A hybrid rectangle-Gaussian grid for continuous convolution integrals: With application in gravity forward modelling

2017 ◽  
Author(s):  
Leyuan Wu
Keyword(s):  
Forward Modelling ◽  
Gravity Forward Modelling ◽  
Convolution Integrals

Elliptical harmonic method for gravity forward modelling of 2D bodies

2021 ◽  
Vol 95 (5) ◽  
Author(s):  
Cheng Chen ◽  
Shaofeng Bian ◽  
Motao Huang
Keyword(s):  
Forward Modelling ◽  
Harmonic Method ◽  
Gravity Forward Modelling

Experiences with the use of mass-density maps in residual gravity forward modelling

2018 ◽  
Vol 62 (4) ◽  
pp. 596-623 ◽  
Author(s):  
Meng Yang ◽  
Christian Hirt ◽  
Robert Tenzer ◽  
Roland Pail
Keyword(s):  
Mass Density ◽  
Forward Modelling ◽  
Residual Gravity ◽  
Gravity Forward Modelling ◽  
Density Maps

A spectral-domain approach for gravity forward modelling of 2D bodies

2019 ◽  
Vol 93 (10) ◽  
pp. 2123-2144
Author(s):  
Cheng Chen ◽  
Shaofeng Bian ◽  
Houpu Li
Keyword(s):  
Spectral Domain ◽  
Forward Modelling ◽  
Spectral Domain Approach ◽  
Gravity Forward Modelling

The tree-canopy effect in gravity forward modelling

2019 ◽  
Vol 219 (1) ◽  
pp. 271-289 ◽  
Author(s):  
Meng Yang ◽  
Christian Hirt ◽  
Moritz Rexer ◽  
Roland Pail ◽  
Dai Yamazaki
Keyword(s):  
Tree Canopy ◽  
Data Sets ◽  
Forward Modelling ◽  
Bare Ground ◽  
Gravity Forward Modelling ◽  
Digital Elevation ◽  
Canopy Effect ◽  
Elevation Model ◽  
Validation Experiments

SUMMARY High resolution and accurate digital terrain models (DTMs) are frequently used as input data sets to define the topographic masses in gravity forward modelling, for example, for terrain corrections in the context of regional gravity modelling. However, over vegetated areas such as forests and scrublands, the radar- and image-based digital elevation models (DEMs) may contain a tree bias, and therefore do not represent the bare-ground surface. The presence of vegetation-induced signals in DEMs, denoted here the tree-canopy effect, will introduce errors in the gravity forward modelling. In this study, the role of the tree-canopy effect in gravity forward modelling calculations is numerically investigated. First, spectral forward modelling techniques were applied to analyse a global tree-canopy bias model with a horizontal resolution of 1 km x 1 km and to quantify its effect on global gravity forward modelling results. We demonstrate that tree-canopy signals in the DEM produce a positive bias in the topographic gravitational field over vegetated areas, with values ranging from 0 to ∼2.7 mGal for gravity disturbances. Second, the role of the tree-canopy effect in high-frequency gravity forward modelling is studied using well-known residual terrain modelling (RTM) techniques. As DEM data sets, we used the 3″ SRTM (Shuttle Radar Topography Mission Digital 9 m Elevation Database) V4.1 (containing vegetation biases) and the 3″ MERIT-DEM (Multi-Error-Removed Improved-Terrain Digital elevation model) as a representation of the bare-ground elevations. Using Tasmania and the Amazon rainforest regions as test areas with significant tree-canopy signals we show that the tree-height effect on RTM calculations is of high-frequency nature, with rather small signals which reach in extreme cases amplitudes of ∼1–2 mGal occurring at forest boundaries. Third, using ground gravity observations, validation experiments were performed over the Australian Alps, Tasmania and the Canadian Rocky Mountains. All validation experiments show that the bare-ground elevation model MERIT-DEM performs better than SRTM V4.1 in terms of reduction of the discrepancies between modelled and observed gravity values. As a general conclusion, bare-ground DEM models should be preferred in any gravity forward modelling application to avoid or reduce the tree-canopy effect.

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

2019 ◽  
Vol 93 (9) ◽  
pp. 1707-1737 ◽  
Author(s):  
Blažej Bucha ◽  
Christian Hirt ◽  
Michael Kuhn
Keyword(s):  
Forward Modelling ◽  
Gravity Forward Modelling

Forward modelling of circular loop source and calculation of whole area apparent resistivity based on TEM

2018 ◽  
Vol 35 (2) ◽  
pp. 183-198 ◽  
Author(s):  
Jun ZHANG ◽  
Yanging WU ◽  
Hongchun YI
Keyword(s):  
Apparent Resistivity ◽  
Forward Modelling ◽  
Circular Loop

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

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