Studia Geophysica et Geodaetica最新文献

{"title":"Tracing real-valued reference rays in anisotropic viscoelastic media","authors":"Ludĕk Klimeš","doi":"10.1007/s11200-022-0906-6","DOIUrl":"10.1007/s11200-022-0906-6","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 3-4","pages":"124 - 144"},"PeriodicalIF":0.9,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4590998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extremely strong anisotropy of out-of-phase component of AC magnetic susceptibility in hematite single crystals and its origin","authors":"František Hrouda,&nbsp;Josef Ježek,&nbsp;Martin Chadima","doi":"10.1007/s11200-022-0829-2","DOIUrl":"10.1007/s11200-022-0829-2","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 3-4","pages":"187 - 205"},"PeriodicalIF":0.9,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5146424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anisotropic VSP reverse-time migration with optimal pure aeoustic wave and complex wavefield separation","authors":"Zhiming Ren,&nbsp;Zhefeng Wei,&nbsp;Chenghong Zhu","doi":"10.1007/s11200-022-0717-9","DOIUrl":"10.1007/s11200-022-0717-9","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 3-4","pages":"145 - 161"},"PeriodicalIF":0.9,"publicationDate":"2022-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5029388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Velocity analysis of noisy seismic data based on RSVD weighted semblance","authors":"Yankai Xu,&nbsp;Siyuan Cao,&nbsp;Xiao Pan,&nbsp;Siyuan Chen,&nbsp;Mingjun Cai,&nbsp;Jialiang Zhang","doi":"10.1007/s11200-021-0327-y","DOIUrl":"10.1007/s11200-021-0327-y","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 1-2","pages":"48 - 61"},"PeriodicalIF":0.9,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Expressions for the calculation of isotropic Gaussian filter kernels in the spherical harmonic domain","authors":"Dimitrios Piretzidis,&nbsp;Michael G. Sideris","doi":"10.1007/s11200-021-0272-9","DOIUrl":"10.1007/s11200-021-0272-9","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 1-2","pages":"1 - 22"},"PeriodicalIF":0.9,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4149091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Erratum to “Improving the accuracy of the expanded anisotropic eikonal equation at larger offsets using Levin’s T-transformation”","authors":"Humbang Purba,&nbsp;Awali Priyono,&nbsp;Wahyu Triyoso,&nbsp;Mochamad Apri","doi":"10.1007/s11200-022-0901-y","DOIUrl":"10.1007/s11200-022-0901-y","url":null,"abstract":"","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 1-2","pages":"80 - 80"},"PeriodicalIF":0.9,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4148837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation of latest marine gravity field models derived from satellite altimetry over the Gulf of Guinea (Central Africa) with shipborne gravity data","authors":"Paul Gautier Kamto,&nbsp;Loudi Yap,&nbsp;Sévérin Nguiya,&nbsp;Ludovic Houetchak Kandé,&nbsp;Joseph Kamguia","doi":"10.1007/s11200-021-0157-y","DOIUrl":"10.1007/s11200-021-0157-y","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 1-2","pages":"23 - 37"},"PeriodicalIF":0.9,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11200-021-0157-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4149095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rotationally invariant viscoelastic medium with a non-symmetric stiffness matrix","authors":"Luděk Klimeš","doi":"10.1007/s11200-021-1106-5","DOIUrl":"10.1007/s11200-021-1106-5","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 1-2","pages":"38 - 47"},"PeriodicalIF":0.9,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4337146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geoelectrical imaging and spatial distribution of alluvial materials of the Sanaga River (Cameroon, Central Africa)","authors":"Renaud Menanga Tokouet,&nbsp;Joseph Quentin Yene Atangana,&nbsp;Mbida Yem,&nbsp;Emile Ekomane,&nbsp;Ferdinand Deffo,&nbsp;Florent Daniel Akono,&nbsp;Mike-Franck Mienlam Essi","doi":"10.1007/s11200-020-1083-0","DOIUrl":"10.1007/s11200-020-1083-0","url":null,"abstract":"<div><p>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 (&lt;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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"66 1-2","pages":"62 - 79"},"PeriodicalIF":0.9,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4337747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of the nonlinear optimisation in regional gravity field modelling using spherical radial base functions","authors":"Hany Mahbuby,&nbsp;Yazdan Amerian,&nbsp;Amirhossein Nikoofard,&nbsp;Mehdi Eshagh","doi":"10.1007/s11200-020-1077-y","DOIUrl":"10.1007/s11200-020-1077-y","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"65 3-4","pages":"261 - 290"},"PeriodicalIF":0.9,"publicationDate":"2021-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11200-020-1077-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4489264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}