Topographic Effect

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Lars E. Sjöberg - One of the best experts on this subject based on the ideXlab platform.

  • The secondary indirect Topographic Effect in physical geodesy
    Studia Geophysica et Geodaetica, 2015
    Co-Authors: Lars E. Sjöberg
    Abstract:

    The use of Stokes’ integral by the remove-compute-restore technique is the most common way to determine the geoid today. The method includes direct, primary and secondary indirect Topographic Effects. This article is mainly devoted to the secondary indirect Topographic Effect (SITE), which reaches the extreme values of 265 mGal and −0.6 mGal for the uncompensated and Helmert condensation compensated gravity anomalies, respectively. The corresponding Effects on the geoid height reach the magnitudes of 328 m and −0.5 m, respectively. Here we emphasize that the SITE is a direct Effect, needed in a rigorous gravity anomaly. For surface as well as for classical gravity anomalies, located at the geoid, the SITE can be interpreted as a shift in the normal gravity along the ellipsoidal normal to the point where the normal potential equals the Topographically reduced geopotential at the computation point. We show that it may yield a bias of the order of −0.9 m in the Himalayas if not properly considered in the surface anomaly. This bias does not change when using a Topographic compensation model, e.g., by Helmert condensation of the topography. The problem is avoided when using the no-topography gravity anomaly with or without compensation.

  • on the Topographic Effects by stokes formula
    Journal of Geodetic Science, 2014
    Co-Authors: Lars E. Sjöberg
    Abstract:

    Traditional gravimetric geoid determination re- lies on Stokes' formula with removal and restoration of the Topographic Effects. It is shown that this solution is in error of the order of the quasigeoid-to-geoid difference, which is mainly due to incomplete downward continuation (dwc) of gravity from the Earth's surface to the geoid. A slightly improved estimator, based on the surface Bouguer gravity anomaly, is also biased due to the imperfect harmonic dwc the Bouguer anomaly. Only the third estimator, which uses the (harmonic) surface no-topography gravity anomaly, is consistent with the boundary condition and Stokes' for- mula, providing a theoretically correct geoid height. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the "sec- ondary indirect Topographic Effect", which is a necessary correction in removing all Topographic signals.

  • on the isostatic gravity anomaly and disturbance and their applications to vening meinesz moritz gravimetric inverse problem
    Geophysical Journal International, 2013
    Co-Authors: Lars E. Sjöberg
    Abstract:

    In this study,we showthat the traditionally defined Bouguer gravity anomaly needs a correction to become 'the no-topography gravity anomaly' and that the isostatic gravity anomaly is better defined by the latter anomaly plus a gravity anomaly compensation Effect than by the Bouguer gravity anomaly plus a gravitational compensation Effect. This is because only the newisostatic gravity anomaly completely removes and compensates for the Topographic Effect. F. A. Vening Meinesz' inverse problem in isostasy deals with solving for the Moho depth from the known external gravity field and mean Moho depth (known, e.g. from seismic reflection data) by a regional isostatic compensation using a flat Earth approximation. H. Moritz generalized the problem to that of a global compensation with a spherical mean Earth approximation. The problem can be formulated mathematically as that of solving a non-linear Fredholm integral equation. The solutions to these problems are based on the condition of isostatic balance of the isostatic gravity anomaly, and, theoretically, this assumption cannot be met by the old definition of the isostatic gravity anomaly. We show how the Moho geometry can be solved for the gravity anomaly, gravity disturbance and disturbing potential, etc., and, from a theoretical point of view, all these solutions are the same.

  • combined Topographic Effect applied to the biased type of the modified stokes formula
    Bollettino di geodesia e scienze affini, 2002
    Co-Authors: Artu Ellmann, Lars E. Sjöberg
    Abstract:

    Traditionally, in geoid determination by Stokes formula the Topographical masses are removed and, after the formula is applied, restored, ensuing the direct and indirect Topographic Effects, respectively. In contrast, the combined Topographic Effect on the geoid, as a sum of these Effects can replace the traditional approaches. This paper concerns the development of the combined Effect to be applied to the biased type of modified Stokes formula. The surface spherical harmonics of the power series of elevation have been used. Generally, the combined Effect is proportional to the elevation squared and only slightly dependent on the modification coefficients utilized in the geoid determination process. Numerical results are presented to illustrate the range of the combined Effect in the geoid modelling.

Alfred J Zinck - One of the best experts on this subject based on the ideXlab platform.

  • land use classification in mountainous areas integration of image processing digital elevation data and field knowledge application to nepal
    International Journal of Applied Earth Observation and Geoinformation, 2001
    Co-Authors: D P Shrestha, Alfred J Zinck
    Abstract:

    Remote sensing data help in mapping land resources, especially in mountainous areas where accessibility is limited. In such areas, land degradation is a main concern. Land is degraded not only by natural processes but also by human activities through inappropriate land use practices. Land cover and land use mapping is thus very important for evaluating natural resources. Classification of remote sensing data in mountainous terrain is problematic because of variations in the sun illumination angle. This results in biased reflectance data, the distribution of which does not fulfil normality as required by the maximum likelihood classifier. In the present work the Topographic Effect is corrected by normalising the spectral bands by the total intensity. Classification results are further refined by using ancillary data and expert knowledge of the area. The integration of image processing and spatial analysis functions in GIS improves the overall classification result from 67 to 94 percent (a 27 percent increase).

Xiaoming Zhou - One of the best experts on this subject based on the ideXlab platform.

  • retrieval of land surface temperature with Topographic Effect correction from landsat 8 thermal infrared data in mountainous areas
    IEEE Transactions on Geoscience and Remote Sensing, 2021
    Co-Authors: Xiaolin Zhu, Sibo Duan, Wei Zhao, Pei Leng, Maofang Gao, Xiaoming Zhou
    Abstract:

    Accurate estimation of land surface temperature (LST) is crucial for ecological environment monitoring and climate change studies in mountainous areas. The current LST retrieval algorithms were developed without accounting for the Topographic Effect, which can only be used to retrieve LST over relatively flat surfaces. Due to the impact of 3-D structure of mountainous surfaces, rugged terrain makes the processes of thermal radiation more complex. In this study, a radiative transfer equation (RTE)-based single-channel algorithm was proposed to retrieve LST with Topographic Effect correction from the Landsat 8 thermal infrared (TIR) data in mountainous areas. This algorithm accounts for the changes in the thermal radiation components in the TIR RTE caused by the Topographic Effect. According to the analysis of simulation data, sky-view factor (SVF), atmospheric water vapor content, surface emissivity of target pixel, and average LST of the surrounding terrain have significant influence on the magnitude of the Topographic Effect. The differences between the LST retrieved without/with Topographic Effect correction from the Landsat 8 TIR data are related to SVF. The Topographic Effect should be taken into account in the LST retrieval algorithm when SVF is smaller than 0.7. The largest LST difference of approximately 1 K occurs in the deep valley. The results indicate that LST without Topographic Effect correction could be overestimated to be as high as 1 K. Due to a lack of in situ LST measurements, the performance of the LST retrieval algorithm in mountainous areas was only evaluated by comparing the brightness temperature (BT) at the top of the atmosphere (TOA) simulated by the DART+MODTRAN model and the TIR RTE over mountainous surfaces at three subregions. There is a good consistency between BT at the TOA simulated by the DART+MODTRAN model and the TIR RTE over mountainous surfaces at the three subregions, with a root-mean-squared error (RMSE) of less than 0.23 K.

Antonio G Camacho - One of the best experts on this subject based on the ideXlab platform.

  • novel treatment of the deformation induced Topographic Effect for interpretation of spatiotemporal gravity changes laguna del maule chile
    Journal of Volcanology and Geothermal Research, 2021
    Co-Authors: Peter Vajda, Pavol Zahorec, Craig A Miller, Helene Le Mevel, Juraj Papco, Antonio G Camacho
    Abstract:

    Abstract In volcano gravimetry, when analyzing residual spatiotemporal (time-lapse) gravity changes, the accurate deformation-induced Topographic Effect (DITE) should be used to account for the gravitational Effect of surface deformation. Numerical realization of DITE requires the deformation field available in grid form. We compute the accurate DITE correction for gravity changes observed at the Laguna del Maule volcanic field in Chile over three nearly annual periods spanning 2013–2016 and compare it numerically with the previously used free-air Effect (FAE) correction. We assess the impact of replacing the FAE by DITE on the model source parameters of analytic inversion solutions and apply a new inversion approach based on model exploration and growing source bodies. The new inversion results based on the DITE correction shift the position of the mass intrusion upwards by a few hundred meters and lower the total mass of the migrated fluids to roughly a half, compared to the inversion results based on the local-FAE correction. Our new Growth inversion results indicate that vertical dip-slip faults beneath the lake, as well as the Troncoso fault play active roles in hosting migrating liquid. We also show that for the study period, the DITE at Laguna del Maule can be accurately evaluated by the planar Bouguer approximation, which only requires the availability of elevation changes at gravity network benchmarks. We hypothesize that this finding may be generalized to all volcanic areas with flatter or less rugged terrain and may modify interpretations based on the commonly used FAE corrections.

Peter Vajda - One of the best experts on this subject based on the ideXlab platform.

  • novel treatment of the deformation induced Topographic Effect for interpretation of spatiotemporal gravity changes laguna del maule chile
    Journal of Volcanology and Geothermal Research, 2021
    Co-Authors: Peter Vajda, Pavol Zahorec, Craig A Miller, Helene Le Mevel, Juraj Papco, Antonio G Camacho
    Abstract:

    Abstract In volcano gravimetry, when analyzing residual spatiotemporal (time-lapse) gravity changes, the accurate deformation-induced Topographic Effect (DITE) should be used to account for the gravitational Effect of surface deformation. Numerical realization of DITE requires the deformation field available in grid form. We compute the accurate DITE correction for gravity changes observed at the Laguna del Maule volcanic field in Chile over three nearly annual periods spanning 2013–2016 and compare it numerically with the previously used free-air Effect (FAE) correction. We assess the impact of replacing the FAE by DITE on the model source parameters of analytic inversion solutions and apply a new inversion approach based on model exploration and growing source bodies. The new inversion results based on the DITE correction shift the position of the mass intrusion upwards by a few hundred meters and lower the total mass of the migrated fluids to roughly a half, compared to the inversion results based on the local-FAE correction. Our new Growth inversion results indicate that vertical dip-slip faults beneath the lake, as well as the Troncoso fault play active roles in hosting migrating liquid. We also show that for the study period, the DITE at Laguna del Maule can be accurately evaluated by the planar Bouguer approximation, which only requires the availability of elevation changes at gravity network benchmarks. We hypothesize that this finding may be generalized to all volcanic areas with flatter or less rugged terrain and may modify interpretations based on the commonly used FAE corrections.

  • Deformation-induced Topographic Effect due to shallow dyke: Etna December 2018 fissure eruption case study
    'Central Library of the Slovak Academy of Sciences', 2021
    Co-Authors: Peter Vajda, Pavol Zahorec, Juraj PapČo, Richard Czikhardt
    Abstract:

    Gravitational Effect of surface deformation is in 4D microgravimetry treated as the deformation-induced Topographic Effect (DITE). The DITE field is computed using Newtonian volumetric integration which requires high resolution digital elevation model (DEM) and vertical displacement field in areal form. If only elevation changes on benchmarks of the gravimetric network are available, instead of the vertical displacement field, the DITE on benchmarks can be evaluated only approximately, using a planar Bouguer or a normal free-air-Effect (nFAE) approximation. Here we analyze the adequacy and accuracy of these two approximations in a case study for the December 2018 fissure eruption on Etna accompanied by significant surface deformation caused primarily by a relatively shallow dyke. The outcome is that in volcanic areas of similar morphology as that over the Etna summit area, and for surface deformation fields due to relatively shallow dykes, neither the Bouguer nor the nFAE approximation of the DITE is accurate enough. In such situations the residual gravity changes should be computed with both the Bouguer and nFAE corrections and interpreted as two marginal cases. In addition we analyze also a correction for the Effect of benchmark elevation change based on the Topographically modelled (predicted) vertical gradient of gravity (VGG) meant to approximate the in-situ VGG values at benchmarks. This correction does not appear suitable to approximate the DITE in conditions of our case study or in broader sense