<i>Theory of the Earth's Gravity Field</i>

Pick, Miloš; Pícha, Jan; Vyskočil, Vincenc; Rapp, Richard H.

doi:10.1063/1.3128595

Cited by 28 publications

(29 citation statements)

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“…The size and resolution of this partition are related to the gravity stations distribution (diameter and step) and, also, are conditioned by the capacity of the computer. The gravity attraction, A i j , at the ith station P i (x i , y i , z i ), due to the jth prism, for unit density, is given by Pick et al (1973):…”

Section: Inversion Methodsmentioning

confidence: 99%

Gravity inversion by means of growing bodies

Camacho¹,

Montesinos²,

Vieira³

2000

GEOPHYSICS

129

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This paper presents a gravity inversion method for determining the volumes of bodies with pre-established density contrasts. The method works step-by-step on a prismatic partition of the subsurface volume, expanding the anomalous bodies to fit the observed gravity values in a systematic exploration of model possibilities. The process is treated in a 3-D context; at the same time, it can determine a simple regional trend. Moreover, positive and negative density contrasts are simultaneously accepted. The solution is obtained by a double condition: (1) the 2 -fitness to the observed gravity data (model fitness) and (2) the minimization of the total (weighted) anomalous mass (model smoothness). A positive parameter is used to balance the two minimization terms. The method is applied to a simulated example and also to a real example: the volcanic island of Gran Canaria (Canary Islands, Spain). In both cases, the results obtained show the possibilities of the method.

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Section: Inversion Methodsmentioning

confidence: 99%

Gravity inversion by means of growing bodies

Camacho¹,

Montesinos²,

Vieira³

2000

GEOPHYSICS

129

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“…where H (r, ψ) is the well-known extended Hotine's kernel with the following definition (Pick et al 1973, Eq. 1572:…”

Section: Integral Formulae For Local Gravity Field Recoverymentioning

confidence: 99%

On the integral inversion of satellite-to-satellite velocity differences for local gravity field recovery: a theoretical study

Eshagh

Šprlák

2015

Celest Mech Dyn Astr

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The gravity field can be recovered locally from the satellite-to-satellite velocity differences (VDs) between twin-satellites moving in the same orbit. To do so, three different integral formulae are derived in this paper to recover geoid height, radial component of gravity anomaly and gravity disturbance at sea level. Their kernel functions contain the product of two Legendre polynomials with different arguments. Such kernels are relatively complicated and it may be impossible to find their closed-forms. However, we could find the one related to recovering the geoid height from the VD data. The use of spectral forms of the kernels is possible and one does not have to generate them to very high degrees. The kernel functions are well-behaving meaning that they reduce the contribution of far-zone data and for example a cap margin of 7 • is enough for recovering gravity anomalies. This means that the inversion area should be larger by 7 • from all directions than the desired area to reduce the effect of spatial truncation error of the integral formula. Numerical studies using simulated data over Fennoscandia showed that when the distance between the twin-satellites is small, higher frequencies of the anomalies can be recovered from the VD data. In the ideal case of having short distance between the satellites flying at 250 km level, recovering radial component of gravity anomaly with an accuracy of 7 mGal is possible over Fennoscandia, if the VD data is contaminated only with the spatial truncation error, which is an ideal assumption. However, the problem is that the power of VD signal is very low when the satellites are close and it is very difficult to recognise the signal amongst the noise of the VD data. We also show that for a successful determination of gravity anomalies at sea level from an altitude of 250 km mean VDs with better accuracy than 0.01 mm/s are required. When coloured noise at this level is used for the VDs at 250 km with separation of 300 km, the accuracy of recovery will be B Mehdi Eshagh 123 M. Eshagh, M. Šprlák about 11 mGal over Fennoscandia. In the case of using the real velocities of the satellites, the main problems are downward/upward continuation of the VDs on the mean orbital sphere and taking the azimuthal integration of them.

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“…where A ij is the vertical attraction for unit density for the j-th parallelepiped cell upon the i-th observation point (e.g., Pick et al, 1973), …”

Section: General Approachmentioning

confidence: 99%

Structure of Alluvial Valleys from 3-D Gravity Inversion: The Low Andarax Valley (Almería, Spain) Test Case

Camacho

Carmona

García‐Jerez

et al. 2014

Pure Appl. Geophys.

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This paper presents a gravimetric study ( We interpret several low density alignments as corresponding to SE faults striking about N 140-145ºE. Some detected basement elevations (as one, previously known by boreholes, in Viator village) are apparently connected with the fault pattern. The outcomes of this work are:(1) new gravimetric data, (2) new methodological options, and (3) resulting structural conclusions.3

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Theory of the Earth's Gravity Field

Cited by 28 publications

References 0 publications

Gravity inversion by means of growing bodies

Gravity inversion by means of growing bodies

On the integral inversion of satellite-to-satellite velocity differences for local gravity field recovery: a theoretical study

Structure of Alluvial Valleys from 3-D Gravity Inversion: The Low Andarax Valley (Almería, Spain) Test Case

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