Magnetic Gradiometer Theory

Projects General Guidance
1

Hello,

I've been doing some research into gradiometers and I think I'd like to try building one with an Arduino and two magnetometers (probably MAG3110s).

I'm mainly interested in if anyone else has done this. The primary purpose of this is to make a device similar to what is used for archaeological surveying. However, the literature on this sort of topic is quite sparse.

My understanding is the benefit of using two magnetometers is that instead of measuring a 3D vector (Bx,By,Bz), the gradient tensor is measured instead, defined as:

g_ij = dB_i/dB_j

for i,j ∈ {x,y,z}.

If I have two magnetometers, I can generate a more complicated data set by taking the difference between two sensors and hopefully, improve my signal to noise ratio.

My other understanding of such gradiometers is that the second magnetometers is used to measure the background stray fields (such as that from the Earth). If this were to be subtracted from the other magnetometer's measurement, a more pure measurement is made.

As I said, I've been finding the information on this topic a bit sparse. Some other member's contributions would be greatly appreciated.

Thank you

2

This sounds interesting, but can you post a reference to the use of the tensor? I don't see the point of subtracting the measurements of one magnetometer from another.

A couple of considerations:

(1) Consumer grade magnetometers are almost useless "out of the box". They MUST be carefully calibrated to be useful. Here is an overview. I personally recommend the program Magneto for calculating the correction matrix and offset. Particularly when calculating ratios between measurements along different axes, it is absolutely essential that the axes be on the same scale (they aren't, out of the box).

(2) Mathematical operations performed on raw data increase the noise in the derived quantities. Look up any treatment of error propagation to see this. Hence I question the phrase "more pure measurement".

(3) I also question the characterization of the Earth's magnetic field as "stray". Surely the measurements you wish to make reflect distortions in the local magnetic field.

3

jremington:
This sounds interesting, but can you post a reference? I don't see the point of subtracting the measurement of one magnetometer from another.

The paradigm I'm planning to use here is called a Common Mode Rejection scheme. This is typically described as:

he magnetic gradient is normally calculated by subtracting the outputs of two total field magnetometers which are separated by a baseline[1][2]

[1]Optimizing a direct string magnetic gradiometer for geophysical exploration - PubMed
[2]http://research-repository.uwa.edu.au/files/3244604/Sunderland_Andrew_2009.pdf

I know the second reference is a thesis, but I think that emphasises how much I've been struggling to find enough hard information on this area. The only other references I can provide are the plethora of images of bored archeologists walking around a field with two magnetometers stacked vertically:

http://www.expins.com/p/items/106080.jpg

My understanding of why this work is that irrespective of vertical position, both magnetometers will experience a very similar torque from external magnetic fields (primarily the Earth). The lower down magnetometer will pick up a stronger signal from magnetic material buried in the Earth however. Taking a difference between these two measurements therefore removes the constant background whilst retaining the signal from the buried object. That's my understanding anyway.

jremington:
(1) Consumer grade magnetometers are almost useless "out of the box". They MUST be carefully calibrated to be useful. Here is an overview. I personally recommend the program Magneto for calculating the correction matrix.

I've just bought a pair of MAG3110s and yes, I agree, they'll definitely need to be calibrated. However, because what I'm interested in is a difference measurement, as long as they both reproduce the same results when I measure the same object with them, any biases due to miscalibration will be subtracted out. Thank you very much for the software recommendation.

jremington:
(2) Any mathematical operation performed on raw data increases the noise in the output. Hence I question the phrase "more pure measurement" and the characterization of the Earth's magnetic field as "stray". Surely the measurements you are making reflect distortions in the local magnetic field.

So I suppose one issue I'm going to encounter here is ensuring synchronicity in the data capture. Both measurements will need to have the same time-axis. I think the magnetometers I've bought have an interrupt pin however.

Thank you for your informative post!