A numerical study of residual terrain modelling (RTM) techniques and the harmonic correction using ultra-high-degree spectral gravity modelling

Hirt, Christian; Bucha, Blažej; Yang, Meng; Kühn, Michael

doi:10.1007/s00190-019-01261-x

Cited by 19 publications

(23 citation statements)

References 43 publications

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“…Under some approximations (cf. Hirt et al, ; Rexer et al, ; also see ESM sections S1 and S3), it facilitates the separate modeling of long‐wavelength (here more than 10 km) and short‐wavelength (less than 10 km) topographic gravity signals, based on the following procedure: The 3″ MERIT topographic surface was accurately expanded into a set of SH coefficients to degree 2,160. We performed an ultrahigh degree SH analysis up to degree 43,200 to mitigate downsampling errors on the estimated coefficients (Hirt et al, ).…”

Section: Methods and Computationsmentioning

confidence: 99%

“…Hirt et al, ; Rexer et al, ; also see ESM sections S1 and S3), it facilitates the separate modeling of long‐wavelength (here more than 10 km) and short‐wavelength (less than 10 km) topographic gravity signals, based on the following procedure: The 3″ MERIT topographic surface was accurately expanded into a set of SH coefficients to degree 2,160. We performed an ultrahigh degree SH analysis up to degree 43,200 to mitigate downsampling errors on the estimated coefficients (Hirt et al, ). The reference surface is rigorously self‐consistent with the 3″ MERIT topographic surface. For modeling the long‐wavelength gravity signal implied by the degree 2,160 SH topography, spectral‐domain techniques as described in, for example, Chao and Rubincam () and Hirt and Kuhn () were used.…”

Section: Methods and Computationsmentioning

confidence: 99%

“…Under some approximations (cf. Hirt et al, 2019;Rexer et al, 2018; also see ESM sections S1 and S3), it facilitates the separate modeling of longwavelength (here more than 10 km) and short-wavelength (less than 10 km) topographic gravity signals, based on the following procedure:…”

Section: Methods and Computationsmentioning

confidence: 99%

“…The 3″ MERIT topographic surface was accurately expanded into a set of SH coefficients to degree 2,160. We performed an ultrahigh degree SH analysis up to degree 43,200 to mitigate downsampling errors on the estimated coefficients (Hirt et al, 2019). The reference surface is rigorously self-consistent with the 3″ MERIT topographic surface.…”

Section: Methods and Computationsmentioning

confidence: 99%

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SRTM2gravity: An Ultrahigh Resolution Global Model of Gravimetric Terrain Corrections

Hirt

Yang

Kühn

et al. 2019

Geophysical Research Letters

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We present a new global model of spherical gravimetric terrain corrections that take into account the gravitational attraction of Earth's global topographic masses at 3″ (~90 m) spatial resolution. The conversion of Shuttle Radar Topography Mission‐based digital elevation data to implied gravity effects relies on the global evaluation of Newton's law of gravitation, which represents a computational challenge for 3″ global topography data. We tackled this task by combining spatial and spectral gravity forward modeling techniques at the 0.2‐mGal accuracy level and used advanced computational resources in parallel to complete the 1 million CPU‐hour‐long computation within ~2 months. Key outcome is a 3″ map of topographic gravity effects reflecting the total gravitational attraction of Earth's global topography at ~28 billion computation points. The data, freely available for use in science, teaching, and industry, are immediately applicable as new in situ terrain correction to reduce gravimetric surveys around the globe.

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Section: Methods and Computationsmentioning

confidence: 99%

Section: Methods and Computationsmentioning

confidence: 99%

Section: Methods and Computationsmentioning

confidence: 99%

Section: Methods and Computationsmentioning

confidence: 99%

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SRTM2gravity: An Ultrahigh Resolution Global Model of Gravimetric Terrain Corrections

Hirt

Yang

Kühn

et al. 2019

Geophysical Research Letters

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“…For these points, the direct forward modelling yields the non-harmonic gravitational potential and does therefore not anymore correspond to values observed in harmonic condition, such as observations in the boundary value problem (cf. [34]). It is well-known that some kind of a harmonic correction is required for these points [2].…”

Section: Forward Modelling In Space Domainmentioning

confidence: 99%

TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations

Yang¹,

Hirt

Pail³

2020

Remote Sensing

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With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation model (DEM) in the Newtonian integration. For efficient and accurate gravity forward modelling in the spatial domain, we developed a new MATLAB-based program called, terrain gravity field (TGF). Our new software is capable of calculating the gravity field generated by an arbitrary topographic mass-density distribution. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries (i.e., polyhedron, prism, tesseroid and point-mass) and DEMs with different spatial resolutions. Compared to some publicly available algorithms depending on one type of geometric approximation, this enables accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent gravity field functionals, supports two types of density inputs (constant density value and digital density map), and considers the curvature of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. In this contribution, the TGF software is introduced to the geoscience community and its capabilities are explained. Results from internal and external numerical validation experiments of TGF confirmed its accuracy at the sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms the capability of TGF for dealing with large datasets. Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations.

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Cap integration in spectral gravity forward modelling up to the full gravity tensor

Bucha

Hirt

Kühn

2019

J Geod

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A numerical study of residual terrain modelling (RTM) techniques and the harmonic correction using ultra-high-degree spectral gravity modelling

Cited by 19 publications

References 43 publications

SRTM2gravity: An Ultrahigh Resolution Global Model of Gravimetric Terrain Corrections

SRTM2gravity: An Ultrahigh Resolution Global Model of Gravimetric Terrain Corrections

TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations

Cap integration in spectral gravity forward modelling up to the full gravity tensor

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