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Gravitational field forward modeling method of random polyhedron whose density is polynomial

A polyhedron and polynomial technology, applied in the direction of measuring gravitational field, measuring device, instrument, etc., can solve the problem of singularity in calculation

Active Publication Date: 2018-01-09
CENT SOUTH UNIV
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Problems solved by technology

At the same time, when the observation point is close to the geological body, especially inside the geological body, there is a singularity in the calculation of the gravity potential and the gravity field

Method used

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  • Gravitational field forward modeling method of random polyhedron whose density is polynomial
  • Gravitational field forward modeling method of random polyhedron whose density is polynomial
  • Gravitational field forward modeling method of random polyhedron whose density is polynomial

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Embodiment Construction

[0147] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0148] The gravitational calculation method that the present invention relates to comprises the following steps:

[0149] Step 1. The calculation expressions of the gravity potential and the gravity field caused by the polyhedron are converted into simple volume integrals.

[0150] Step 2. Convert volume integrals to area integrals: establish a local coordinate system, derive the iterative calculation method for volume integrals of any high-order polynomials through vector identity, divergence theorem, and gradient theorem, and convert them into area integrals.

[0151] Step 3. Convert area integrals to line integrals: establish a local polar coordinate system, deduce the iterative calculation and solution method of area integrals, and convert the area integrals into line integrals by introducing solid angles to eliminate the singularity in the...

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Abstract

The invention discloses a gravitational field forward modeling method of a random polyhedron whose density is a polynomial. The method includes the steps of 1. determining coordinates of points and sides, a density polynomial expression and an observation point coordinate of a random polyhedron, and obtaining a gravitational potential and gravitational field calculation expression containing volume integral; 2. establishing a local coordinate system, and through a vector identical equation, a divergence theorem and a gradient theorem, establishing an iterative calculation method of volume integral, and converting volume integral into surface integral; 3. establishing a local polar coordinate system, establishing an iterative calculation method of surface integral, and through introductionof a solid angle, eliminating singularity in surface integral, and converting the surface integral into line integral; and 4. establishing a geometrical relationship, and solving line integral throughiterative calculation, thereby obtaining a gravitational field. The gravitational field forward modeling method of a random polyhedron whose density is a polynomial can rapidly calculate the gravitational potential and gravitational field generated by a random polyhedron with high precision whose density changes in the form of an any-order polynomial in a horizontal direction and a vertical direction.

Description

technical field [0001] The invention relates to a gravity forward modeling method in the field of geophysics, in particular to a gravity high-precision analytical calculation method for aviation, ground and well gravity exploration and the like. A high-precision forward modeling method for gravity potential and gravity field generated at any observation point for any polyhedron whose density is an arbitrary high-order polynomial. Background technique [0002] Gravity prospecting is an important and basic method in earth prospecting methods, and it is widely used in resource prospecting, deep geological structure prospecting, Moho boundary prospecting and hydrological environment geophysical prospecting. Gravity prospecting includes aerial gravity prospecting, surface gravity prospecting and borehole gravity prospecting. The measured gravity data is related to the real density distribution of underground geological bodies. Through analytical signal analysis or direct inversi...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G01V7/06G06F17/11
Inventor 陈超健任政勇汤井田
Owner CENT SOUTH UNIV
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