With pleasure Doug.

Could you please verify that this forum is meant to be a technical forum as implied by your subsections of “patents,” “electronics,” “geophysics,” “Structural Geology, plate tectonics,”… etc?

If so, I assume therefore technical posts should be welcome and not denigrated because they are not “politically-correctly” over-simplified to the point of being inaccurate? (Like global warming deniers require.)

2nd attempt to explain VRM. This is the simplest I can manage, take it or leave it:

Soils are full of tiny magnetic particles. A very small percentage of these are small perfect magnetic ferrite crystals close to small range in size about 30nm (like a cube with a length of a few hundred atoms), and that are “pure” magnets (“saturated”); behave like super-strong minuscule magnets called SPM = super-paramagnetism, but, these particles in this size range can suddenly spontaneously randomly flip their field direction because of random thermal vibrations within the crystal. These are the particles that cause VRM, and all the other magnetic particles do not.

When a PI metal detector applies a magnetic field to these particles during the transmit period, a small percentage of the VRM particles are gradually coaxed into aligning with the transmit field because it biases the random thermal flipping. The smaller crystals align more quickly, but the bigger ones take longer. The percentage that align depends on the strength of the transmit field. But when the transmit field is turned off, the crystals that had been coaxed to align with the transmit field, then randomly in time flip back to net neutral soil fields, with the smaller ones decaying to neutral faster than the larger ones. The small particles having faster “time constant” decays and the bigger particles having longer time constant decays.

In the frequency domain, one can measure the response of VRM soils versus transmit frequency.

If the Tx frequency is low, then (a small percentage) of both the smaller particles and also the bigger particles have time to randomly be coaxed to align with the transmit sine field, but at higher frequencies only the smaller particles can flip in time. The stronger the field, the higher the percentage that align.

How does this show up on a plot? Well because at low frequencies more VRM particles (bigger + smaller) align than at higher transmit frequencies (only smaller particles), this means that the measured magnetic permeability is higher at low frequencies than high frequencies. And because over millions of years nature has produced a very near uniformly random distribution of these magnetic particles sizes in soils, the distribution of time constants of the VRM particles is likewise uniformly random. So a graph of the magnetic permeability versus log frequency gives the blue curve in figure 2 of

This shows the decreasing magnetic permeability of VRM soils and is called a log-linear because it is a sloped straight line (the “linear” bit) versus the log of frequency (the “log” bit). This blue curve is responding directly to the immediate transmit field, and is called the “in-phase” component or “reactive” component. So the standard VRM soil model has a “log-linear” reactive magnetic permeability.

Now look at the red curve. This is from the VRM particles having a delayed response because of their TCs, and is called the “quadrature” or “resistive” component. Resistive here means “loss of energy.” This is because the magnetic energy of the VRM particles is being randomly “destroyed” and appearing as heating the particles. The red curve has zero slope; the same “uniform” value for all frequencies, and this is called a “log-uniform” distribution. So the standard model of VRM soils has a “log-uniform” resistive component. Only the resistive component, the “delayed signal,” appears as a PI receive decaying VRM signal; the resistive component is what matters for PI Rx, not the reactive.

In an ideal PI, where the transmit field is just a single sudden magnetic switching off (after an infinite time of applying the field), called a “magnetic step,” all the particles of all TCs decay simultaneously after turn off. For the standard soil model with a log-uniform resistive permeability, the aggregate of all the TCs signals decaying together gives a logarithmic decaying signal, which, when measured in an ideal receive coil, gives the famous 1/t signal.

Last issue (no idea what the hell this "issue" is about), demod in the frequency domain that cancels DC/LF signals. US7432715. Multiplies Rx by sine/cos of synced Tx signal to give reactive and resistive and cancels any DC/low frequency because average of Rx*sin(wt) or Rx*cos(wt) = 0 unless Rx is also sin(wt) or cos(wt). And here is a sync demod that does not intrinsically balance DC/LF: US4303879