Hi Roger:

I am starting to like this idea quite a bit bacuase of the ability for it to temper the aftershock effect, but I still have a concern.

Lets say for simplicity I have a catalog of 100 days. There are 100 quakes that meet the criteria for my prediction, which is a quake of whatever magnitude within the next 24 hours. If all 100 catalog quakes occurred on one day, the probability would be 1%. If one quake occurred per day for each of the 100 days, the probability would be 100%. Correct?

OK, I want to look at the 100 catalog quakes in one 24 hour period. If all 100 quakes occurred from one midnight to the next midnight, my probability is 1%. If all 100 quakes occur between noon one day and noon the next day, my probablity now doubles to 2%, because quakes are now falling in two different windows.

Granted this is an extreme example, but how do we deal with the placement of windows within the catalog? Most predicitions will not be as clean cut as one whole day, or even some value that is evenly divisable into the catalog windows. How does a prediction window of 70.5 hours fit into the catalog of 100 days? What do you do with the remainder (34.04 hours in this case)? My first thought is to tally up every possible 24 hour (in this example) period in the catalog, down to the resolution of whatever the catalog is accurate to. So, we would tally, for my example, based on a catalog that records quakes down to the second, a window by window tally would look like:

Day 1 00:00:00 > Day 1 23:59:59
Day 1 00:00:01 > Day 2 00:00:00
Day 1 00:00:02 > Day 2 00:00:01
Day 1 00:00:03 > Day 2 00:00:02

etc etc etc etc until ....

Day 99 23:59:58 > Day 100 23:59:57
Day 99 23:59:59 > Day 100 23:59:58
Day 100 00:00:00 > Day 100 23:59:59

In this example, there would be 86,400 windows.
The total would be 8,640,000 windows.

We then take the hit windows and divide by the total windows, giving probability. I think that would eliminate the situation I described, correct?

Michael