The gravitational potential and its derivatives of a right rectangular prism with depth-dependent density following an n-th degree polynomial

Interpretation and inversion of microgravity anomalies belong to important tasks of near-surface geophysics, mostly in cavities detection in engineering, environmental and archaeological applications. One of the mostly used concepts of inversion in applied gravimetry is based on the approximation of the model space by means of 2D or 3D elementary sources with the aim to estimate their densities by means of the solution of a corresponding linear equation system. There were published several approaches trying to obtain correct and realistic results, which describe real parameters of the sources. In the proposed contribution we analyse the properties of two additional functionals, which describe additional properties of the searched solution – namely so-called L2-smoothing and minimum support focusing stabilizers. For the inversion itself, we have used the regularized conjugate gradient method. We have studied properties of these two stabilizers in the case of one synthetic model and one real-world dataset (microgravity data from St. Nicholas church in Trnava). Results have shown that proposed algorithm with the minimum support stabilizer can generate satisfactory model results, from which we can describe real geometry, dimensions and physical properties of interpreted cavities.

show abstract

“…The vertical component (V z ) of the gravitational attraction vector is then given by (e.g. Karcol, 2018):…”

Section: Methodsmentioning

confidence: 99%

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Zvara

Pašteka

Karcol

2021

Contrib. Geophys. Geod.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In very recent years, several efforts have been paid to address above issues. For a prism, Jiang et al [2017], Karcol [2018] and Fukushima [2018] successfully find closedform solutions of gravity field for density contrast varying along depth by following a polynomial function of arbitrary orders. For a prism, Zhang and Jiang [2017] derived closedform solutions of gravity field for density contrast varying both in horizontal and vertical directions and following polynomial functions of arbitrary orders.…”

Section: Introductionmentioning

confidence: 99%

Exact gravity field for polyhedrons with polynomial density contrasts of arbitrary orders

Ren¹,

Chen²,

Zhong³

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, researchers have adopted methods such as the isostasy model to reduce the errors caused by the difference of the crustal density [ 5 , 7 , 8 ]. Roland et al described the density distribution, which varied with depth, using polynomials and derived the gravitational potential and its first and second derivatives of the rectangular prism with indefinite density [ 9 ]. In the case of ocean water, as the density of seawater is less than that of the crust, the gravitational effect includes the mass deficiency of seawater relative to the land.…”

Section: Introductionmentioning

confidence: 99%

Influence of Differences in the Density of Seawater on the Measurement of the Underwater Gravity Gradient

Xian

Bian

et al. 2023

Sensors

View full text Add to dashboard Cite

In preparing gravity gradient reference maps for navigation purposes, researchers have tended to use a constant value for the density of seawater. However, the actual seawater density at a particular location may vary due to the effects of longitude, latitude and bathymetry. In this study, the right rectangular prism method was used to calculate the disturbing gravity gradient caused by the mass deficiency of seawater for three different seawater profiles in an area east of Taiwan. For this purpose, two seawater density models were used as alternatives to the constant seawater density model, and the alteration in the gravity gradient was calculated to quantify the error in the gravity gradient as a result of using a constant seawater density. The results demonstrated that the error in the gravity gradient can reach 1E for water at large depths. Moreover, the difference between the amplitude of the error of the corrected thermocline and that for the uncorrected seawater density model was found to be quite small. If a gravity gradient reference map with accuracy better than 1E is to be realized, the seawater density cannot be taken as constant during forward modeling.

show abstract

The gravitational potential and its derivatives of a right rectangular prism with depth-dependent density following an n-th degree polynomial

Cited by 10 publications

References 13 publications

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Exact gravity field for polyhedrons with polynomial density contrasts of arbitrary orders

Influence of Differences in the Density of Seawater on the Measurement of the Underwater Gravity Gradient

Contact Info

Product

Resources

About