Here are my thoughts on this misunderstood subject.
The step potential is created by you taking a step to a higher voltage, not a sudden change in the voltage potential. I like the topographic representation since topography like the voltage does not usually change instantaneously. The rings are just lines of equal elevation/potential on a continuous function You can get sever distortions from the idea circle by local effects (buried conductors, soil type, moisture content, etc.). The problem with hopping is falling and getting a large potential across your total body. And no Glen, a birds feet do not tingle, since they have a very small voltage differential between them.
I don't think the frequency has much to do with the resistance since the reactive part of the impedance will not change that much relative to the resistance. I also don't think skin depth is an issue since we are talking about a distributed system. It is also probably safe to ignore transmission line effects. There are a number of sites where you can find the resistivity of the earth under different conditions, but you cannot accurately measure it with a conventional ohm meter (DMM).
As far as the zone of influence goes there are some unstated assumptions in the 33ft guideline. Line voltage and soil conditions/characteristics are the big ones, but it is probably not too bad. What I would worry about is that anything that touches the interior of the zone can potentially increase the zone in weird ways. If you have a tree that is not contacting the line but was uprooted next to the fallen line can you safely cut the top out if it is 100' away? This is well outside the 33' zone, but given that the roots/stump are at an elevated potential I would make the assumption the whole tree was. The likely situation is that the top will be at a lower potential since it will likely be somewhat grounded by all the limbs touching/in the ground, but what happened when you finish the cut and the top is no longer connected to the tree but the saw still is? You always have to consider the sneak paths!
Thinking that the voltage is being entirely dissipated in the zone isn't really correct either! To me the zone represents the point where the differential voltage has not decayed to a safe level. The fact of electricity is that the current created by the downed line must be returned to the source. This could be the primary generation site or a distribution center. In actuality there are two zones! One where the current goes into the ground and one where it returns to the source. To me this is best represented as the contact resistance to/from the earth. The effects in the zone are nonlinear because of the half spherical nature of the contact. There is a mostly linear decay between the fault and the source. The correct way to explain the contact resistance is to setup and solve an advanced calculus equation, but I don't think many here would appreciate that so here is a mental way to think about it.
The line has a certain current flowing in it which is going into the ground. The ground isn't a very good conductor (it has a high unit resistance). From basic electronics the voltage drop is equal to the current times the resistance. Since the point that the line contacts the ground represents a small area (has high resistance) the incremental voltage drop is high in that local area. As we move farther from the contact point the area the current flow across increases as the square of the distance (½ the surface area of a sphere) so the incremental voltage drop is reduced by that same amount. At some point the incremental voltage drop is no longer a safety issue which is the edge of the safe zone.
Here are a couple of last things. The voltage isn't what is dangerous! It is the current that actually kills you. Here is a
link to more information. One extreme example of this is that Tesla used to grab coils that produced half a million volts without harming himself. The other thing is that the power system does not use the earth as the return for the hot lines! Most power systems are balanced three phase either Y or delta and what we call a neutral in residential or Y circuits is locally created and connected.
That's enough for now!
Cary