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Studia Geophysica et Geodaetica
Journal Prestige (SJR): 0.38
Citation Impact (citeScore): 1
Number of Followers: 1  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-1626 - ISSN (Online) 0039-3169
Published by Springer-Verlag Homepage  [2468 journals]
  • 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
       
  • 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
       
  • 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
       
  • Magnetic susceptibility in soil pedons developed on different parent rocks
           in Kerman province (Iran)

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      Abstract: Abstract Lithology and soil formation affect magnetic susceptibility and its distribution along soil pedons. Kerman province in Iran is typical for variable lithology. However, only limited data on soil magnetic susceptibility in this province and its relation to the lithology are available. We investigate the effect of soil properties and processes on magnetic susceptibility values of soils with different geology in central Iran. Seven soil pedons with different lithology including sedimentary and igneous bedrocks were selected in arid and semi-arid parts of northern Kerman. Routine physical and chemical properties, different forms of iron, and mass-specific magnetic susceptibility values were measured in all the collected samples. Four selected samples underwent magnetic separation. Two of them, which yielded the highest amount of magnetically extracted material, were subjected to X-ray diffraction analysis. In addition, polished sections from the sample with the highest mass-specific magnetic susceptibility were prepared. The results show that lithology strongly affects the magnetic susceptibility in the studied soils, ranging from the minimum value of 4.3 × 10−8 m3 kg−1 (in the soils developed on Cretaceous marls and limestone) to 1264 × 10−8 m3 kg−1 (on andesite rocks). Frequency-dependent susceptibility values of soils (from 0 to 5.3%) showed that coarse multi domain grains inherited from parent material were the main source of magnetism in the area under study. The average amount of free, non-crystalline, crystalline, and active iron oxides in the studied samples were 0.5, 9.96, 8.45, and 0.05 g kg−1, respectively. The weighted mean for different factors was calculated in three depth ranges. Slope of linear regression was used to investigate the relation between mass-specific susceptibility and physicochemical parameters for different soil depths. The argilluviation process caused a decrease in the magnetic susceptibility in moderately developed soils of the region. The highest magnetic susceptibility values were found for Cambic Calcisols, followed by the Abruptic Solonetz, both developed on the andesite and gypsiferous marl. A positive relationship between magnetic susceptibility and Feo, Fed and Fed — Feo, and a negative correlation between magnetic susceptibility and Feo/Fed were found. According to X-ray diffraction analyses, diamagnetic minerals are dominant, while antiferromagnetic minerals are rare. The results suggest that changes in the magnetic susceptibility values are highly affected by the processes of soil formation, lithology, and soil classification.
      PubDate: 2023-01-11
      DOI: 10.1007/s11200-021-0771-8
       
  • Regionally adjusted ground motion model: Case study of the ML6.2 (Mw6.4)
           Petrinja (Croatia) 2020 earthquake

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      Abstract: Abstract In the wake of recent 2020 ML ≥ 5.5 earthquakes in Croatia, Zagreb ML5.5 and Petrinja ML6.2, the insufficient instrumental network as well as the lack of regional ground motion prediction equation (GMPE) were identified as the drawbacks of our engineering community. The former is related to the quality definition of active seismicity (most of the instruments are installed in the southern part of Croatia with fewer installed around Zagreb in the northwestern part of Croatia), and the latter is related to the proper number of strong motion recordings. In Croatia, there is a sparse database of ground motion recordings for moderate earthquakes which makes a well-designed ground motion selecting procedure hardly achievable. Following this, strong motion BSHAP database for empirical estimation of the response spectrum based on Fourier amplitude spectrum and the ground motion duration using Random Vibration Theory approach adjusted to source, propagation, and local site conditions was used. Regionally adjusted ground motion model estimations for the ML6.2 Petrinja 2020 earthquake scenario are comparable with the previously published GMPEs models for this part of Europe and for the Western part of North America. However, model-to-model variability and uncertainties in local GMPE exceeded those of global GMPEs and are influenced by statistically less stable and more limited datasets. Model is applicable for magnitudes up to Mw6.5 and Joyner-Boore distances up to 200 km with usable frequency range between 0.4 and 33 Hz. The presented model is a step forward toward performing hybrid-empirical seismic hazard studies in areas with sparse ground motions such as the region of Croatia.
      PubDate: 2022-10-01
      DOI: 10.1007/s11200-022-0914-6
       
  • Hybrid geoid model over peninsular Malaysia (PMHG2020) using two
           approaches

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      Abstract: Abstract We describe the development of a hybrid geoid model for Peninsular Malaysia, based on two approaches. The first approach is utilising an ordinary method fitting the gravimetric geoid to the geometric undulation derived from GNSS-levelling data; the second approach directly fits the gravimetric geoid to the reference mean sea level derived from the tide measurements of Port Klang tide gauge station. The hybrid geoid model fitted to Port Klang (PMHGG2020_PK) is produced by adding an offset of 0.446 m to the gravimetric geoid, based on the comparison at the tide gauge benchmark. To calculate the gravimetric geoid, a new model for Peninsular Malaysia (PMGG2020) has been developed based on Least-Squares Modification of Stokes’ Formula with Additive correction (LSMSA). Three different sources of gravity data which are terrestrial, airborne, and satellite altimetry-derived gravity anomaly (DTU17) have been combined to construct the geoid model. The height information has been extracted from the newly released global digital elevation model, TanDEM-X DEM. GO_CONS_GCF_2_SPW_R4 model derived from GOCE data provides long-wavelengths gravity field up to maximum degree and order 130. The gravity datasets are gridded by 3D Least-Squares Collocation method. The PMGG2020 model is consistent with the geometric geoid heights from 173 GNSS-levelling measurements, with a standard deviation of ±5.8 cm. Evaluation of the hybrid geoid model constructed from the first approach shows a significant improvement over the two existing hybrid geoid models. The accuracy of ±4.6 cm has been achieved after evaluating by 20 GNSS-levelling points, externally. Hybrid geoid model fitted to Port Klang has also been evaluated via 173 GNSS-levelling points, and the result shows that 71% of the total data exhibit height differences lower than 10 cm. The overall results indicate that the hybrid geoid model developed in this study can be valuable as an alternative to the current modern height system in Peninsular Malaysia for surveying and mapping.
      PubDate: 2022-10-01
      DOI: 10.1007/s11200-021-0769-2
       
  • New methods for numerical evaluation of ultra-high degree and order
           associated Legendre functions

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      Abstract: Abstract We improve the precision and computation speed of the fully-normalized associated Legendre functions (fnALFs) for ultra-high degrees and orders of spherical harmonic transforms. We take advantage of their numerical behaviour of and propose two new methods for solving an underflow/overflow problem in their calculation. We specifically discuss the application of the two methods in the fixed-order increasing-degree recursion computation technique. The first method uses successive ratios of fnALFs and the second method, called the Midway method, starts iteration from tiny initial values, which are still in the range of the IEEE double-precision environment, rather than from sectorial fnALFs. The underflow/overflow problem in the successive ratio method is handled by using a logarithm-based method and the extended range arithmetic. We validate both methods using numerical tests and compare their results with the X-number method in terms of precision, stability, and speed. The results show that the relative precision of the proposed methods is better than 10−9 for the maximum degree of 100000, compared to results derived by the high precision Wolfram’s Mathematica software. Average CPU times required for evaluation of fnALFs over different latitudes demonstrate that the two proposed methods are faster by about 10–30% and 20–90% with respect to the X-number method for the maximum degree in the range of 50–65000.
      PubDate: 2022-10-01
      DOI: 10.1007/s11200-022-0830-9
       
  • Tracing real-valued reference rays in anisotropic viscoelastic media

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      Abstract: Abstract The eikonal equation in an attenuating medium has the form of a complex—valued Hamilton—Jacobi equation and must be solved in terms of the complex—valued travel time. A very suitable approximate method for calculating the complex—valued travel time right in real space is represented by the perturbation from the reference travel time calculated along the real—valued reference rays to the complex—valued travel time defined by the complex—valued Hamilton—Jacobi equation. The real—valued reference rays are calculated using the reference Hamiltonian function. The reference Hamiltonian function is constructed using the complex—valued Hamiltonian function corresponding to a given complex—valued Hamilton—Jacobi equation. The ray tracing equations and the corresponding equations of geodesic deviation are often formulated in terms of the eigenvectors of the Christoffel matrix. Unfortunately, a complex—valued Christoffel matrix need not have all three eigenvectors at an S—wave singularity. We thus formulate the ray tracing equations and the corresponding equations of geodesic deviation using the eigenvalues of a complex—valued Christoffel matrix, without the eigenvectors of the Christoffel matrix. The resulting equations for the real—valued reference P—wave rays and the real—valued reference common S—wave rays are applicable everywhere, including S—wave singularities.
      PubDate: 2022-10-01
      DOI: 10.1007/s11200-022-0906-6
       
  • Extremely strong anisotropy of out-of-phase component of AC magnetic
           susceptibility in hematite single crystals and its origin

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      Abstract: Abstract So far unknown anisotropic properties of out-of-phase magnetic susceptibility (opMS) of hematite and their bearing on understanding the origin of hematite magnetism were investigated on example of four single crystals from Minas Gerais, Brazil. The research comprised measurement of directional variation of field-dependent and frequency-dependent opMS and testing whether the anisotropy of opMS can be represented by the second rank tensor. It was found that the opMS shows strong field dependence along basal plane and only weak field dependence along c-axis. As for the frequency dependence, it is virtually non-existent along the basal plane. Along the c-axis, the opMS is similar at frequencies 976 and 3904 Hz, while at 15616 Hz it is clearly higher. Consequently, opMS is dominantly due to weak field hysteresis. The minimum opMS directions are parallel to the c-axis, while the other two principal directions lie within basal plane. The degree of anisotropy is extremely high (ratio of maximum opMS to minimum opMS ≫100) and the anisotropy ellipsoid is very oblate. In stereographic diagrams, the opMS contours very roughly resemble the theoretical contours calculated from opMS tensor. However, the differences between measured and theoretical values in directional opMS are clearly higher than the measuring error and are distributed very non-homogeneously. This indicates that the second rank tensor is only very approximate representative of the spatial variation of the directional opMS of hematite single crystals. Earlier model of hematite magnetism assuming slightly scanted antiferromagnetism along the c-axis and strongly canted antiferromagnetism or even weak ferromagnetism along the basal plane is supported.
      PubDate: 2022-08-30
      DOI: 10.1007/s11200-022-0829-2
       
  • Anisotropic VSP reverse-time migration with optimal pure acoustic wave and
           complex wavefield separation

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      Abstract: Abstract Ignoring anisotropy characteristic of subsurface media may lead to misplaced images and low resolution of the target for the reverse-time migration (RTM). The mature anisotropic RTM methods are mainly based on the pseudoacoustic wave approximation. Although these schemes have high computational efficiency, most of pseudo-acoustic wave equations (PWEs) inevitably encounter SV-wave artifacts or instability for anisotropic modeling and imaging. To improve the anisotropic RTM quality, we develop a combination of optimal pure acoustic wave and complex wavefield separation to conduct anisotropic RTM for both surface and vertical seismic profiling (VSP) acquisition geometries. Among the proposed scheme, we derive an optimal pure acoustic wave dispersion relation, and solve the corresponding wave equation by incorporating finite-difference and Poisson solver. The modified equation can remove SV-wave artifacts and instability of PWEs. Wavefield separation approach can choose desired wavefield components along different directions to carry out the final imaging, which can effectively suppress low-frequency imaging noise. Moreover, the hybrid absorbing boundary condition is adopted to suppress artificial boundary reflections during wavefield extrapolation. Basic theory and modeling examples demonstrate that the developed schemes can generate RTM results with high accuracy.
      PubDate: 2022-08-27
      DOI: 10.1007/s11200-022-0717-9
       
  • Velocity analysis of noisy seismic data based on RSVD weighted semblance

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      Abstract: Abstract The accuracy of velocity spectrum affects the subsequent processing of seismic data. Though the singular value decomposition (SVD) weighted semblance has a higher velocity resolution than conventional semblance, its performance is degraded for noisy seismic data. A rectified SVD weighted semblance method (RSVD), aiming to improve the accuracy of velocity spectrum for seismic data contaminated by noise, is proposed. In this approach, the weighting function is constructed from the first two singular values and their mean square error obtained via SVD of noisy seismic data after normal moveout (NMO) with scanning velocity. Synthetic and field examples demonstrate that the proposed method performs better than the SVD weighted semblance in enhancing the accuracy of velocity spectra for noisy near-offset common midpoint gathers in layered isotropic media.
      PubDate: 2022-04-30
      DOI: 10.1007/s11200-021-0327-y
       
  • Erratum to “Improving the accuracy of the expanded anisotropic eikonal
           equation at larger offsets using Levin’s T-transformation”

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      PubDate: 2022-04-04
      DOI: 10.1007/s11200-022-0901-y
       
  • Expressions for the calculation of isotropic Gaussian filter kernels in
           the spherical harmonic domain

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      Abstract: Abstract The isotropic Gaussian filter has been used extensively in Gravity Recovery and Climate Experiment (GRACE) temporal gravity field solutions, and is still being applied to GRACE Follow-On products to remove high-frequency errors and improve the estimation of mass transport events on the Earth’s surface. For such applications, the only known rigorous method to calculate the spherical harmonic coefficients of an isotropic Gaussian filter is by the use of a second-order recurrence relation. As an alternative, an approximate expression is also used frequently. In this paper, we provide some additional expressions for the calculation of isotropic Gaussian filter kernels in the spherical harmonic domain. Specifically, we derive a new recurrence relation, a closed-form expression, expressions involving modified Bessel functions of the first kind, and a new approximate expression. We also examine and compare them from a computational viewpoint. The results of our numerical investigations indicate that the new recurrence relation and the closed-form expression are unstable in a way similar to the second-order recurrence relation that has been used so far. The expressions involving modified Bessel functions, and particularly the ones using exponentially scaled modified Bessel functions, provide a simple, elegant and stable way of calculating isotropic Gaussian filter coefficients, since routines for their stable evaluation are readily available in many programming languages. Alternatively, the new approximate expression can be used, which is also stable and offers better accuracy than previous approximations.
      PubDate: 2022-04-04
      DOI: 10.1007/s11200-021-0272-9
       
  • Rotationally invariant viscoelastic medium with a non-symmetric stiffness
           matrix

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      Abstract: Abstract 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.
      PubDate: 2022-02-08
      DOI: 10.1007/s11200-021-1106-5
       
  • Geoelectrical imaging and spatial distribution of alluvial materials of
           the Sanaga River (Cameroon, Central Africa)

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      Abstract: Abstract 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.
      PubDate: 2022-02-08
      DOI: 10.1007/s11200-020-1083-0
       
 
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