm in 1989 with the maximum surface-wave magnitude M_s of 5.9. A high-resolution 3D P-wave velocity model of the crust in this region was obtained with double-difference tomography using seismic data from July 2009 to June 2019. The results show that the Datong-Yanggao seismic sequence occurred, in general, within the NE rupture zone of the earthquake swarm of 1989. The sequences from 1991, 1999, and 2010 were in the rupture zone of 1989. A series of earthquakes developed in this region, which is at the intersection of multiple faults and a low-velocity anomaly of the intermediate-lower crust. A gap of length of about 3 km was found at the southwest end of the NE Dawangcun Fault (near Lujialing). Several moderate earthquake ruptures failed to break through it. It was speculated that it may be a potential asperity. There is a possibility of an earthquake with magnitude about 5 from the gap. The relocation results for the earthquakes show that intensive small-earthquake events in Datong Window corresponding to moderate-to-strong earthquakes in Shanxi Graben were highly clustered horizontally and distributed vertically in a column. In contrast, when there was no moderate earthquake in Shanxi Graben after intensive small-earthquake events, the spatial distribution of these events in Datong Window was scattered and dispersive.

The 3×3×3×3 frequency-domain stiffness tensor is complex-valued in viscoelastic media. The 3 × 3 Christoffel matrix is then also complex-valued. Using a simple example, we demonstrate that a complex-valued Christoffel matrix need not have all three eigenvectors at an S-wave singularity, and we thus cannot apply the eigenvectors to calculating the phase-space derivatives of the Hamiltonian function.

Perturbations of elastic moduli and density can be decomposed into Gabor functions. The wave field scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves can be estimated using the first-order Born approximation with the paraxial ray approximation. For a particular source generating a short-duration broad-band incident wave field with a smooth frequency spectrum, each Gabor function generates at most a few scattered sensitivity Gaussian packets propagating in determined directions. Each of these scattered Gaussian packets is sensitive to just a single linear combination of the perturbations of elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered sensitivity Gaussian packet does not fall into the aperture covered by the receivers and into the recording frequency band. We illustrate this loss of information using the difference between the 2-D Marmousi model and the corresponding smooth velocity model. We decompose the difference into Gabor functions. For each of the 240 point shots, we consider 96 receivers. For each shot and each Gabor function, we trace the central ray of each sensitivity Gaussian packet. If a sensitivity Gaussian packet arrives to the receiver array within the recording time interval and frequency band, the recorded wave field contains information on the corresponding Gabor function. We then decompose the difference into the part influencing some recorded seismograms, and the part on which we recorded no information and which thus cannot be recovered from the reflection experiment.

Several kinds of approximation of the gravitational potential of a homogeneous body by truncated spherical harmonics series are in use in physical geodesy. However, only one of them is capable of a representation converging to the true potential in the whole layer between the Brillouin sphere and the Bjerhammar sphere of the body. We aim at providing various majorizations, namely upper bounds, of the error with the double purpose of proving explicitly the convergence in the sense of different norms and of giving computable bounds, that might be used in numerical studies. The first aim is reached for all the norms. For the second, however, it turns out that among the bounds, when applied to the example of the terrain correction of the Earth, only those referring to the mean absolute error and the mean squared error at the level of Brillouin sphere of minimum radius give significant and useful results. In order to make the computation an easy exercise, a simple approximate formula has been developed requiring only the use of the distribution function of the heights of the surface of the body with respect to the Bjerhammar sphere.

The differences between local and reference geopotential values are the fundamental quantities of interest in the geodetic boundary value problem approach for connecting independent height reference frames. The local gravity potential values are usually derived from gravimetric and geometric geoid undulations. In determining the short-wavelength components of the gravimetric geoid, a harmonic or analytical downward continuation of the external harmonic functions of gravity to the geoid is necessary. This study analyses the stability of the Poisson downward continuation technique with respect to varying the spatial resolution of surface gravity data in Ireland in order to estimate an effective grid resolution on this reduction. Results of the study show that the minimum range of 500-m resolution provides an unconditionally stable solution to downward continuation without the need for regularisation of the computation algorithm. In this case, downward continued data contribute from −13 to 12 mm to geoid heights and from −0.128 to 0.118 m²s⁻² to local gravity potential value at Malin-Head tide gauge station in Ireland.