(a) A component of the surface gravity field varies horizontally with wavelength .…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch The shape and gravity of the Earth: potential, geoid, isostasy and flexure

Problem

(a) A component of the surface gravity field varies horizontally with wavelength

\lambda = 200\,\mathrm{km}

. Using the flat-Earth result that a Fourier component of wavenumber

k=2\pi/\lambda

decays with height above the source region as

e^{-k\Delta z}

, estimate the fraction of its surface amplitude that would still be present in data collected by an aircraft flying at

\Delta z = 100\,\mathrm{km}

above the surface (an unrealistic altitude, chosen only to make the estimate clean). (b) A ground survey finds an isolated, roughly circular gravity anomaly with half-width

x_{1/2} = 600\,\mathrm{m}

(the anomaly falls to half its peak value at

600\,\mathrm{m}

from the centre). Using the half-width rule for a buried sphere,

x_{1/2} = 0.766\,z

, estimate the greatest depth

z

at which a single compact body could lie and still produce this anomaly.

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