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- Estimation of the minimal detectable horizontal acceleration of GNSS CORS
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Abstract: Abstract Earth’s surface velocities are routinely extracted from Global Navigation Satellite System (GNSS) position time series. In addition to velocity estimates, acceleration may be a crucial parameter for modeling non-linear motion. Typically, a statistical hypothesis test is employed to evaluate the significance of the involved parameters and guide the selection of the appropriate model. In this contribution, we formulate a statistical test procedure from the generalized likelihood ratio test to analyze the significance of the acceleration in the model. The proposed procedure is compared with results obtained using the Akaike Information Criterion and Bayesian Information Criterion. Additionally, Minimal Detectable Horizontal Acceleration is provided as an indicator of the sensitivity of the acceleration detection. The GNSS time series of position estimates from the Nevada Geodetic Laboratory were used for this study. The experiments demonstrated a good agreement between the statistical test proposed and the information criteria approach. Therefore, the proposed statistical test may be another criterion to help the user in the important task of model selection.
PubDate: 2024-08-19
- Geophysical structure of a local area in the lunar Oceanus Procellarum
region investigated using the gravity gradient method-
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Abstract: Abstract Compared to gravity method, the gravity gradient has multi-component advantages and can emphasize short wavelength features. By providing more detailed features in the image display, it could present a more accurate determination of the spatial distribution of the underling anomaly body. In our study, based on the gravity gradient data that was synthesized from the high-precision gravity model from Gravity Recovery and Interior Laboratory mission, we analyzed the tectonic structure of the Moon’s shallow layers in Oceanus Procellarum region. Bouguer anomalies of gravity gradient are used for geological boundary recognition and three-dimensional density inversion. Theta Map method is adopted for the edge identification of geological structures. It fully utilizes the characteristics of multi-components combination of gravity gradient to sharpen the boundaries identification of abnormal bodies. During the density inversion, in order to decrease the non-unique solution problem, the depth weight constraint is added to the inversion equation. Furthermore, the method of wavelet coefficient compression and Least Squares QR-decomposition is applied to accelerate the inverse calculation of large ill-conditioned equations. According to the result illustration, we found that: 1) The combination of gravity tensors has a strong boundary recognition ability in the horizontal direction. There is close consistency with the results of density inversion. 2) Our study supports the expansion and intrusion hypothesis of lunar magma in the research zone of Oceanus Procellarum, since the distribution of density tomography results at different depths is higher than the normal assumed crust density of the Moon in the majority of areas. Moreover, the intrusion source in our research area is concentrated at a direction depth of 30–45 km below the mean lunar radius surface approximately.
PubDate: 2024-08-19
- The area of rhumb polygons
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Abstract: Abstract The formula for the area of a rhumb polygon, a polygon whose edges are rhumb lines on an ellipsoid of revolution, is derived and a method is given for computing the area accurately. This paper also points out that standard methods for computing rhumb lines give inaccurate results for nearly east- or west-going lines; this problem is remedied by the systematic use of divided differences.
PubDate: 2024-08-19
- Effect of the 2021 Cumbre Vieja eruption on precipitable water vapor and
atmospheric particles analysed using GNSS and remote sensing-
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Abstract: abstract The eruption of Mount Cumbre Vieja, La Palma, Spain, on 19th September 2021 released large amounts of gas and volcanic ash into the atmosphere that spread over hundreds of kilometers. Subsequently, the volumes of gaseous, and water vapor components in the troposphere were highly disturbed. In general, the release of a large amount of water vapor during an eruption increases the value of path delay and vertical column density of SO2. Therefore, this study analyzed their variations to determine the impact of eruption. The precise point positioning on Global Navigation Satellite System (GNSS) observation data were processed to obtain zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) contents, while Sentinel 5P, and MODIS remote sensing imagery were used to determine SO2 column density, aerosol index, and surface temperature. Moreover, time series and correlation analysis were computed to analyze the effect of the eruption and the relationship between GNSS and remote sensing parameters. Our findings showed that the variations in precipitable water vapor affected the ZTD value for three GNSS stations around the eruption point, showing a correlation value above 0.98. Meanwhile, the remote sensing data indicated that the SO2 content peaked at the end of September and in October 2021. Similarly, tropospheric delay, and water vapor had the highest fluctuations and increases in the early eruption period. However, the lower atmosphere layer was generally influenced by the autumn climate. The content of particles released into the atmosphere during eruption had minor effect in the middle to the end of the eruption period as rainfall events led to an increase in water vapor. The surface temperature was found to be characterized mostly by autumn condition but showed fluctuations and increased values in the early period of the eruption.
PubDate: 2024-08-19
- Seismic effects at GPS stations: Case study of the 24 August 2016 Amatrice
earthquake-
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Abstract: Abstract The seismic event of the 2016 Amatrice earthquake and its subsequent aftershocks have provided a significant opportunity to study seismic waves and their effects on the Apennine región, a very active seismic area. This research utilizes GPS data from three geodetic networks (ItalPos, NetGEO, and RING) to analyze the seismic waves generated by the earthquake, capturing seismic effects with great precision and resolution. By examining data from various GPS stations within the region, the study demonstrates the efficacy of GPS in providing detailed and accurate representations of ground motion. The study identifies co-seismic displacements and accelerations at monitoring stations by processing and analyzing GPS data, including precise point positioning strategies and wavelet adjustments. Moreover, a least squares adjustment method is employed to optimize the estimation of temporal parameters associated with seismic event detection across the spatial network of stations. The results obtained from GPS data are validated against seismic equipment, affirming their reliability in characterizing seismic events. Furthermore, the study elucidates the propagation of surface waves and path effects over the affected region, contributing to a comprehensive understanding of the earthquake impact. This research underscores the potential of GPS data as a valuable tool for rapid and precise characterization of seismic events, offering insights into ground motion dynamics and facilitating timely response and mitigation efforts.
PubDate: 2024-06-08
DOI: 10.1007/s11200-023-0322-6
- A two-stage seismic data denoising network based on deep learning
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Abstract: Abstract Seismic data with a high signal-to-noise ratio is beneficial in the inversion and interpretation. Thus, denoising is an indispensable step in the seismic data processing. Traditional denoising methods based on prior knowledge are susceptible to the influence of the hypothesis model and parameters. In contrast, deep learning-based denoising methods can extract deep features from the data autonomously and generate a sophisticated denoising model through adaptive learning. However, these methods generally learn a specific model for each noise level, which results in poor representation ability and suboptimal denoising efficacy when applied to seismic data with different noise levels. To address this issue, we propose a denoising method based on a two-stage convolutional neural network (TSCNN). The TSCNN comprises an estimation subnet (ES) and a denoising subnet (DS). The ES employs a multilayer CNN to estimate noise levels, and the DS performs noise suppression on noisy seismic data based on the ES estimation of the noise distribution. In addition, attention mechanisms are implemented in the proposed network to efficiently extract noise information hidden in complex backgrounds. The TSCNN also adopts the L1 loss function to enhance the generalization ability and denoising outcome of the model, and a residual learning scheme is utilized to solve the problem of network degradations. Experimental results demonstrate that the proposed method can preserve event features more accurately and outperforms existing methods in terms of signal-to-noise ratio and generalization ability.
PubDate: 2024-06-08
DOI: 10.1007/s11200-023-0320-8
- Effect of water content and sodium sulfate concentration on the
resistivity of red clay-
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Abstract: Abstract Red clay is widely distributed globally and is closely related to human production and life. The middle reaches of the Yellow River basin in China are characterized by complex geological structures, concentrated rainfall periods. The soluble salts such as sodium sulfate enter the red clay particles along with the infiltrating water, forming a red clay-like saline soil. In order to study the effects of water and salt on red clay soils, this paper uses red clay in the Heyang of Weinan with different ratios of distilled water (10–20%) and Na2SO4 (0–4%), and obtains the resistivity of red clay soils at different frequencies (100 Hz–100 kHz) using an inductance, capacitance and resistance digital bridge tester. The results show that the resistivity of red clay is negatively correlated with water and salt content. With the increase of water content, the increase of conductive paths in the pore water improved the electrical conductivity of the red clay; while when the concentration of Na2SO4 increased, the free moving anions and cations in the pore water increased, the electrical conduction efficiency increased and the resistivity decreased. The high frequency increased the conductivity of red clay by contributing to electrical double layer deformation, whereas the electrode polarization led to inhibition of conductivity under low frequency. A negative power exponential relationship exists between the resistivity of red clay and the test frequency. This study may provide a valuable reference for the rapid identification of the physical properties of red clay and its internal structure.
PubDate: 2024-04-08
DOI: 10.1007/s11200-023-0124-0
- Combined BiLSTM and ARIMA models in middle- and long-term polar motion
prediction-
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Abstract: Abstract As one of the main components of the Earth orientation parameters, short-term prediction of the geodetic polar motion series is crucial in the field of deep-space exploration, high-precision positioning, and timing services, which require high real-time performance. Additionally, its middle- and long-term prediction is equally important in climate forecasting and geodynamics research. In this study, we propose the combined BiLSTM+ARIMA model, which is based on bidirectional long- and short-term memory (BiLSTM) and autoregression integrated moving average (ARIMA). First, ensemble empirical mode decomposition (EEMD) is performed as a filter to decompose the polar motion time series to obtain low- and high-frequency signals. The EOP14 C04 time series provided by International Earth Rotation and Reference Systems Service and decomposed by EEMD includes low-frequency signals like the long-term trend, decadal oscillation, Chandler wobble, and prograde annual wobble, along with shorter-period high-frequency signals. Second, low- and high-frequency signals are predicted using BiLSTM and ARIMA models, respectively. Finally, the low- and high-frequency signal forecast components are reconstructed to obtain geodetic polar motion predictions. In middle- and long-term polar motion prediction, the results show that the proposed model can improve the prediction accuracy by up to 42% and 17%, respectively. This demonstrated that the BiLSTM+ARIMA model can effectively improve the accuracy of polar motion prediction.
PubDate: 2024-04-08
DOI: 10.1007/s11200-023-0134-y
- A comparative study over improved fast iterative shrinkage-thresholding
algorithms: an application to seismic data reconstruction-
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Abstract: abstract Seismic data reconstruction is a crucial process involving the restoration of missing or corrupted traces to create a uniform dataset for subsequent data processing. Various factors such as equipment failures, and surface obstacles, result in irregularly located or corrupted traces. The absence of these traces can compromise the quality and accuracy of the resulting image. To address this issue, the Nonuniform Fast Fourier Transform (NUFFT) method is employed to reconstruct missing traces in datasets with non-uniformly sampled data. It works by interpolating the non-uniformly sampled data onto a regular grid, enabling the traditional Fast Fourier Transform application for data recovery. This interpolation process is adjusted using a kernel function to account for non-uniform sampling and reduce aliasing artifacts. The outcome is a collection of Fourier coefficients that can be utilized to reconstruct missing or incomplete parts of data. This problem is transformed into a linear constraint problem, which is efficiently solved using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). In this study, we explore various techniques aimed at improving the convergence of FISTA, collectively referred to as improved FISTA methods. To validate the NUFFT+FISTA method for data reconstruction, we conducted numerical tests using 3D and 2D synthetic datasets, as well as field data. These tests show the advantages of the Greedy-FISTA in terms of convergence rate and affirm the accuracy of this approach in filling missing data traces.
PubDate: 2024-04-08
DOI: 10.1007/s11200-023-0113-0
- Parameterization of anisotropic media by A-parameters
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Abstract: Abstract Most common parameterization of anisotropic media is by twenty one independent elements aijkl of the density-normalized stiffness tensor or by twenty one independent elements Aαβ 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.
PubDate: 2024-01-13
DOI: 10.1007/s11200-023-1136-2
- On correct definition and use of normal heights in geodesy
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Abstract: Abstract 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.
PubDate: 2024-01-13
DOI: 10.1007/s11200-023-1138-0
- Day to night shift in reflection height of VLF radio waves derived from
IRI model electron density models-
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Abstract: Abstract 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.
PubDate: 2023-11-08
DOI: 10.1007/s11200-022-0959-6
- Anisotropy of out-of-phase magnetic susceptibility in
titanomagnetite-bearing rocks due to weak field hysteresis-
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Abstract: Abstract 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.
PubDate: 2023-08-03
DOI: 10.1007/s11200-023-0603-0
- Self-similarity convolution neural network for seismic noise suppression
in desert environment-
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Abstract: Abstract 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.
PubDate: 2023-08-03
DOI: 10.1007/s11200-022-0535-0
- Mesoproterozoic geomagnetic field strength from Nova Guarita mafic dykes
(Amazon Craton)-
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Abstract: Abstract 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.
PubDate: 2023-07-04
DOI: 10.1007/s11200-022-0647-6
- Medium- and long-term prediction of length-of-day changes with the
combined singular spectrum analysis and neural networks-
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Abstract: Abstract 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 ALOD.
PubDate: 2023-07-04
DOI: 10.1007/s11200-022-0558-6
- A priori and effective estimation of variance factors based on the code
chipping rate in BeiDou navigation satellite system positioning-
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Abstract: Abstract 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.
PubDate: 2023-05-18
DOI: 10.1007/s11200-022-0452-2
- On the topographic bias by analytical continuation in geoid determination
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Abstract: Abstract 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.
PubDate: 2023-04-25
DOI: 10.1007/s11200-022-0337-4
- The gravitational potential and its first- and second-order partial
derivatives of an ellipsoidal tesseroid based on the Cartesian integral
kernel-
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Abstract: Abstract 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.
PubDate: 2023-03-21
DOI: 10.1007/s11200-022-0344-5
- Numerical simulation and time-frequency analysis of borehole acoustic
logging in fractured formations-
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Abstract: Abstract Currently, using the finite difference method to simulate millimeter-sized fractures in formations requires intensive calculations. However, only the time domain characteristics of the calculated borehole acoustic signal are often analysed, while the frequency domain characteristics are ignored. This study aims to obtain the time-frequency characteristics of full acoustic waveforms in different types of fractured formations while reducing operational time and to analyze more comprehensively the influence of fractures on time-frequency characteristics. Therefore, the variable grid finite difference method is used to simulate full acoustic waveforms in boreholes in formations with millimeter-sized horizontal fractures to reduce the computational time of the finite difference method. Afterwards, the wavelet transform is used to analyze the influence of fracture width, fracture number, and radial extension length on the waveform time-frequency characteristics. The results show that with increasing fracture width or number, the P- and S-wave arrival times are delayed, amplitude attenuation is enhanced, and the dominant frequency increases gradually. The frequency and amplitude attenuation of each Stoneley wave component also increases, and the arrival time of the 20–28 kHz high-frequency Stoneley wave is delayed. When the fracture radial length is limited, an increase in radial length delays the P- and S-wave arrival times, and the amplitude attenuation increases. The main S-, Stoneley, and pseudo-Rayleigh wave frequencies increase, and the Stoneley wave and pseudo-Rayleigh wave amplitude attenuation increases. When the fracture radial length is infinite, the P-wave and pseudo-Rayleigh wave amplitude attenuation increases, whereas that of the S-wave and Stoneley wave decreases. This study reveals the influence of fractures on the time-frequency characteristics of full acoustic waveforms in boreholes, provides a theoretical basis for the time-frequency analysis of full acoustic waveforms, and is significant for further clarification of the propagation characteristics of borehole acoustic waves in fractured formations.
PubDate: 2023-01-11
DOI: 10.1007/s11200-021-1145-y
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