detection of dc pulse
We captured surge pulses greater than 400 amps in our surge products by placing a 3.9 mH inductor with 29 ohms DC resistance 3/8" from a main conductor. Field intensity at that level was about 1.9 Tesla.

The inductor had a 75 volt TVS across it to protect the bridge rectifier it fed, which consisted of 4 1N4148 diodes with a 4 nS response time. This drove a pulse stretcher made with a 4.7 K resistor and a 470pF capacitor to ground.

This went to our display board where that stretched signal drove a 2N3904 NPN transistor, which drove the trigger input of a CMOS 555 timer. It had a fixed pulse width of 1 mS to drive a simple LCD counter with its own built-in lithium battery and reset button.

These few parts were needed because the counter could not sense nS or even uS wide pulses, so it was best just to rectify it and stretch it. It also prevented the counting of individual pulses from the same surge event, like those ring waves shown by the OP. That entire wave counts as only one surge event.

This meant that surges over 400 amps (to ignore contactor noise, etc) could not be counted faster than a 1 mS delay would allow. This was very practical because an identical lightning surge on the same lines would be at least a minute later, if at all.

I freely give up this once private information because over 7 years have passed and UL has constantly been updating what it considered a valid test.

EDIT: To capture a 'live' or high-powered pulse that is many thousands of voltage and thousands of amps, there is NO cheap way to do so.

Pearson Electronics of California has a monopoly on high current-high frequency CT's. One rated at 200 kA and -3 dB at 1 MHZ cost about $1,200 USD.

To measure voltage across a load we used Tektronix high voltage probes in differential mode. The are rated at 100 M ohm 15 pF - 3dB at 75 MHZ, and 40 kV max AC plus peak. They divided the input by 1,000. The probe ground wires were NOT used.The MOVs we tested clamped at 2 kV max for a 40 mm MOV rated for 1000 VAC. If an open circuit occurred the worst the probes would see is the 32 KVDC charge from the capacitor bank.

Because we did official UL testing we had a Tektronix Dual-channel oscilloscope sampling at 100Msps. They (and us) were only concerned that the large 40 mm MOV's could survive a 20 kA pulse, which took about 22 kVDC on the capacitor bank.

As soon as the capacitor bank had charged to the correct voltage, my software activated a heavy air-driven contactor that dumped the charge into the DUT (Device Under Test).

The point I am making is that testing of really powerful surges, especially to UL standards is very expensive. Our capacitor bank was 30 each 1.8 uF 60 kV capacitors with 3/4-10 threaded rod sticking out the top. They were $3,000 each.

I was writing the software in LabView while this was being built so I built an emulation circuit with 30 volt/10 amp surges and just added emulated and simulation modes to the software to scale everything as needed. It gave me the same wave forms with a million times less power.