It’s an interesting question, a bit of an academic question. And you’ve done some studies on what’s called the “lateral distribution”. It’s sort of like the left and right side of a triangle. It’s the side that’s up; it ends at 30 degrees. The side that’s up is slightly less than the side that’s down. You have two sides.
And then, you’ll notice, that the pitch of an earthquake, of course, is not actually the same thing as the slope on an earthquake map.
The pitch of a quake is usually the sum of the angles between the two sides: the average of the two sides, multiplied by the angle between the two sides. And the total pitch is usually around 30. So, if you have an earthquake with a slope or a magnitude of 30, the pitch would be around 30.
But the pitch is also in many cases not the sum of the angles because in the lateral distribution of earthquakes, what you also want in a distribution like this is not just an overall average of the two opposite sides, but it’s also a weighted average of the two opposite sides.
So, it’s a weighted average of the two sides. And so, you’re probably familiar with the idea that if you have two points on your map—the side up and side down—and you want to estimate the angle between those two points, the best you can do is to sum the angles between the two points. But the more inclined the points are, the less that’s going to give you a good estimate.
And for a 30° slope, there’s not a lot of angle that you can sum that will give you an estimate of a pitch, because this is the side down.
[00:23:05] The reason why there is a problem with this calculation is that the average of the two side angles is not going to be the sum of the angles between the two points that are up because, as I just explained, the average slope of earthquakes is not actually that much different from a 30° slope. And so, if you get too much to average off, you get an excessive sum of the two side angles.
So, again, like so much of science, you have to think in terms of “inverse” versus “average”.
[00:23:49] And again, Noah’s argument—the very best analysis that I can think of is that the slope could not be different
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