Earth resistivity meter design
This is a big project and cannot be answered in detail in a simple way. The crux of your question/problem seems to be the generation of the 40 - 100V 'AC' with a variable/preset 'constant current' so that's what I've concentrated on. There are other solutions but this is how I would approach it.

Taking an overview of the project gave me a block diagram like this. 



I've expanded the blocks for the 'AC' generation. By generating a DC high voltage first and then converting it to AC using an H bridge it allows the output frequency to the probes be easily changed. The output is a squarewave. The probes need an AC signal to prevent polarisation but the waveform is not important.

Rather than trying to produce a constant current I went for the same approach as described in the EPE project - using switched current limiting resistors. This produces a very simple and easily constructed (bi-directional) circuit.

The high voltage (shown as 100V but could be 40V if needed) is generated using any suitable dc-dc converter (such as an LT8331). By adding an H bridge circuit, supplied by the high voltage, the bridge outputs can be continuously reversed by a bi-phase clock/driver circuit supplying current to the probes. (a more common use is to reverse current through a motor) There are lots of examples of this type of circuit on the net.

This H bridge could be driven by a simple 'clock' type oscillator (such as a 555 astable) or from a microcontroller output (with suitable interfaces to protect against the high voltage). 

Looking at the rest of the circuit I think you'll also need to include a GPS module (so you know where the reading was taken), some form of data logging system (to record the data), an interface to an external computer if the data isn't portable (i.e. on a memory stick or card), a microcontroller to handle the data flow,timing readings, key input, display etc., some form of  voltage measurement system that can be converted to digital data for the data logger, a keyboard or set of keys to operate different functions and some form of display to let you know what's happening. As I said - this is a big project - good luck!