How do Magnetic Gradiometers work?

[Crosshash]

Whenever I've encountered measuring magnetic fields with magnetometers, they've typically been very large magnetic fields (up to a few T). Magnetic fields fall off rapidly with distance and so I generally figured that measuring weak fields at distances on the order of cm (let alone m) was very difficult.

But archeologists seem to use magnetic Gradiometers to find magnetic material buried in the Earth. What I want to know is how do gradiometers acquire this signal gain from multiple magnetometers.

Just as an example, here:
https://www.sparkfun.com/products/12670
is a cheap magnetometer with a sensitivity of ~0.1 muT. With a bit more digging (and a much larger budget), there are magnetometers which can reach the order of a few nT sensitivity. But for weak magnetic fields 10s of centimetres away, this still may not be sensitive enough.

So I'm assuming the gradiometer is comprised of two or more magnetometers, and the difference in field is calculated. But what is the statistics which governs this signal gain? Are there any sources I could read on this sort of measurement? How do variables such as separation distance affect the sensitivity. What if more magnetometers are used? What about an array of magnetometers (or even, a matrix)?

Hopefully I've explained my question okay. Apologies since this isn't strictly a Condensed Matter question.

Thank you

 

[f95toli]

No, as far as I am aware this is never done using two magnetometers; what is used is a single magnetometer but with a gradiometric pickup-coil. This is certainly true for SQUID based magnetometers and I would assume it is also the case for fluxgates.

There is plenty of information about gradiometer coils available on the web.

 

[Crosshash]

No, as far as I am aware this is never done using two magnetometers; what is used is a single magnetometer but with a gradiometric pickup-coil. This is certainly true for SQUID based magnetometers and I would assume it is also the case for fluxgates.

There is plenty of information about gradiometer coils available on the web.

I'm a bit of a layman when it comes to this sort of thing, but from the literature I've read, it looks like most gradiometers utilise two magnetometers. Much of my understanding stems from this paper:
http://library.seg.org/doi/abs/10.1190/1.2164759

but from the fairly limited articles on wikipedia:

Magnetometers used in geophysical survey may use a single sensor to measure the total magnetic field strength, or may use two (sometimes more) spatially separated sensors to measure the gradient of the magnetic field (the difference between the sensors).

In this (albeit old) paper: http://adsabs.harvard.edu/abs/1961RScI...32..444M , a ~4 m baseline between sensors was used to construct a magnetic gradiometer with a sensitivity of 5 nT/m

The guy in this picture also looks like he's using two sensors to construct his gradiometer:

But like I said, my understanding of this field is poor. Irrespective, are there no gains to be had from attempting to measure magnetic fields using multiple magnetometers?

 

[marcusl]

Geophysicists place magnetometers on even longer baselines (many km) to characterize magnetic fields along earthquake fault lines. The idea behind all gradiometers is to produce some level of spatial localization to a local source. Fields from distant sources have essentially equal strength at the two sensors and are therefore canceled away. The field from a nearby source is different at the two sensors, however, so does not cancel. The distance to the source will be of comparable magnitude (although smaller) than the separation between sensors.

To take a simple example, imagine that the magnetometers in the photo above are pointed down to the ground. The lower one is maybe 1/2 meter above the ground and the upper about 2/3 meter higher. Exact analysis is complex, but we can perform a rule of thumb analysis with ease by assuming that the field for a small magnetic source (an iron coin or cup or something like that) falls off with distance as 1/r^3. The gradiometer response is therefore proportional to (1/(d+.5)^3 - 1/(d+1.17)^3), where d is depth below the ground surface. You can graph this and see that sensitivity to magnetic objects falls off beyond about ~0.33 to 0.5 m below ground. The sensors in your photo appear to point off to the right of the operator so the geometry is different, but at least you can see how it works.