We summarize the correlation of 
values and PGA for each of
the individual earthquakes analyzed in Figure 1;
Figure 2 shows a similar plot for PGV.
The correlation and regressions of versus PGA and PGV for the data from all
eight earthquakes combined are shown in Figures 3 and 4,
respectively.
Figure 3: Modified Mercalli intensity plotted against peak ground acceleration for
all events combined. Circles denote data; horizontal lines above data depict
the range of the geometric mean, plus and minus one standard deviation.
The solid line is regression from this study, the dashed line is assigned (see text for details).
The dotted line is that of [Trifunac and Brady, 1975].
Figure 4: Modified Mercalli intensity plotted against peak ground velocity for
all events combined. Circles denote data; horizontal lines above data depict
the range of the geometric mean, plus and minus one standard deviation.
The solid line is regression from this study, the dashed line is assigned (see text for details).
The dotted line is that of [Trifunac and Brady, 1975].
While there is no fundamental reason to expect a simple relationship between
Modified Mercalli intensity ( ) and recorded ground motion parameters,
over a range of accelerations and velocities
a simple power-law representation is adequate and convenient.
We find that for PGA in the limited range of V 
VIII,
and for peak velocity (PGV) within the range
V IX,
The correlation coefficients (r) for Equations (1) and (2) are 0.597 and 0.686, respectively.
Here the regressions are made on the geometric mean of the peak horizontal ground motion
values for a given intensity unit. For acceleration, IX is not
used in the regression since the peak acceleration values appear to
saturate, and hence a simple power-law relation will not suffice. Likewise
at IV, PGA and PGV are biased high due to lack of digitization of
data from stations with lower values and hence they are not used in the regression.
For IV, peak velocities do not continue decreasing,
suggesting perhaps not only the above-mentioned bias, but also that a higher
noise level (likely introduced in the integration of digitized recordings)
may be controlling the peak values.
Requiring that the ground motion recording sites and observation points have
similar surface geology, in addition to the maximum distance requirement, did not
significantly reduce the scatter shown in Figures 3 and 4.
However, this may be a limitation of the map scale used in the geology classification
[]park98, and a more detailed association of the geology at the strong
motion sites and intensity observations may be useful. Naturally, though, the
association of an instrumental, point measurement of ground motion with an
intensity observation defined as the maximum or average over a designated areal extent
would be expected to show substantial scatter, particularly
if the area does not contain the point measurement. This is a fundamental
limitation originating from the definition of seismic intensity which requires an
(unspecified) area be assigned a given intensity value based on the
representative or average level of damage in the region; any single
point observation in that area is not sufficient to satisfy such a definition.
As seen in Figures 3 and 4,
low levels of shaking intensity correlate fairly well with both PGA and PGV,
while high intensities correlate best with peak velocity. Basically, peak
acceleration levels off at high intensity while peak velocity continues to grow.
In contrast the ground velocities, derived by integration of digitized analog
accelerograms, are noisier at low levels of motion and the scatter is somewhat larger.
By comparing maps of instrumental intensities with for the eight above-mentioned
earthquakes, we have found that a relationship that follows acceleration for
<VII and follows velocity for >VII works fairly well in reproducing the
observed .
Using peak acceleration to estimate low intensities is intuitively consistent with the
notion that lower (<VI) intensities are assigned based on felt accounts, and people are more
sensitive to ground acceleration than velocity. Higher intensities are defined by the level of
damage; the onset of damage at the intensity VI to VII range is usually characterized by
brittle-type failures (masonry walls, chimneys, unreinforced masonry, etc.) which are
sensitive to higher-frequency accelerations. With more substantial damage (VII and
greater), failure begins in more flexible structures, for which peak velocity is more
indicative of failure []hall96. Our assumption is consistent with the recent
analysis of [Sokolov and Chernov, 1998] which showed that seismic intensities correlate well for
rather narrow ranges of Fourier amplitude spectra of ground acceleration, with 0.7-1.0 Hz being
most representative of > VIII, while the 3-6 Hz range best represents V to VII;
the 7-8 Hz range best correlates with the lowest range. In addition, [Boatwright el al., 1999]
have found that for the Northridge earthquake, PGV and the 3-0.3 Hz averaged spectral velocity are
better correlated with intensity (VI and greater) than peak acceleration and their correlation with
intensity and peak spectral velocity is strongest at 0.67 Hz.
While the range of > V is well fit by a power law relation, this trend does not hold
for lower intensities. Since we are also interested in estimating intensity at lower values with
the peak ground motions, and our current collection of data from historical earthquakes
does not provide constraints for lower intensity, we have imposed the following relationship
(shown as a dashed line in Figure 3) between PGA and :
The basis for the above relationship comes from correlation of TriNet peak ground motions
recordings for recent magnitude 3.5 to 5.0 earthquakes with intensities derived from
voluntary response from Internet users [Wald et al., 1999b] for the same events. We determined
that the boundary between ``not felt'' and ``felt'' ( I and II, respectively)
regions corresponds to approximately one-to-two cm/sec/sec, at least for this range of magnitudes.
We then assigned the slope such that the curve would intersect the relationship in Equation (1)
at equal to V. We plan to refine this relationship as more digital data become available.
The corresponding equation for PGV and (shown as a dashed line
in Figure 4) is:
Table 1 gives the peak ground motion ranges that correspond to each unit Modified Mercalli intensity value according to our regression of the observed peak ground motions and intensities for California earthquakes.
Table 1: Ranges of Ground Motions for Modified Mercalli Intensities
