Minor conversion of Nuttli mN formula
Before we look at graphs of Ohio wave amplitudes, lets manipulate the mN formula so that I can plot a "magnitude line" on the log-log plot of amplitude vs. distance in kilometers.
Recall that the Nuttli mN formula is:
mN = 3.75 + 0.90 log(D) + log (A/T)
where D is distance in degrees, A is peak amplitude in microns, and T is period of amplitude measurement. -> I'll first convert D to X, distance in kilometers -> I'll then rewrite A/T as peak ground velocity, which introduces a factor of 2*pi. -> Finally, move the terms around to obtain:
log(V) = mN - 1.1 - 0.90 log(X)
where V is the peak ground velocity in micron/sec. This gives a linear equation for log(V) versus log(X), and -0.90 is the predicted amplitude decay log slope. One part of this study is to determine the observed decay slope.
In the following plots, I will graph the peak amplitude in digital units from the OhioSeis seismograms. For periods longer than the instrument response corner at about 1 sec, the seismogram is proportional to ground velocity, and I convert d.u. to velocity at the LLg period of 1.5 sec. The P and S wave peak amplitudes are usually at a higher frequency, hence their velocity amplitudes are actually larger than implied by the left-hand scale of d.u.
On the other hand, as practical seismologists we must detect and measure the wave amplitudes as we see them in the seismogram.
|