Reverse Delays - how do they work?

["Rainer Thelonius Balthasar Straschill" <rs@moinlabs.de>]

I just spent some time thinking about reverse delays, which several boxes 
do
offer (among them, to take a few devices used often among loopers, the 
Line6
DL4, the TC Electronics D2, the Boss DD20 and the EH SMM w/ Hazari).

So here's my take (without listening to these devices) what is possible how
to implement that effect - and I'd like your ideas what are the preferred
implementations, and wheter there are other ways to reach this.

In a normal delay, it's rather simple: taking feedback aside for one 
moment,
and assuming an ideal delay (i.e. what goes in does come out sometime
later), it's like a conveyor belt. You put the things (your playing) on one
side, and after a finite (and constant) time, it comes out at the other 
end.
Another (more audio-tech) analogy is the endless tape, where you record, 
the
tape goes round, gets played back and immediately recorded again.

This approach will not work if we want a reverse delay, because the things
need to come out in different order than the order they were put in. So how
can you do it?

APPROACH ONE: Turning around
Again taking the conveyor belt analogy, after the conveyor belt is full, we
can simply turn it around and reverse the direction of travel. If we do
feedback in a normal way (i.e. part of the output gets put on the conveyor
belt again), we will end up with the contents playing back
reverse-forward-reverse-... etc.
The problem here: how do we know when to turn around the conveyor belt? If
we just do it after the belt is full (i.e. it has run from beginning to
end), our LTI system turns into being non-time-variant and for that reason,
very hard to guess in its behaviour by the user. We could use a trigger to
tell the delay when we start to fill the belt. With that, the delay between
the trigger and the perceived beginning of delay playback is just the delay
length.
I believe (due to the availability of a trigger threshold), this is the way
the D2 works.

APPROACH TWO: Running two ways
I will take the endless tape analogy here. Assume the tape is stationary 
and
the heads are moving, and the behaviour stays the same (according to
Einstein). Now ignore for one moment the problem of heads getting into each
others' way. Now let's move the recording head in one direction and the
playback head in the other direction. Having feedback according to the
original meaning of the word (feeding back the output to the input) would
also give us the reverse-forward effect. However, we can replace that with
an approach which only erase the tape partially. With that, everything in
the delay output is always reverse, and never reverse-of-reverse.
Note that with that approach, the perceived length of the delay is cut in
half.
Also, the "when to turn the belt" problem gets replaced by the "when do the
heads meet" problem.
Due to the fact that in the DL4, the reverse delay time is half that of all
other delays, I believe it uses this approach.


Now...what other approaches are there? Is there one that is time-invariant
without a trigger (and causal)? Is there another possibility? Any thoughts?
Are you using reverse delays at all?

        Rainer