Measuring_the_gravity_gradient Gravity_gradiometry
1 measuring gravity gradient
1.1 units
1.2 gravity gradient tensor
1.3 comparison gravity
measuring gravity gradient
gravity measurements reflection of earth’s gravitational attraction, centripetal force, tidal accelerations due sun, moon, , planets, , other applied forces. gravity gradiometers measure spatial derivatives of gravity vector. used , intuitive component vertical gravity gradient, gzz, represents rate of change of vertical gravity (gz) height (z). can deduced differencing value of gravity @ 2 points separated small vertical distance, l, , dividing distance.
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{\displaystyle g_{zz}={\partial g_{z} \over \partial z}\approx {g_{z}\left(z+{\tfrac {l}{2}}\right)-g_{z}\left(z-{\tfrac {l}{2}}\right) \over l}}
the 2 gravity measurements provided accelerometers matched , aligned high level of accuracy.
units
the unit of gravity gradient eotvos (abbreviated e), equivalent 10 s (or 10 mgal/m). person walking past @ distance of 2 metres provide gravity gradient signal approximately 1 e. mountains can give signals of several hundred eotvos.
gravity gradient tensor
full tensor gradiometers measure rate of change of gravity vector in 3 perpendicular directions giving rise gravity gradient tensor (fig 1).
fig 1. conventional gravity measures 1 component of gravity field in vertical direction gz (lhs), full tensor gravity gradiometry measures components of gravity field (rhs)
comparison gravity
being derivatives of gravity, spectral power of gravity gradient signals pushed higher frequencies. makes gravity gradient anomaly more localised source gravity anomaly. table (below) , graph (fig 2) compare gz , gzz responses point source.
fig 2. vertical gravity , gravity gradient signals point source buried @ 1 km depth
conversely, gravity measurements have more signal power @ low frequency therefore making them more sensitive regional signals , deeper sources.
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