The surface half-wavelength of a spherical-harmonic term of degree is approximately

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history · 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

The surface half-wavelength of a spherical-harmonic term of degree nn is approximately λ1/2≈πa/n\lambda_{1/2} \approx \pi a/n, with mean Earth radius a=6371 kma = 6371\,\mathrm{km}. ((a)) A satellite gravity model is complete to degree n=90n = 90. What is the shortest surface half-wavelength it resolves? ((b)) A gravity feature of interest has a half-wavelength of about 250 km250\,\mathrm{km}. What minimum degree nn is needed to resolve it?

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