Studia Geophysica et Geodaetica最新文献

Physical heights is one of the most important topics in physical geodesy. Their original concept, introduced in the 19-th century, defined physical heights as lengths of plumblines of the Earth’s gravity field between the geoid and points of interest. There are orthometric heights of surface points, that have been traditionally estimated by spirit levelling and measured gravity; however, the knowledge of the density distribution of topographic masses (masses between the geoid and Earth’s surface) is required that significantly affects their determinability. This was also the main reason why a new type of physical heights was proposed in the mid of the 20-th century. Normal heights approximate orthometric heights in a sense that the Earth’s gravity field is replaced by the normal gravity field, an analytic model based on the theory of an equipotential ellipsoid. This height system has been introduced since that time in different countries in Europe and beyond. Contrary to the classical height system based on orthometric heights, its counterpart based on normal heights may have slightly different definitions. Moreover, normal heights are often defined as heights of points above the quasigeoid. This contribution reviews alternative definitions of normal heights and respective height systems. It is argued that both orthometric and normal heights refer to the geoid. In the case physical heights are estimated by satellite positioning, normal heights must be computed through the height anomaly estimated at each point of interest, whether it is below, at or above the Earth’s surface. On the contrary, orthometric heights of all points along the same plumbline, be it below, at or above the Earth’s surface, are estimated by introducing one value of the geoid height. Normal heights of surface points can be estimated by spirit levelling easier than orthometric heights as no topographic mass density hypothesis is required; however, one has to keep in mind the gravity field approximation used both for their definition and realization.

Most common parameterization of anisotropic media is by twenty one independent elements a_ijkl of the density-normalized stiffness tensor or by twenty one independent elements A_αβ of the density-normalized matrix of elastic parameters in the Voigt notation. These parameters are commonly of significantly different sizes, are dimensional, in (km/s)², often appear in combinations. We are offering an alternative parameterization by twenty one A-parameters (anisotropic parameters), which removes the mentioned disadvantages and possesses some additional useful properties. For example, axes or planes of coordinate systems, in which A-parameters are defined, need not be related to symmetry axes or planes of the considered anisotropy symmetry as required in other similar parameterizations. In combination with the first-order weak-anisotropy approximation, in which anisotropy is considered as the first-order perturbation of reference isotropy, parameterization by A-parameters yields insight into the role of individual A-parameters in the wave propagation problems. For example, it turns out that in the first-order weak-anisotropy approximation, P- and S-wave velocities are each controlled by fifteen A-parameters. A set of six of them appears only in the expression for P-wave velocity, a set of other six A-parameters appears only in S-waves velocity expressions. Remaining set of nine A-parameters is common for both waves. We present transformation of A-parameters, analogue to Bond transformation, and useful formulae for the weak-anisotropy approximation for anisotropy of any symmetry and arbitrary tilt.

The Very Low Frequency (VLF) radio wave propagation characteristics play a very important role in understanding the behaviour of the D-region. The earth-ionosphere wave guide theory has been used to evaluate the reflection height of VLF radio waves using the electron density profiles obtained from the International Reference Ionosphere (IRI) 2012 and 2016 models. For calculating the conductivity parameter, two different collision frequency models have been used. The diurnal shift in reflection height of 16-kHz VLF waves is evaluated for the midpoint of Visakhapatnam-Rugby path using the two IRI models and the results are compared with those values derived from VLF phase measurements made at Visakhapatnam. The theoretically evaluated values using the FT-2001 option for the D-region electron density profile in the IRI-2012 and IRI–2016 models are in good agreement with those obtained from phase measurements, especially in summer. The day to night shift in reflection height obtained using exponential collision critical frequency model are in good agreement with those derived from VLF phase measurements. The diurnal shift in reflection height of VLF radio waves during winter months derived from IRI models are much lower than those obtained from measurements.

Properties of the out-of-phase susceptibility (opMS) of rocks and artificial specimens whose opMS is due to weak-field hysteresis, containing magnetite and titanomagnetite, were investigated and theoretical relation between degrees of the in-phase susceptibility (ipMS) and opAMS was confirmed experimentally. Pure magnetite shows virtually no field dependence of ipMS and zero opMS in fields less than 500 A m⁻¹. In low-Ti titanomagnetite, the intensity of the ipMS variation is very low, hardly reaching 1% of the initial value. In high-Ti titanomagnetite, the intensity of ipMS variation is relatively strong reaching 50% of the initial value and that of opMS variation is even much stronger reaching multiples of the initial value. The anisotropy of ipMS (ipAMS) of artificial specimens consisting of disseminated magnetite powder in plaster of Paris is well defined, while the opAMS is virtually undetectable. In titanomagnetite-bearing volcanic and dyke rocks, the ipAMS evidently reflects the character of lava flow. The opAMS ellipsoids resemble the ipAMS ellipsoids, the degree of opAMS being significantly higher than that of ipAMS. The principal directions of ipAMS and opAMS are related closely in specimens with high-Ti titanomagnetites and only poorly in specimens with low-Ti titanomagnetites. In specimens with high-Ti titanomagnetites, there is a linear relation and very strong correlation (R² = 0.95) between the degree of opAMS and the square of the degree of ipAMS corresponding to the theoretical relation between these degrees.

Seismic signals are inevitably disturbed by random noise in the acquisition process, which greatly degrades seismic data. In order to improve the quality of seismic data, we propose a self-similarity convolutional neural network (SS-Net) for seismic data denoising by introducing the coherence of seismic events into convolutional neural network (CNN). The SS-Net consists of two modules, the directional matching module (DMM) and the denoising module. The DMM stacks similar seismic data blocks to generate three-dimensional (3D) groups by calculating the similarity between seismic data blocks with the same directional characteristics. For the 3D groups with redundant structural information, the following denoising module with the multi-channel convolution adaptively extracts and squeezes the structural feature characteristic of each 3D group, which enhances the characteristics of seismic signals and avoids confusion caused by local similarity of seismic signals and random noise. In addition, the skip connection is adopted by SS-Net to transport the sparse feature to the following denoising process, to reduce the loss of signal features extracted by multi-channel convolutional layers due to increased network depth. We validate the denoising performance of the SS-Net on the synthetic and field desert seismic data. The filtered results confirm that the SS-Net can suppress seismic random noise more thoroughly and recover the seismic events with complex morphology better than the competitive denoising methods.

Real-time estimates of the Earth orientation parameters (EOP) are currently unavailable for users owing to the delay caused by complex data processing and heavy computation procedures. Accurate short-term predictions of the EOP are therefore essential for several real-time applications such as navigation and tracking of interplanetary spacecrafts and precise orbit determination of Earth satellites, whilst medium- and long-term predictions are required for Global Navigation Satellite System (GNSS) autonomous satellite navigation, climate forecasting as well as for astrogeodynamic studies. Universal time (UT1 – UTC) or its first time derivative, length of day (ΔLOD), representing the changes of the Earth’s rotation rate, are the most challenging to predict among the EOP. Various methods and techniques have been used to improve ΔLOD predictions since the present prediction accuracy is yet unsatisfactory even up a few days into the future. This study employs a popular time-series analysis method, called singular spectrum analysis (SSA), in combination with the neural network (NN) technique for medium- and long-term prediction of ΔLOD up to 2 years in the future. The SSA is first applied to extracting the predominant periodic components including annual and semiannual oscillations and irregular short-period signals in ΔLOD data. These extracted predominant periodic components are then extrapolated by the proposed SSA-based data filling strategy. Next, the residuals (the difference between these predominant components and the data themselves) are modeled and predicted by the NN technique. The predicted ΔLOD value is sum of the extrapolation of the predominant periodic components and the prediction of the residuals. The results show that the accuracy of the 180-day ahead predictions is worse than that by the combination of least squares (LS) extrapolation and a stochastic method including autoregressive and NN technology in terms of the mean absolute prediction error. However, the proposed SSA extrapolation in combination with NN modeling can achieve a noticeably better accuracy for the medium- and long-term predictions out 180 days than the combined LS + stochastic technology. The improvement in the prediction accuracy for lead time of 1 year and 2 years can reach up to 53% and 56%, respectively. The combined SSA extrapolation and NN modeling is thus very promising for medium- and long-term prediction of ΔLOD.

Palaeointensity data from the Precambrian are key to understanding the timing of the Earth’s Inner Core Nucleation (ICN). Due to the scarcity of data, the ICN timing is still poorly constrained and is thought to have occurred between 2500 to 500 Ma. Numerical dynamo simulation models predict an increase in entropy, a stronger driving force for convection that could affect the field strength and show an anomaly in the palaeointensity record at ICN. We present new estimates of the geomagnetic field intensity (palaeointensity) from the Mid-Mesoproterozoic (1406 ± 1424 Ma) Nova Guarita dyke swarm, in the northern Mato Grosso State (SW Amazon Craton, Brazil). To obtain palaeointensity estimates, we used the non-heating Preisach method, with palaeointensity criteria at the specimen, and site level. Five sites provided accepted palaeointensity results, yielding virtual dipole moment (VDM) estimate of 65 ± 12 ZAm² at 1416 ± 13 Ma, 53 ± 4 ZAm² at 1418 ± 3 Ma, 12 ± 2 and 8 ± 2 ZAm² at 1418 ± 5 Ma, and 71 ± 16 ZAm² at 1424 ± 16 Ma, thus an average estimate of 43 ± 30 ZAm² for ∼1410 Ma. The estimate is similar to the average VDM data (∼50 ZAm²), calculated for the period from 1600 to 1000 Ma. This average represents only a snapshot of the Earth’s magnetic field strength. While the new data are too limited in time to contribute directly to the question of ICN, they nevertheless contribute to constraints useful for assessing numerical simulations of the Mesoproterozoic geodynamo.

In multi-frequency and multi-constellation BeiDou Navigation Satellite System (BDS), the observation type is increased, and the observation precision is inevitably different. Consequently, it is difficult to determine the variance factors of various observations. Variance component estimation can reasonably determine the weights of different types of observations and greatly improve positioning accuracy, but the prerequisite is that there are enough redundant observations, which may not be met in the case of BDS. In addition, it has relatively high time and space complexity. In this study, a priori and effective estimation of variance factors based on the code chipping rate is proposed to properly adjust and determine the observation weights in BDS, thus better characterizing the observation precision while simplifying the calculation. Both static and kinematic experiments were conducted to verify the effectiveness of the new method. The results show that the proposed method is suitable for both open and obstructed environments, and the accuracy and reliability of single point positioning are improved while high efficiency is met.

We consider the topographic bias in gravimetric geoid determination when analytically downward continuing the disturbing potential from the Earth’s surface to sea level. The total bias is subdivided into those of the Bouguer shell or plate and the terrain. In this process, the potential of the Bouguer shell always has a downward continuation bias in the process, which increases with the square of the topographic height and typically exceeds 1–2 cm for elevations higher than 1 km. The main conclusion is that the terrain does not provide a potential bias except possibly for masses located inside a dome of height of about 0.4 times the height of the computation point, and base radius equal to the height of the computation point. This result implies that the potential of all terrain masses of arbitrary density located exterior to the Bouguer shell as well as those outside the dome are unbiasedly downward continued to sea level.

Gravity forward modelling is a fundamental problem in the fields of geophysics and geodesy at regional and global scales. Considering the curvature of the Earth, tesseroids are suitable to accurately simulate the theoretical gravity field. In general, the spherical tesseroid is regarded as an ideal model, but it cannot consider the oblateness of the Earth. Therefore, we define an ellipsoidal tesseroid at the local Cartesian coordinate system. Then we propose the formulas of the gravitational potential and its first- and second-order partial derivatives of the ellipsoidal tesseroid based on the Cartesian integral kernel. To enhance the practicality, we approximate the ellipsoidal tesseroid to the spherical tesseroid and derive the formulas of the gravitational potential and its partial derivatives. Moreover, we discuss the formulas of the gravity field for the model with linear variable density. The ellipsoidal tesseroid, which is selected as the fundamental mass element, can more accurately simulate the gravity and gravity gradient anomalies of the Earth. Compared with methodologies that make use of integral kernels expressed in spherical coordinate system, the formulas based on the Cartesian integral kernel are given in compact and computationally attractive form. Besides, these formulas can avoid the polar singularity of the spherical coordinate system. The numerical simulation and comparison with previous methods validate the new ellipsoidal tesseriod formulas.