Calculation of gravity due to a vertical cylinder using a spherical harmonic series and numerical integration

Na, Sung-Ho; Rim, Hyoungrea; Shin, Youngki; Lim, Mutaek; Park, Yeong-Sue

doi:10.1071/eg14123

Cited by 4 publications

(4 citation statements)

References 3 publications

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“…However, this closed-form analytical solution only allows the computation of the vertical deformation at a point along the axis of symmetry. Semi-analytical solutions can be derived using spherical harmonic series of Legendre polynomials (Na et al, 2015). Examinations of both gravity (Na et al, 2015) and, more recently, thermo-poro-elastic deformation (Mantiloni et al, 2020) have shown that the solutions are accurate under the assumption that the height h of the cylinder is much smaller than its radius R (h/R ≪ 1).…”

Section: Cylindrical Sourcementioning

confidence: 99%

“…Semi-analytical solutions can be derived using spherical harmonic series of Legendre polynomials (Na et al, 2015). Examinations of both gravity (Na et al, 2015) and, more recently, thermo-poro-elastic deformation (Mantiloni et al, 2020) have shown that the solutions are accurate under the assumption that the height h of the cylinder is much smaller than its radius R (h/R ≪ 1). The analytical solutions for thin diskshaped sources (Mantiloni et al, 2020) can be easily generalized to model thick cylindrical sources by stacking two or more disks (Nespoli et al, 2021;Belardinelli et al, 2022).…”

Section: Cylindrical Sourcementioning

confidence: 99%

“…The analogy between gravitational and displacement potential permits the generation of equations mathematically similar to those describing the gravitational field due to an assigned density distribution, by replacing the displacement field u with the gravity acceleration g (Goodier, 1937;Sternberg and McDowell, 1957;Fung, 1965;Wang, 2000). Exact closed analytical solutions for gravity acceleration have been widely devised for simplified geometries of homogeneous density distributions (Blakely, 1996), whereas semi-analytical approaches have been used when analytical solutions cannot be straightforwardly derived (Na et al, 2015;Hemmings et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

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Evidence of poro-elastic inflation at the onset of the 2021 Vulcano Island (Italy) unrest

Stissi,

Currenti,

Cannavò

et al. 2023

Front. Earth Sci.

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Thermal and pore-pressure variations induced by the circulation of hydrothermal-magmatic fluids in porous and permeable media contribute to ground deformation in volcanic areas. Here, we use solutions for the calculation of the displacements induced by pore-pressure and temperature changes for simplified geometry sources embedded in an elastic half-space with homogeneous mechanical and porous properties. The analytical solution for a spherical source is reviewed, and a semi-analytical approach for the calculation of the displacement for a cylindrical source is presented. Both models were used for the inversion of the daily deformation data recorded on Vulcano Island (Italy) during the 2021 unrest. Starting from September 2021, Vulcano Island experienced an increase in gas emission, seismic activity, and edifice inflation. The deformation pattern evolution from September until mid-October 2021 is indicative of a spatially stationary source. The modeling of the persistent and continuous edifice inflation suggests a deformation source located below the La Fossa crater at a depth of approximately 800 m from the ground surface undergoing a volume change of approximately 105 m3, linked to the rise in fluids from a deeper magmatic source. Corroborated by other sources of geophysical and geochemical evidence, the modeling results support that thermo-poro-elastic processes are sufficient to explain the observed displacement without necessarily invoking the migration of magma to shallow levels. Our findings demonstrate that thermo-poro-elastic solutions may help interpret ground deformation and gain insights into the evolution of the hydrothermal systems, providing useful implications for hazard assessment during volcanic crises.

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Section: Cylindrical Sourcementioning

confidence: 99%

Section: Cylindrical Sourcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evidence of poro-elastic inflation at the onset of the 2021 Vulcano Island (Italy) unrest

Stissi,

Currenti,

Cannavò

et al. 2023

Front. Earth Sci.

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“…At an off-axis (i.e. eccentric) point, however, these parameters can be evaluated either numerically (Sung Ho Na et al 2015;Singh 1977; Nagy Based on the theory of superposition one can compute the gravitational field of the cylindrical ring with arbitrary accuracy by increasing the resolution of its approximate model. For a given geometrical resolution, an algorithm developed by the authors builds up the model with optimal number of elements constrained by the base geometry of the elementary volume element.…”

Section: Computation Of the Gravitational Attraction Of The Cylindric...mentioning

confidence: 99%

Newtonian (moving mass) calibration of tilt and gravity meters and the investigation of some factors influencing its accuracy

Papp

Csáki

Benedek

2022

J Geod

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The idea of moving mass calibration (MMC) of relative gravity meters dates back to the seventies of the last century. Probably the MMC apparatus built in the underground Mátyáshegy Gravity and Geodynamics Laboratory Budapest has been used most extensively and several spring type instruments (LaCoste and Romberg and Scintrex) have been investigated and calibrated by it. Its test mass is a cylindrical ring having a weight of 3 tons. Its main advantage is simplicity in terms of metrology. The same principle and technology can be used to test compact tilt sensors having nanoradian resolution capability. Up to now rigorous testing methods below microradian range were not available in practice. The analysis of the so-called off-axis variation of the gravitational vector generated by the vertical movement of the cylindrical ring mass of the Mátyáshegy MMC device, however, showed that a sufficiently accurate reference signal having (15 ± 0.02) nrad peak-to-peak amplitude can be provided for calibration. It is just in the range of tilt induced by earth tide effect, which is a “standard” signal component in the time series recorded in observatory environment. In the first part of the paper, a discussion of the proposed methodology of tilt meter calibration is given. Then the analysis of the effect of volumetric discretization of the cylindrical ring on the accuracy of calibration is provided. Finally, possible material inhomogeneities of the ring mass and their gravitational effects are investigated by forward simulations and inversion. For this purpose the results of 300 gravimeter calibration experiments, analysed and published earlier, were utilized.

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Residual Terrain Modelling: The Harmonic Correction for Geoid Heights

Yang

Hirt

et al. 2022

Surv Geophys

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Calculation of gravity due to a vertical cylinder using a spherical harmonic series and numerical integration

Cited by 4 publications

References 3 publications

Evidence of poro-elastic inflation at the onset of the 2021 Vulcano Island (Italy) unrest

Evidence of poro-elastic inflation at the onset of the 2021 Vulcano Island (Italy) unrest

Newtonian (moving mass) calibration of tilt and gravity meters and the investigation of some factors influencing its accuracy

Residual Terrain Modelling: The Harmonic Correction for Geoid Heights

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