Applied Geophysics potential field methods

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APPLIED GEOPHYSICS POTENTIAL FIELD METHODS JEANNOT TRAMPERT

description

Applied Geophysics potential field methods. Jeannot Trampert. GausS ’ Theorem. For any vector F. STOKES’ Theorem. For any vector F. Potential field theory. i rrotational conservative field. A force F derives from a scalar potential Φ if . The work done by force F (see Stokes) . - PowerPoint PPT Presentation

Transcript of Applied Geophysics potential field methods

Page 1: Applied Geophysics  potential field methods

APPLIED GEOPHYSICS

POTENTIAL FIELD METHODS

JEANNOT TRAMPERT

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GAUSS’ THEOREM

For any vector F

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STOKES’ THEOREM

For any vector F

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POTENTIAL FIELD THEORY

A force F derives from a scalar potential Φ if

The work done by force F (see Stokes)

irrotational conservative field

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POTENTIAL FIELD THEORY

A force field B derives from a vector potential A if

A is not unique (gauge conditions divA=0 or divA=-dφ/dt)

divergence free incompressible solenoidal field

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GRAVITY

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GRAVITY

Gauss

Stokes

PoissonLaplace

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GRAVITYGravity measures spatial variations of the gravitational field due to lateral variations in density.

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ELECTROSTATICS (CHARGES AT REST)

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Gauss

Stokes

PoissonLaplace

ε = permittivity

ELECTROSTATICS (CHARGES AT REST)

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MAGNETOSTATICS (MOVING CHARGES)

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MAGNETOSTATICS (MOVING CHARGES)

Lorentz

Ampere

μ = permeability

If no currents (j=0) B derives from a scalar potential

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BOUNDARY VALUE PROBLEMS

Poisson

Laplace

• ρ is a source term• Solutions to the Laplace equation are called harmonic

functions• Poisson and Laplace are elliptic pde • Boundary value problem: Find φ in a volume V given

the source and additional information on the surface:• Dirichlet: φ specified on the surface• Neumann: gradφ specified on the surface

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MAGNETOSTATICSGeomagnetics measures spatial variations of the intensity of the magnetic field due to lateral variations in magnetic susceptibility.

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ELECTROMAGNETICSMOVING CHARGES IN TIME VARYING FIELDS

Maxwell’s equations

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ELECTRO MAGNETICS

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GRAVITY METHOD

The acceleration of a mass m due to another mass M at a distance r is given by

We can only directly measure g in the vertical direction. In exploration, we usually directly deal with g, in large scale problems it is easier to work with the scalar potential (geoid)

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GRAVITY METHOD

The contributions are summed in the vertical direction.

Unit: 1 m/s2

Earth surface 9.8 m/s2

980 cm/s2

980 Gal980000 mGalanomalies order of mGal

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MEASURING GRAVITY

Falling body measurements

Mass and spring measurements

Pendulum measurements

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PENDULUMThe period T of a pendulum is related to g via K which represents the characteristics of the pendulum

K is difficult to determine accurately Relative measurements

Precision 0.1mGal Precision of T 0.1 ms Long measurements

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MASS ON SPRINGLacoste introduced a zero-length spring (tension proportional to length) first used in the Lacoste-Romberg gravitymeter. Zero length-string is very sensitivity to small changes in g. In the Worden gravitymeter spring and lever are made from quartz minimizes temperature changes 0.01 mGal precision

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ABSOLUTE GRAVITY MEASUREMENTSIf we only survey a small region, relative measurements are enough (assume reference g), but comparing different regions requires the knowledge of absolute gravity. IGSN-71Absolute measurements (z=gt2/2)