Pub Date : 2021-02-01DOI: 10.1007/s11200-020-0158-2
Luděk Klimeš
In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In this paper, we thus derive the representation theorem for viscoelastic waves in a medium with a non-symmetric stiffness matrix. The representation theorem expresses the wave field at a receiver, situated inside a subset of the definition volume of the viscoelastodynamic equation, in terms of the volume integral over the subset and the surface integral over the boundary of the subset. For the given medium, we define the complementary medium corresponding to the transposed stiffness matrix. We define the frequency-domain complementary Green function as the frequency-domain Green function in the complementary medium. We then derive the provisional representation theorem as the relation between the frequency-domain wave field in the given medium and the frequency-domain complementary Green function. This provisional representation theorem yields the reciprocity relation between the frequency-domain Green function and the frequency-domain complementary Green function. The final version of the representation theorem is then obtained by inserting the reciprocity relation into the provisional representation theorem.
{"title":"Representation theorem for viscoelastic waves with a non-symmetric stiffness matrix","authors":"Luděk Klimeš","doi":"10.1007/s11200-020-0158-2","DOIUrl":"https://doi.org/10.1007/s11200-020-0158-2","url":null,"abstract":"<p>In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In this paper, we thus derive the representation theorem for viscoelastic waves in a medium with a non-symmetric stiffness matrix. The representation theorem expresses the wave field at a receiver, situated inside a subset of the definition volume of the viscoelastodynamic equation, in terms of the volume integral over the subset and the surface integral over the boundary of the subset. For the given medium, we define the complementary medium corresponding to the transposed stiffness matrix. We define the frequency-domain complementary Green function as the frequency-domain Green function in the complementary medium. We then derive the provisional representation theorem as the relation between the frequency-domain wave field in the given medium and the frequency-domain complementary Green function. This provisional representation theorem yields the reciprocity relation between the frequency-domain Green function and the frequency-domain complementary Green function. The final version of the representation theorem is then obtained by inserting the reciprocity relation into the provisional representation theorem.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"65 1","pages":"53 - 58"},"PeriodicalIF":0.9,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-0158-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4022304","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}
Pub Date : 2021-02-01DOI: 10.1007/s11200-020-1251-2
Yumeng Jiang, Siyuan Cao, Siyuan Chen, Duo Zheng
Seismic wavelet extraction always plays a central role in high-resolution seismic processing. Conventional methods assume that seismic data are stationary when a constant wavelet is considered, which ignores the time-varying characteristics of seismic wavelets. In reality, seismic data are nonstationary because of attenuation, scattering, and other physical processes during propagation, which means that the frequency spectrum of seismic signal changes from shallow to deep formations. We have developed a time-varying wavelet extraction method by using a highly energy-concentrated time-frequency representation technique. Time-varying wavelets are generated according to the local frequency spectrum at every instant. In addition, because the estimations of parameters for wavelet extraction are fully data-driven, the results of the proposed method are more accurate and suitable for the nonstationary nature of actual seismic data. Synthetic tests indicate the reliability and robustness of the proposed method, even under noise contamination. By applying the time-varying wavelet extracted using the proposed method to seismic inversion on a field data example, we obtain the deconvolution result with improved resolution and a better fit to the well-log reflectivity compared to that by using conventional wavelet extraction methods.
{"title":"A data-driven method for time-varying wavelet extraction based on the local frequency spectrum","authors":"Yumeng Jiang, Siyuan Cao, Siyuan Chen, Duo Zheng","doi":"10.1007/s11200-020-1251-2","DOIUrl":"https://doi.org/10.1007/s11200-020-1251-2","url":null,"abstract":"<p>Seismic wavelet extraction always plays a central role in high-resolution seismic processing. Conventional methods assume that seismic data are stationary when a constant wavelet is considered, which ignores the time-varying characteristics of seismic wavelets. In reality, seismic data are nonstationary because of attenuation, scattering, and other physical processes during propagation, which means that the frequency spectrum of seismic signal changes from shallow to deep formations. We have developed a time-varying wavelet extraction method by using a highly energy-concentrated time-frequency representation technique. Time-varying wavelets are generated according to the local frequency spectrum at every instant. In addition, because the estimations of parameters for wavelet extraction are fully data-driven, the results of the proposed method are more accurate and suitable for the nonstationary nature of actual seismic data. Synthetic tests indicate the reliability and robustness of the proposed method, even under noise contamination. By applying the time-varying wavelet extracted using the proposed method to seismic inversion on a field data example, we obtain the deconvolution result with improved resolution and a better fit to the well-log reflectivity compared to that by using conventional wavelet extraction methods.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"65 1","pages":"70 - 85"},"PeriodicalIF":0.9,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-1251-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4021352","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}
Pub Date : 2021-01-08DOI: 10.1007/s11200-020-1122-x
Ignacio Barbero, Cristina Torrecillas, Raúl Páez, Gonçalo Prates, Manuel Berrocoso
Macaronesia is a complex oceanic region spanning three tectonic plates in the northeast Atlantic ocean. It is composed of four archipelagos, widely distributed and limited to the east by the Iberian Peninsula and north-western coast of Africa. This study aims to clarify recent Macaronesian kinematics from 19 GNSS stations located on the four archipelagos and the Iberian and African coastlines. The analysis is based on nearly 15 years of common data acquisition and aimed to detect new effects of intraplate tectonics or similar local/regional events consistent with calculated ground displacements. Evaluating the GNSS stations residual velocities relative to those expected from the NNR-MORVEL56 model, higher residuals were found at continental coastal stations (Africa) than at oceanic ones (Canaries and Madeira). From the computed strain rate map, the possible existence of a shear zone connecting the Gloria and Transmoroccan fault systems, already mentioned by other authors, was depicted. Cluster statistical analysis of the horizontal residual velocities helped to identify tectonic boundaries in Macaronesia and four groups of analogous intraplate residual velocities within this region. Three of four groups were identified in the Azores, highlighting the African-Nubian-Eurasian diffuse plate boundary in this region. Furthermore, in the Canary Islands, two distinct kinematic behaviours were detected, possibly due to the activity along a previously detected tectonic fault between Tenerife and Gran Canaria, where some stations have similar intraplate residuals to those at Madeira and Cape Verde stations, while others have similar intraplate residuals to those of continental stations. Finally, all stations on oceanic crust, except Cape Verde, present recent ground subsidence which may be attributed to isostatic adjustment.
{"title":"Recent Macaronesian kinematics from GNSS ground displacement analysis","authors":"Ignacio Barbero, Cristina Torrecillas, Raúl Páez, Gonçalo Prates, Manuel Berrocoso","doi":"10.1007/s11200-020-1122-x","DOIUrl":"https://doi.org/10.1007/s11200-020-1122-x","url":null,"abstract":"<p>Macaronesia is a complex oceanic region spanning three tectonic plates in the northeast Atlantic ocean. It is composed of four archipelagos, widely distributed and limited to the east by the Iberian Peninsula and north-western coast of Africa. This study aims to clarify recent Macaronesian kinematics from 19 GNSS stations located on the four archipelagos and the Iberian and African coastlines. The analysis is based on nearly 15 years of common data acquisition and aimed to detect new effects of intraplate tectonics or similar local/regional events consistent with calculated ground displacements. Evaluating the GNSS stations residual velocities relative to those expected from the NNR-MORVEL56 model, higher residuals were found at continental coastal stations (Africa) than at oceanic ones (Canaries and Madeira). From the computed strain rate map, the possible existence of a shear zone connecting the Gloria and Transmoroccan fault systems, already mentioned by other authors, was depicted. Cluster statistical analysis of the horizontal residual velocities helped to identify tectonic boundaries in Macaronesia and four groups of analogous intraplate residual velocities within this region. Three of four groups were identified in the Azores, highlighting the African-Nubian-Eurasian diffuse plate boundary in this region. Furthermore, in the Canary Islands, two distinct kinematic behaviours were detected, possibly due to the activity along a previously detected tectonic fault between Tenerife and Gran Canaria, where some stations have similar intraplate residuals to those at Madeira and Cape Verde stations, while others have similar intraplate residuals to those of continental stations. Finally, all stations on oceanic crust, except Cape Verde, present recent ground subsidence which may be attributed to isostatic adjustment.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"65 1","pages":"15 - 35"},"PeriodicalIF":0.9,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-1122-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4340939","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}
Pub Date : 2021-01-08DOI: 10.1007/s11200-020-1121-y
Poulommi Mondal, Debasis D. Mohanty
The present study produces very new SKKS splitting measurements from the Northeast India, suggesting the region as tectonically more heterogeneous and complex in nature. It fills the gap of anisotropic parameters from an epicentral range of 140°–180° in order to understand the lithospheric deformation patterns of the terrain in a better way. The splitting parameters namely polarisation direction of fast waves (?) and delay time are the manifestation of anisotropic effects of a medium. The present SKKS splitting measurements from nine broadband seismic stations in Northeast India incorporate new understandings of deformation patterns for this region. At the Himalayan collision zone and sub-Himalayan region, the deformation pattern showing a perfect alignment of the ? parallel to the collisional arc (Main Boundary Thrust, Main Central Thrust), suggests that a localized strain derived from N-S Indo-Eurasian collision is the major source behind its complex tectonics. The SKKS splitting measurements at Assam foredeep region streamline the effect of Kopili fault in controlling the deformation patterns in a NW-SE direction. There is a significant difference in anisotropic behaviour of stations at the northern Shillong plateau compared to the stations at its southern proximity. The absolute plate motion (APM) parallel to ? in northern fringe of the plateau strictly indicates the influence of asthenospheric flow, which in turn is driven by APM of Indian plate in a no net rotation reference frame. On the other hand, major regional structures like the Dauki and Dapsi faults control the anisotropic pattern at the southern extremity of this plateau.
{"title":"Mantle deformation and seismic anisotropy beneath Northeast India inferred from SKKS birefringence","authors":"Poulommi Mondal, Debasis D. Mohanty","doi":"10.1007/s11200-020-1121-y","DOIUrl":"https://doi.org/10.1007/s11200-020-1121-y","url":null,"abstract":"<p>The present study produces very new SKKS splitting measurements from the Northeast India, suggesting the region as tectonically more heterogeneous and complex in nature. It fills the gap of anisotropic parameters from an epicentral range of 140°–180° in order to understand the lithospheric deformation patterns of the terrain in a better way. The splitting parameters namely polarisation direction of fast waves (?) and delay time are the manifestation of anisotropic effects of a medium. The present SKKS splitting measurements from nine broadband seismic stations in Northeast India incorporate new understandings of deformation patterns for this region. At the Himalayan collision zone and sub-Himalayan region, the deformation pattern showing a perfect alignment of the ? parallel to the collisional arc (Main Boundary Thrust, Main Central Thrust), suggests that a localized strain derived from N-S Indo-Eurasian collision is the major source behind its complex tectonics. The SKKS splitting measurements at Assam foredeep region streamline the effect of Kopili fault in controlling the deformation patterns in a NW-SE direction. There is a significant difference in anisotropic behaviour of stations at the northern Shillong plateau compared to the stations at its southern proximity. The absolute plate motion (APM) parallel to ? in northern fringe of the plateau strictly indicates the influence of asthenospheric flow, which in turn is driven by APM of Indian plate in a no net rotation reference frame. On the other hand, major regional structures like the Dauki and Dapsi faults control the anisotropic pattern at the southern extremity of this plateau.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"65 1","pages":"36 - 52"},"PeriodicalIF":0.9,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-1121-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4340940","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}
Pub Date : 2021-01-08DOI: 10.1007/s11200-020-1024-y
Bahattin Erdogan, Serif Hekimoglu, Utkan Mustafa Durdag
In Conventional Deformation Analysis (CDA), at least two different epochs are adjusted by using the Least Squares Estimation (LSE) method and compared statistically. The effect of the geometry of the network is an essential part of the adjustment model and the LSE method smears the effects of the displaced point over the other nondisplaced points. In this study, to remove these spoiling effects and to increase the reliability of the deformation analysis, a new approach is introduced. This approach depends on the analysis of the differences between observations of the two epochs, and also considers the principles of the model error approach. All possible combinations of the differences of the observations are considered as model errors in Gauss-Markov model and the estimated model error for the combination, that has the smallest variance, is compared with a critical value to answer the question whether it is significant or not. To compare the results of the new approach with the CDA, the Monte Carlo simulation technique and mean success rate are used in a leveling network. As a consequence, according to the simulation results, the new approach is better than the CDA by 7.6% and 9.7% for one and two displaced points, respectively, when the deformation network is designed as a subnetwork.
{"title":"A new univariate deformation analysis approach considering displacements as model errors","authors":"Bahattin Erdogan, Serif Hekimoglu, Utkan Mustafa Durdag","doi":"10.1007/s11200-020-1024-y","DOIUrl":"https://doi.org/10.1007/s11200-020-1024-y","url":null,"abstract":"<p>In Conventional Deformation Analysis (CDA), at least two different epochs are adjusted by using the Least Squares Estimation (LSE) method and compared statistically. The effect of the geometry of the network is an essential part of the adjustment model and the LSE method smears the effects of the displaced point over the other nondisplaced points. In this study, to remove these spoiling effects and to increase the reliability of the deformation analysis, a new approach is introduced. This approach depends on the analysis of the differences between observations of the two epochs, and also considers the principles of the model error approach. All possible combinations of the differences of the observations are considered as model errors in Gauss-Markov model and the estimated model error for the combination, that has the smallest variance, is compared with a critical value to answer the question whether it is significant or not. To compare the results of the new approach with the CDA, the Monte Carlo simulation technique and mean success rate are used in a leveling network. As a consequence, according to the simulation results, the new approach is better than the CDA by 7.6% and 9.7% for one and two displaced points, respectively, when the deformation network is designed as a subnetwork.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"65 1","pages":"1 - 14"},"PeriodicalIF":0.9,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-1024-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4340927","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}
Pub Date : 2020-11-09DOI: 10.1007/s11200-020-1028-7
Sattam Almadani
This study aims to quantify the rate of coseismic deformation in the Gulf of Aqaba. Earthquake catalogue, Gutenberg-Richter relationship and fault plane solutions were integrated to measure the size and shape of deformation using the moment-tensor summation technique. First, the Gutenberg-Richter relationship was established using seismicity data from the period of 1964–2019. Then, the moment-tensor summation based on 44 focal mechanism solutions was used to calculate the shape of deformation. The eigenvalues of moment-tensor reflect the diversity of focal mechanism solutions that alternate from normal to strike-slip fault styles in the deformation zone. The analysis reveals a dominant shear deformation in the Gulf of Aqaba that extends in a direction of N42.2°E at a rate of 2.6 ± 0.04 mm yr?1and shortens in the direction of N305.2°E at a rate of 2.0 ± 0.02 mm yr?1. These results suggest that the active deformation occurring in the Gulf of Aqaba is due to the relative tectonic movements between the Arabian and African plates, as well as Sinai subplate.
本研究旨在量化亚喀巴湾同震形变的速率。结合地震目录、古腾堡-里希特关系和断层平面解,利用矩张量求和技术测量变形的大小和形状。首先,利用1964-2019年的地震活动数据建立了古腾堡-里希特关系。然后,采用基于44个焦点机构解的矩张量求和来计算变形形状。矩张量特征值反映了震源机制解的多样性,震源机制解在变形带正断层和走滑断层之间交替存在。分析表明,亚喀巴湾的主要剪切变形以2.6±0.04 mm /年的速率向N42.2°E方向延伸。沿N305.2°E方向以2.0±0.02 mm / yr的速率缩短。这些结果表明,亚喀巴湾的活动变形是由于阿拉伯板块和非洲板块以及西奈板块之间的相对构造运动造成的。
{"title":"Rate of seismic deformation in the Gulf of Aqaba inferred from moment-tensor summation","authors":"Sattam Almadani","doi":"10.1007/s11200-020-1028-7","DOIUrl":"https://doi.org/10.1007/s11200-020-1028-7","url":null,"abstract":"<p><i>This study aims to quantify the rate of coseismic deformation in the Gulf of Aqaba. Earthquake catalogue, Gutenberg-Richter relationship and fault plane solutions were integrated to measure the size and shape of deformation using the moment-tensor summation technique. First, the Gutenberg-Richter relationship was established using seismicity data from the period of 1964–2019. Then, the moment-tensor summation based on 44 focal mechanism solutions was used to calculate the shape of deformation. The eigenvalues of moment-tensor reflect the diversity of focal mechanism solutions that alternate from normal to strike-slip fault styles in the deformation zone. The analysis reveals a dominant shear deformation in the Gulf of Aqaba that extends in a direction of N42.2°E at a rate of 2.6 ± 0.04 mm yr</i><sup>?1</sup><i>and shortens in the direction of N305.2°E at a rate of 2.0 ± 0.02 mm yr</i><sup>?1</sup>. <i>These results suggest that the active deformation occurring in the Gulf of Aqaba is due to the relative tectonic movements between the Arabian and African plates, as well as Sinai subplate</i>.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"64 4","pages":"504 - 519"},"PeriodicalIF":0.9,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-1028-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4399623","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}
Full waveform inversion (FWI) is a non-linear inverse problem that can be sensitive to noise. The tolerance of the noise-interference characteristics depends on the types of misfit functions. To date, different misfit functions, such as the least-squares norm (L2), the least-absolute-value norm (L1), and combinations of the two (e.g., the Huber and hybrid criteria), have been applied to FWI. The L2 norm is highly sensitive to non-Gaussian errors in the data and gives rise to high-amplitude artifacts in reconstructed models. For non-Gaussian noise data, the L1 norm and the Huber and hybrid criteria always reliably reconstruct models. However, the Huber and hybrid criteria require tedious error investigations to estimate their threshold criterion. Thus, the L1 norm is adopted here to improve the anti-noise ability of the FWI. The step length is closely related to the misfit function, and an optimal step-length estimation method can rapidly make the FWI algorithm reach the global minimum, with a reduced number of iterations and fewer extra forward modeling simulations during each iteration. The step length can usually be obtained using the exact or inexact line search method. Generally, the exact line search method is faster than the inexact one. Therefore, we derived an exact line search method for the L1 norm in the FWI process. Its effectiveness was tested using noise-free data from Overthrust and the SEG/EAGE salt models. The results demonstrate that this method can recover high-resolution velocity models with low computational costs. Numerical tests using the synthetic Overthrust model contaminated by strong noise were used to further validate the robustness of this exact line search method.
{"title":"Exact line search method for using the L1-norm misfit function in full waveform inversion","authors":"Xiaona Ma, Guanghe Liang, Shanhui Xu, Zhiyuan Li, Haixin Feng","doi":"10.1007/s11200-020-0904-5","DOIUrl":"https://doi.org/10.1007/s11200-020-0904-5","url":null,"abstract":"<p><i>Full waveform inversion (FWI) is a non-linear inverse problem that can be sensitive to noise. The tolerance of the noise-interference characteristics depends on the types of misfit functions. To date, different misfit functions, such as the least-squares norm (L2), the least-absolute-value norm (L1), and combinations of the two (e.g., the Huber and hybrid criteria), have been applied to FWI. The L2 norm is highly sensitive to non-Gaussian errors in the data and gives rise to high-amplitude artifacts in reconstructed models. For non-Gaussian noise data, the L1 norm and the Huber and hybrid criteria always reliably reconstruct models. However, the Huber and hybrid criteria require tedious error investigations to estimate their threshold criterion. Thus, the L1 norm is adopted here to improve the anti-noise ability of the FWI. The step length is closely related to the misfit function, and an optimal step-length estimation method can rapidly make the FWI algorithm reach the global minimum, with a reduced number of iterations and fewer extra forward modeling simulations during each iteration. The step length can usually be obtained using the exact or inexact line search method. Generally, the exact line search method is faster than the inexact one. Therefore, we derived an exact line search method for the L1 norm in the FWI process. Its effectiveness was tested using noise-free data from Overthrust and the SEG/EAGE salt models. The results demonstrate that this method can recover high-resolution velocity models with low computational costs. Numerical tests using the synthetic Overthrust model contaminated by strong noise were used to further validate the robustness of this exact line search method</i>.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"64 4","pages":"483 - 503"},"PeriodicalIF":0.9,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-0904-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4399628","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}
Pub Date : 2020-10-27DOI: 10.1007/s11200-020-1023-z
Ramazan Alpay Abbak
A precise gravimetric geoid model is determined by using Stokes formula assuming that there is no topography above the geoid. Then, the geoid model is simply corrected by considering the constant crustal density of 2670 kg m?3 for topographical mass. In fact, the actual density of topographical mass differs about ±20% from the constant value. Recently a global crustal density model within 30″ resolution has been released by the University of New Brunswick in Canada. The paper is devoted to the study of the effect of using this model on the accuracy of gravimetric geoid in a mountainous region in Turkey. Numerical results prove that the differences in the geoid height due to this model may reach up to several decimetres, which should not be ignored in a precise geoid modelling with 1-cm geoid. Thus, it is concluded that the effect of topographical density variations, contained in this model, is significant and should be taken into account in precise geoid determination, particularly in mountainous regions.
在假定大地水准面之上没有地形的情况下,利用Stokes公式确定了精确的重力大地水准面模型。然后,通过考虑地壳密度为2670 kg m?3为地形质量。事实上,地形质量的实际密度与恒定值相差约±20%。最近,加拿大新不伦瑞克大学发布了一个30″分辨率的全球地壳密度模型。本文研究了在土耳其某山区使用该模型对重力大地水准面精度的影响。数值结果表明,该模型对大地水准面高度的影响可达几分米,这在1厘米大地水准面精确建模中是不可忽视的。因此,该模型中包含的地形密度变化的影响是显著的,在精确确定大地水准面时应予以考虑,特别是在山区。
{"title":"Effect of a high-resolution global crustal model on gravimetric geoid determination: a case study in a mountainous region","authors":"Ramazan Alpay Abbak","doi":"10.1007/s11200-020-1023-z","DOIUrl":"https://doi.org/10.1007/s11200-020-1023-z","url":null,"abstract":"<p>A precise gravimetric geoid model is determined by using Stokes formula assuming that there is no topography above the geoid. Then, the geoid model is simply corrected by considering the constant crustal density of 2670 kg m<sup>?3</sup> for topographical mass. In fact, the actual density of topographical mass differs about ±20% from the constant value. Recently a global crustal density model within 30″ resolution has been released by the University of New Brunswick in Canada. The paper is devoted to the study of the effect of using this model on the accuracy of gravimetric geoid in a mountainous region in Turkey. Numerical results prove that the differences in the geoid height due to this model may reach up to several decimetres, which should not be ignored in a precise geoid modelling with 1-cm geoid. Thus, it is concluded that the effect of topographical density variations, contained in this model, is significant and should be taken into account in precise geoid determination, particularly in mountainous regions.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"64 4","pages":"436 - 451"},"PeriodicalIF":0.9,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-1023-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5060189","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}
Pub Date : 2020-10-27DOI: 10.1007/s11200-020-1013-1
Shigang Xu, Yang Liu
To improve the modeling accuracy and adaptability of traditional temporal second-order staggered-grid finite-difference (SFD) methods for 3D acoustic-wave modeling, we propose a modified time-space-domain temporal and spatial high-order SFD stencil on a cuboid grid. The grid nodes on a double-pyramid stencil and the standard orthogonality stencil are used to approximate temporal and spatial derivatives. This stencil can adopt different grid spacing in each spatial axis, and thus it is more flexible than the existing one with the same grid spacing. Based on the time-space-domain dispersion relation, the high-order FD coefficients are generated by using Taylor expansion and least squares. Numerical analyses and modeling examples demonstrate that our proposed schemes have higher accuracy and better stability than other conventional schemes, and thus larger time steps can be used to improve the computational efficiency in 3D case.
{"title":"Modeling 3D acoustic-wave propagation using modified cuboid-based staggered-grid finite-difference methods with temporal and spatial high-order accuracy","authors":"Shigang Xu, Yang Liu","doi":"10.1007/s11200-020-1013-1","DOIUrl":"https://doi.org/10.1007/s11200-020-1013-1","url":null,"abstract":"<p>To improve the modeling accuracy and adaptability of traditional temporal second-order staggered-grid finite-difference (SFD) methods for 3D acoustic-wave modeling, we propose a modified time-space-domain temporal and spatial high-order SFD stencil on a cuboid grid. The grid nodes on a double-pyramid stencil and the standard orthogonality stencil are used to approximate temporal and spatial derivatives. This stencil can adopt different grid spacing in each spatial axis, and thus it is more flexible than the existing one with the same grid spacing. Based on the time-space-domain dispersion relation, the high-order FD coefficients are generated by using Taylor expansion and least squares. Numerical analyses and modeling examples demonstrate that our proposed schemes have higher accuracy and better stability than other conventional schemes, and thus larger time steps can be used to improve the computational efficiency in 3D case.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"64 4","pages":"465 - 482"},"PeriodicalIF":0.9,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-1013-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5064932","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}
This study presents an optimized gravity-sparse inversion method. The proposed method minimizes the global objective function using interior-point method for boundary constraints and a general weighting function comprising the depth, compactness, and kernel weighting functions of the density models. For the compactness weighting function, practical experiments demonstrate that the recovered model becomes more compact with an increasing value for the relative exponential factor β. However, if no appropriate boundary-constraint method is applied, the inversion results cannot be controlled within the designated constraint bounds when β needs to be set to a large value to obtain compact inversion results. The interior-point method allows the use of a larger β to obtain more compact inversion results without violating the boundary constraints. Additionally, models in close proximity can more clearly be recognized using this method. To improve the computational efficiency and obtain a more accurate regularization parameter, the preconditioned conjugate gradient and L-curve, or line search methods, were also applied. The proposed method was applied for three synthetic examples: two positive bodies adjacent to each other at different depths inverted using noise-free gravity anomaly data, three bodies (positive or negative) at different depths inverted using noise-free or contaminated gravity anomaly data, and three bodies (positive or negative) characterized by a certain dip angle inverted using contaminated gravity anomaly data. This method was also applied for the inversion of a Woodlawn sulfide body, Missouri iron ore body, and granitoid rock body in the Rio Maria region in the state of Para, Brazil. In all six test cases, larger β values were used and the density models were recovered with sharper boundaries within the designated bounds.
{"title":"Gravity sparse inversion using the interior-point method and a general model weighting function","authors":"Wenwu Zhu, Junhuan Peng, Sanming Luo, Xiangang Meng, Jinzhao Liu, Chuandong Zhu","doi":"10.1007/s11200-020-0831-5","DOIUrl":"https://doi.org/10.1007/s11200-020-0831-5","url":null,"abstract":"<p>This study presents an optimized gravity-sparse inversion method. The proposed method minimizes the global objective function using interior-point method for boundary constraints and a general weighting function comprising the depth, compactness, and kernel weighting functions of the density models. For the compactness weighting function, practical experiments demonstrate that the recovered model becomes more compact with an increasing value for the relative exponential factor β. However, if no appropriate boundary-constraint method is applied, the inversion results cannot be controlled within the designated constraint bounds when β needs to be set to a large value to obtain compact inversion results. The interior-point method allows the use of a larger β to obtain more compact inversion results without violating the boundary constraints. Additionally, models in close proximity can more clearly be recognized using this method. To improve the computational efficiency and obtain a more accurate regularization parameter, the preconditioned conjugate gradient and L-curve, or line search methods, were also applied. The proposed method was applied for three synthetic examples: two positive bodies adjacent to each other at different depths inverted using noise-free gravity anomaly data, three bodies (positive or negative) at different depths inverted using noise-free or contaminated gravity anomaly data, and three bodies (positive or negative) characterized by a certain dip angle inverted using contaminated gravity anomaly data. This method was also applied for the inversion of a Woodlawn sulfide body, Missouri iron ore body, and granitoid rock body in the Rio Maria region in the state of Para, Brazil. In all six test cases, larger β values were used and the density models were recovered with sharper boundaries within the designated bounds.</p>","PeriodicalId":22001,"journal":{"name":"Studia Geophysica et Geodaetica","volume":"64 4","pages":"419 - 435"},"PeriodicalIF":0.9,"publicationDate":"2020-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11200-020-0831-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4950540","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}