Measuring earth currents - tips?

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Is there any best way to measure earth currents with a scope where the act of measuring does not effect what is being measured?

I want to track down the last traces of noise in my phono stage and suspect that it is a mix of mainsbourne EMI pick up and localised ground loops, the first stage of the amp seems very sensitive to these.

I wondering if I will end up chasing my tail where the measuring effects what is being measured.
 
I think you'll have a very hard time, as you've perhaps figured out the meter itself will dramatically affect the situation.
- if we use battery powered multimeter then you are right - there isn't a big problem. But if we start to use mains-connected devices (oscillograph or else) - then the problem arises at full height.
For example: my Tektronix 2465A have some portion of bad old film X2 caps in power supply (I had changed only one yet, it was several years ago). So when I connect the osc probe to the device under test (audio power amplifier for example) and look at on-line spectrogram - I clearly see additional mains harmonics (they were much lower several years ago, so I see that some more X2 caps died).
The solution may be, for example, to use battery powered oscillograph - modern digital devices give us such a possibility.
 
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Are you focusing on pre-amplifier circuitry, or the wiring and pickup outside the pre-amplifier, or a main amplifier ?

If it relates to quite low noise and hum levels (considering the phono input application), then I'd suggest using a soundcard and software spectrum analyser setup, which can provide a noise floor well below any record. In that same vein, you won't be able to lower the record noise floor, so reducing circuit based noise has a diminishing return on effort.
 
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