Bulletin of the Seismological Society of America, Vol. 96, No. 6, pp. 2206–2220, December 2006, doi: 10.1785/0120060045
MMI Attenuation and Historical Earthquakes in the Basin and Range
Province of Western North America
by William H. Bakun
Abstract Earthquakes in central Nevada (1932–1959) were used to develop a
modified Mercalli intensity (MMI) attenuation model for estimating moment magnitude M for earthquakes in the Basin and Range province of interior western North
America. M is 7.4–7.5 for the 26 March 1872 Owens Valley, California, earthquake,
in agreement with Beanland and Clark’s (1994) M 7.6 that was estimated from
geologic field observations. M is 7.5 for the 3 May 1887 Sonora, Mexico, earthquake,
in agreement with Natali and Sbar’s (1982) M 7.4 and Suter’s (2006) M 7.5, both
estimated from geologic field observations.
MMI at sites in California for earthquakes in the Nevada Basin and Range apparently are not much affected by the Sierra Nevada except at sites near the Sierra
Nevada where MMI is reduced. This reduction in MMI is consistent with a shadow
zone produced by the root of the Sierra Nevada. In contrast, MMI assignments for
earthquakes located in the eastern Sierra Nevada near the west margin of the Basin
and Range are greater than predicted at sites in California. These higher MMI values
may result from critical reflections due to layering near the base of the Sierra Nevada.
Introduction
The Basin and Range (B&R) province (Fig. 1) is part of
a wide, diffuse, seismically active plate boundary that accommodates the relative motion of the Pacific and North
American plates via east–west extension and right-lateral
shear (Hammond and Thatcher, 2004). The 3 May 1887 Sonora, Mexico, B&R M 7.5 earthquake is the largest historical
normal faulting earthquake in North America. The 1954
Fairview-Dixie Valley sequence of M 6 and M 7 earthquakes contained a significant component of right-lateral slip
(Hodgkinson et al., 1996b). Also, the 26 March 1872 Owens
Valley event (Beanland and Clark, 1994) on the west margin
of the B&R is one of the three largest historical strike-slip
California earthquakes—only the 1857 M 7.9 Fort Tejon and
1906 M 7.8 San Francisco earthquakes were larger.
Despite recurrence times of thousands-to-tens of thousands of years for individual B&R faults (Wallace, 1981),
several magnitude 7 B&R earthquakes have occurred in the
past 150 years. The clustering of many of these historical
earthquakes in the Central Nevada Seismic Zone (CNSZ)
may be explained at least in part by stress triggering (Hodgkinson et al., 1996a). The 1932–1959 magnitude 51⁄2–71⁄2
earthquakes in the CNSZ provide a unique opportunity to
model modified Mercalli intensity (MMI) attenuation for
B&R earthquakes. This article will develop a model of MMI
attenuation with distance for CNSZ earthquakes and test its
usefulness for other B&R events. With this model, M 7.5
will be estimated from MMI assignments for the 3 May 1887
Sonora, Mexico, earthquake, consistent with the M 7.4 and
7.5 estimated from geologic field observations by Natali and
Sbar (1982) and by Suter (2006), respectively.
Earthquakes in the CNSZ and in the Sierra Nevada (SN)
provide an opportunity to model the effects of the SN on the
distribution of MMI at sites in California. These MMI models
provide a means to estimate M for historical SN earthquakes
using MMI assignments. M 7.4–7.5 will be estimated for the
26 March 1872 Owens Valley, California, earthquake, consistent with the M 7.6 estimated by Beanland and Clark
(1994) from geologic field observations.
It has long been known that the SN delays travel times
from nearby earthquakes, presumably the result of wave
propagation through the root of the SN (Byerly, 1937). Although the existence of a root of the SN centered to the west
of the highest elevation of the SN is generally accepted (e.g.,
see Fliedner et al., 2000), its location and nature are controversial. If there is a SN root, there must be an adjacent
shadow zone (Bolt and Gutdeutsch, 1982) where seismic
amplitudes of crustal phases are diminished. No such
shadow zone has been reported heretofore.
I will modify the B&R model using MMI assignments
for SN events at sites in California to develop an MMI model
for paths through the SN. MMI is higher than predicted by
the B&R model, consistent with critical reflections from layering near the base (root) of the SN. For Nevada B&R events,
MMI at sites within and adjacent to the SN are reduced, consistent with a root of the SN and its shadow zone.
2206
2207
MMI Attenuation and Historical Earthquakes in the Basin and Range Province of Western North America
Let MMI ⳱ C 0 Ⳮ C1 M Ⳮ C2 Dh Ⳮ C3 log Dh .
(1)
C0 and C1 relate the MMI and M scales. C2 can be associated
with intrinsic attenuation and scattering, and C3 with geometric spreading. I used Joyner and Boore’s (1993) onestage maximum likelihood method developed for regression
analysis of strong-motion data to fit the 35 median Dh for
the nine calibration events (Table 2) to obtain the B&R MMI
attenuation model:
MMI B&R ⳱ (0.44 Ⳳ 2.34) Ⳮ (1.70 Ⳳ 0.33)M
ⳮ (0.0048 Ⳳ 0.0014)Dh ⳮ (2.73 Ⳳ 0.49) log Dh ,
Figure 1. Map of the B&R province and surrounding regions. The approximate perimeter of the B&R
(dashed red line) is adapted from Smith and Arabasz
(1991). Epicenters of calibration earthquakes for the
B&R and for the SN MMI attenuation models are
shown as black and blue circles, respectively. Epicenters of test earthquakes are shown as red dots. Locations of the 1872 Owens Valley, California, and 1887
Sonora, Mexico, earthquakes are black triangles.
(2)
where Dh is in kilometers.
There is considerable uncertainty in the coefficients C0
and C1, in part, because local magnitude ML, surface-wave
magnitude MS, and Gutenberg-Richter (1954) magnitude
MG-R were used for events where instrumental M is not
available (see Table 3). The mean and standard deviation of
the difference between observed and predicted MMI, (MMI
ⳮ MMIpred), are 0.007 and 0.58, respectively, for the 35
median Dh. If the MI values in Table 3 are used to calculate
MMIB&R, the standard deviation of (MMI ⳮ MMIB&R) is reduced to 0.34.
Estimates of M and Source Location
Following Bakun and Wentworth (1997), I use (2) to
estimate M from individual intensity observations for a grid
of trial epicenters. That is,
B&R Attenuation Model
Nine CNSZ earthquakes (black circles in Fig. 1) were
used as calibration events to develop an MMI attenuation
model for B&R paths (Table 1). Note that the 1954 Fairview
Peak and Dixie Valley earthquakes are treated as a single
event (no. 9) because the intensities are aggregated in Murphy and Cloud (1956). To avoid potentially significant effects of the SN that might bias the B&R MMI model, the MMI
assignments are restricted to paths that do not cross the SN
or parts of California west of the B&R. That is, only MMI
assignments at B&R sites in Arizona, California, Idaho, Nevada, Oregon, and Utah are used to develop the B&R MMI
attenuation model (Fig. 2).
Most of the strong shaking that is measured by intensity
assignments is generated by slip on the fault near the moment centroid. Although the focal depths of crustal earthquakes vary, the depth of the moment centroid, or the depth
of maximum displacement, is usually about 10 km. I assume
a depth h of 10 km to avoid computations with zero distances
at sites near the source. Dh is (D2 Ⳮ h2)1/2, where D is epicentral distance, and h is assumed to be 10 km. I use the
median Dh of the retained MMI assignments to characterize
the intensity data for each intensity level. The median Dh for
the nine calibration events are listed in Table 2.
MI ⳱ mean (Mi ),
(3)
where
Mi ⳱ {( MMIi ⳮ 0.44 Ⳮ 0.0048Dh,i
Ⳮ 2.73 log(Dh,i )}/1.7.
(4)
MMIi, and Dh,i are the MMI assignment and the hypocentral
distance, respectively, at site i. I find the misfit for each trial
epicenter from
rms [MI] ⳱ [rms (MI ⳮ Mi ) ⳮ rms0 (MI ⳮ Mi )],
(5)
where rms is the root-mean-square function, rms (MI ⳮ Mi)
⳱ {Ri[Wi(MI ⳮ Mi)]2/RiWi2}1/2, rms0(MI ⳮ Mi) is the minimum rms (MI ⳮ Mi) over the grid of trial epicenters, and
Wi is Bakun and Wentworth’s (1997) distance-weighting
function:
Wi ⳱
0.1 Ⳮ cos[(Di /150)(p/2)]
冦0.1
for Di ⬍ 150 km
(6)
for Di ⱖ 150 km.
2208
W. H. Bakun
Table 1
Calibration and Test Earthquakes
Date
No.
†
1
2†
3†
4
5
6†
7†
8†
9†‡
10†
11†
12
13
14§
15
16
17§
18§
19§
20§
21
Event Name
Cedar Mountain
Excelsior Mountains
Hansel Valley mainshock (OT:1505GMT)
Hansel Valley aftershock (OT:1820GMT)
Rainbow Mountain 1
Rainbow Mountain 2
a) Fairview Peak (OT:1107GMT);
b) Dixie Valley (OT:1111GMT)
Arizona–Utah Border
Cache Valley
Truckee
Pocatello Valley
Chino Valley
Mammoth Lakes
Mammoth Lakes (OT:1633GMT)
Mammoth Lakes (OT:1450GMT)
Mammoth Lakes
Chalfant Valley
Epicenter*
State
Yr
Mo
Day
⬚N
⬚W
NV
NV
NV
UT
UT
NV
NV
NV
NV
1932
1933
1934
1934
1934
1939
1954
1954
1954
12
6
1
3
3
5
7
8
12
21
25
30
12
12
11
6
24
16
38.75
39.08
38.28
41.80
41.80
38.58
39.42
39.58
39.32
117.82
119.33
118.37
112.90
112.90
117.83
118.53
118.45
118.20
NV
NV
AZ
UT
CA
ID
AZ
CA
CA
CA
CA
CA
1959
1959
1959
1962
1966
1975
1976
1978
1980
1980
1981
1986
3
6
7
8
9
3
2
10
5
5
9
7
23
23
21
30
12
28
4
4
25
27
30
21
39.60
39.08
36.80
41.92
39.44
42.06
34.66
37.51
37.59
37.49
37.59
37.54
118.02
118.82
112.37
111.73
120.16
112.52
112.50
118.69
118.85
118.83
118.89
118.45
*Stover and Coffman (1993).
†
Calibration event; otherwise, a test event.
‡
Intensities for 9a and 9b are aggregated in Murphy and Cloud (1956).
§
SN event.
For earthquakes with sufficient intensity assignments,
the rms [MI] contours bound the epicentral region. Bakun
and Wentworth (1997) associated rms contour values with
confidence levels that the epicenter was within the contour,
as tabulated in the corrected table 5a of Bakun and Wentworth (1999). The resolution of the source location is largely
controlled by the quantity, spatial distribution, and internal
consistency of the intensity assignments (Bakun and Scotti,
2006). Events with many, consistent intensity assignments
distributed at near sites surrounding the source region can
be precisely and reliably located. Events with only a few
reliable intensity assignments usually cannot be precisely
and reliably located.
The intensity center is the trial source location for which
rms [MI] is minimum (Bakun, 1999). The intensity center
corresponds more to the location of the moment centroid
than to the epicenter (Bakun, 2006).
Following Bakun and Wentworth (1997), MI and rms
[MI] are calculated over a grid of trial source locations and
contoured. In Figures 3–8, 12a, 14, and 15, contours of MI
are shown as red lines and contours of rms [MI] corresponding to the 67% and 95% confidence levels are shown as
green lines. There is a 67% likelihood that the epicenter is
within the 67% contour (inner green contour) and a 95%
likelihood that the epicenter is within the 95% contour (outer
green contour).
MI at a trial location is the best estimate of M for that
source location. The confidence range for M is estimated
using the number of intensity assignments and table 5b of
Bakun and Wentworth (1999).
M for the B&R Calibration Earthquakes
The MI listed in Table 3, estimated using the B&R paths
and (3), are independent estimates of M for the calibration
events. Doser’s (1988) inversions of body waves provide
lower bound estimates of M 6.7 and M 6.1 for events 1 and
3, respectively, consistent with MI 7.1 and 6.1, respectively.
Doser and Kanamori (1987) used the north–south longperiod strainmeter at Pasadena to obtain seismic moment
M0 8.9–19.5 ⳯ 1026 dyne cm for the 1954 Dixie Valley and
Fairview Peak earthquakes, corresponding to an aggregated
M 7.3–7.5. The MMI assignments for these earthquakes are
also aggregated in Murphy and Cloud (1956). If the Fairview
Peak event is twice the size of the Dixie Valley event (Doser
and Kanamori, 1987), MI is 7.3 and 7.1 for the Fairview
Peak and Dixie Valley events, respectively. Doser and Kanamori’s (1987) M0 corresponds to M 7.2 and M 7.0 for the
Fairview Peak and Dixie Valley events, respectively (Ellsworth, 1990). That is, the seismic constraints on M available
for the calibration events are consistent with the MI in
Table 3.
MMI Attenuation and Historical Earthquakes in the Basin and Range Province of Western North America
2209
Table 1). This MS 6.6 mainshock was followed by a significant aftershock at 18h20m UT (event 5 in Table 1). Doser
and Smith (1982) used body-wave displacement spectra to
obtain M0 7.7 ⳯ 1025 dyne cm (corresponding M 6.6) and
M0 3.1 ⳯ 1024 dyne cm (corresponding M 5.6) for events 4
and 5, respectively. The intensity center for the mainshock
is located 30 km southwest of the epicenter. MI is 6.4 at the
intensity center and at the epicenter (Fig. 3). For 160 MMI
assignments, the 95% confidence range is ⳮ0.25, Ⳮ0.17
(Bakun and Wentworth, 1999) so that M for the mainshock
is 6.1 to 6.6 at the 95% confidence level. The confidence
limits for M given for other events in this article are estimated similarly. For the Hansel Valley aftershock (event 5
in Table 1), MI is 5.8 at the intensity center and 5.7 at the
epicenter (Fig. 4). M is 5.5 to 6.0 at the 95% confidence
level for the Hansel Valley aftershock.
1959 Arizona–Utah Border Earthquake
The 21 July 1959 earthquake (event 12 in Table 1) occurred near the Arizona–Utah border within the Colorado
Plateau (Fig. 1). There is no instrumental M available, but
the ML assigned by California Institute of Technology (Caltech) is 5.6. The intensity center is located 22 km northwest
of the epicenter. MI is 5.3 at the intensity center and 5.5 at
the epicenter (Fig. 5). M is 5.1 to 5.7 at the 95% confidence
level.
Figure 2. MMI assignments for B&R sites in California (dots) and sites in Arizona, Idaho, Nevada,
Oregon, and Utah (open circles) for the 23 March
1959 (a) and 16 December 1954 (b) calibration
events. The median Dh for sites not in California
(open squares) are used to define the B&R MMI attenuation model.
1962 Cache Valley, Utah, Earthquake
B&R Test Events
1934 Hansel Valley, Utah, Earthquakes
The largest historical earthquake in Utah occurred in
Hansel Valley on 12 March 1934 at 15h05m UT (event 4 in
The 30 August 1962 (event 13 in Table 1) occurred near
the East Cache fault along the Intermountain Seismic Belt.
Doser and Smith (1982) used body-wave displacement spectra to obtain M0 7.0 ⳯ 1024 dyne cm (corresponding M 5.9),
consistent with Wallace et al.’s (1981) estimate of M0 7.1
⳯ 1024 dyne cm. The intensity center is located 41 km
southeast of the epicenter. MI is 6.2 at the intensity center
and 6.1 at the epicenter (Fig. 6). M is 5.9 to 6.4 at the 95%
confidence level.
Table 2
Intensity Data for Calibration Events
Median Dh
No.
III
IV
V
VI
VII
1
2
3
6
7
8
9
10
11
394.0
166.4
257.1
276.0
130.1
146.2
110.4
290.2
389.7
443.9
153.6
133.8
181.5
60.4
112.0
95.1
195.9
226.0
320.6
131.7
69.3
190.2
39.9
27.7
117.2
336.0
434.5
520.4
98.1
119.5
162.5
35.0
VIII
22.1
32.5
95.1
MMI Source
Neumann (1934)
Neumann (1935)
Neumann (1936)
Bodle (1941)
Murphy and Cloud (1956)
Murphy and Cloud (1956)
Murphy and Cloud (1956)
Eppley and Cloud (1961)
Eppley and Cloud (1961)
2210
W. H. Bakun
Table 3
Earthquake Magnitudes
No.
Name
1
2
3
4
5
6
7
8
9a
9b
10
11
12
13
14
15
16
17
18
19
20
21
Cedar Mountain
Excelsior Mountains
Hansel Valley mainshock
Hansel Valley aftershock
Rainbow Mountain 1
Rainbow Mountain 2
Fairview Peak
Dixie Valley
Arizona–Utah Border
Cache Valley
Truckee
Pocatello Valley
Chino Valley
Mammoth Lakes
Mammoth Lakes
Mammoth Lakes
Mammoth Lakes
Chalfant Valley
Magnitude
Source
Ml*
M (95%
Confidence
Range)†
7.3
6.1
6.5
6.6
5.6
5.5
6.6
6.8
7.1
6.8
6.3
6.1
5.6
5.9
5.9
6.1
4.6¶
5.5
6.2
5.9
5.6
6.2
MG-R 7.2 and MS 7.4 (Ellsworth, 1990); M 6.7 (Doser, 1988)
MG-R (Ellsworth, 1990)
MG-R 6.5 (Ellsworth, 1990); M 6.1 (Doser, 1988)
M (Doser and Smith, 1982)
M (Doser and Smith, 1982)
ML (BRK)**
MG-R (Ellsworth, 1990)
MG-R (Ellsworth, 1990)
MG-R (Ellsworth, 1990)
MG-R (Ellsworth, 1990)
ML (BRK)**
ML (BRK)**
ML (PAS)**
M (Doser and Smith, 1982)
M (Tsai and Aki, 1970)
M (Doser and Smith, 1982)
M (Eberhardt-Phillips et al., 1981)
M (Ekstrom and Dziewonski, 1985)
M (Ekstrom and Dziewonski, 1985)
M (Ekstrom and Dziewonski, 1985)
M (Ekstrom and Dziewonski, 1985)
M (Harvard CMT)
7.1
5.8
6.1
6.4
5.7
5.7
6.8
7.1
7.3‡§
7.1‡§
6.2
5.8
5.5
6.1
5.9
6.0
5.5
5.6
5.9
5.7
5.6
6.2#
6.8–7.2
5.5–6.0
5.8–6.3
6.1–6.6
5.5–6.0
5.4–6.0
6.5–7.0
6.9–7.3
7.0–7.5
6.8–7.3
5.9–6.4
5.5–6.0
5.1–5.7
5.9–6.4
5.7–6.1
5.8–6.3
5.2–5.8
5.3–5.7
5.6–6.1
5.4–5.8
5.4–5.8
5.9–6.3
*Intensity magnitude evaluated at epicenter.
†
Using table 5b of Bakun and Wentworth (1999) for number of MMI assignments at sites not in California.
‡
Assume M0 for Fairview Peak is twice the M0 for Dixie Valley.
§
Aggregate Ml 7.4 for 9a (Fairview Peak) and 9b (Dixie Valley) events.
¶
Based on long-period seismogram at Tucson (D ⳱ 330 km). ML 5.1 (USGS, Golden, Colorado).
#
Using the B&R model for all MMI assignments.
**
ML (BRK) and ML (PAS) are ML estimated by the University of California, Berkeley, and by Caltech, respectively.
1975 Pocatello Valley, Idaho, Earthquake
The 28 March 1975 earthquake (event 15 in Table 1)
occurred in the Pocatello Valley about 40 km northeast of
the 1934 Hansel Valley, Utah, earthquakes. Doser and Smith
(1982) used body-wave displacement spectra to obtain M0
1.9 ⳯ 1025 dyne cm, consistent with M0 2.2 ⳯ 1025 dyne
cm (Bache et al., 1980), 1.6 ⳯ 1025 dyne cm (Wallace et
al., 1981), and 1.2 ⳯ 1025 dyne cm (Williams, 1979). The
corresponding M range from 6.0 to 6.2. The intensity center
is about 5 km west of the epicenter. MI is 6.1 at the intensity
center and 6.0 at the epicenter (Fig. 7). M is 5.8 to 6.3 at
the 95% confidence level.
1976 Chino Valley, Arizona, Earthquake
The 4 February 1976 earthquake (event 16 in Table 1)
in the Chino Valley of western Arizona occurred within the
transition zone between the B&R province and the Colorado
Plateau. The intensity center is located 15 km northwest of
the epicenter (Fig. 8). Eberhardt-Phillips et al. (1981) estimated an M0 of 1.0 ⳯ 1023 dyne cm (corresponding M 4.6),
but their analysis was restricted to the World-Wide Standardized Seismograph Network (WWSSN) signal recorded at
Tucson (D ⳱ 330 km) due to interference at other WWSSN
stations from a Kamchatka teleseism that occurred 7 min
before. ML assigned by Caltech was 5.2 (Stover and Coffman, 1993). MI is 5.6 at the intensity center and 5.5 at the
epicenter. M is 5.2 to 5.8 at the 95% confidence level. The
various estimates of magnitude do not agree but there are
good reasons to assign large uncertainties to EberhardtPhillips et al.’s (1981) M0 and to prefer the MI 5.5.
B&R Test Events—Summary
The magnitude and location estimates obtained using
MMI assignments for the six test events (4, 5, 12, 13, 15,
and 16 in Tables 1 and 3) suggest that the B&R MMI atten-
uation model obtained from central Nevada earthquakes is
appropriate for earthquakes elsewhere in the B&R. Excluding the (M ⳮ MI) ⳱ ⳮ0.9 for the 1976 Chino Valley earthquake as anomalous because M is poorly determined, |(M
ⳮ MI)| ⱕ0.2 for the other five test events. If the ML assigned
by Caltech is used for the 1976 Chino Valley event rather
than M, the instrumental magnitudes for all six test events
are within the Ⳳ2r for M estimated from the intensity data.
The mean distance of the intensity center from the epicenter
is 23 km and epicenters for all six events are within the 95%
confidence region for location.
MMI Attenuation and Historical Earthquakes in the Basin and Range Province of Western North America
Figure 3.
The 12 March 1934 Hansel Valley,
Utah, mainshock (event 4). MMI intensity assignments are circles, the epicenter (Epic.) is a red star,
and the intensity center IC is a green triangle. The
contours of MI (dashed red lines) are the best estimates of M from the MMI assignments for assumed
epicenters on that contour. The rms [MI] contours corresponding to the 67% (innermost contour) and 95%
confidence contours (outermost contour) for location
(Bakun and Wentworth, 1999) are shown as solid
green lines.
Sierra Nevada–California Attenuation Model
The five SN events (events 14 and 17–20 in Table 1)
that are located near the west margin of the B&R are shown
as blue circles in Figure 1. Mi values using (4) for these
events vary with the azimuth of the MMI site from the epicenter (Fig. 9). The Mi for easterly azimuths (B&R paths)
are less than Mi for westerly azimuths (SN paths). By inspection, the effect of different MMI attenuation due to the
SN occurs for epicenter-to-MMI-site azimuths of 145⬚ clockwise through 330⬚. For these SN azimuths, MI ⳱ mean (Mi)
are greater than M for all five events (Fig. 9). For the B&R
azimuths (330⬚ clockwise through 145⬚), MI for the five
events are consistent with M with the mean (MI ⳮ M) ⳱
0.04. The B&R model, (2), is apparently appropriate for MMI
sites located at azimuths 330⬚ clockwise through 145⬚ of
epicenters of SN earthquakes occurring along the west margin of the B&R.
The MMI assignments for paths affected by the SN are
used to construct a SN–California MMI path attenuation
2211
Figure 4.
The 12 March 1934 Hansel Valley,
Utah, aftershock (event 5). See legend to Figure 3 for
definition of symbols and contours.
model (SN model), which is an adaptation of the B&R model
(2). MMI for SN azimuths for the five events are generally
greater than the MMI predicted by (2) for Dh greater than
about 100 km (Fig. 10a). Smoothed dMMI increase linearly
with distance, with the exception of larger MMI for 105 km
⬍ Dh ⬍ 220 km. These larger MMI are removed (Fig. 10b)
if (2) is adjusted by
dA(MMIB&R ) ⳱ ⳮ0.58 Ⳮ 0.0066Dh for all Dh
(7)
and by
dB (MMIB&R ) ⳱ 0.5 sin[(Dh ⳮ 105)p/230]
for 105 km ⬍ Dh ⬍ 220 km.
(8)
That is the SN model is
MMISN ⳱ ⳮ0.14 Ⳮ 1.70M
Ⳮ 0.0018Dh ⳮ 2.73 log Dh ⳮ dB (MMIB&R),
(9)
where Dh is in kilometers. The effect of the SN on the attenuation of MMI is not significant for D less than about 100 km
(Fig. 11), probably because geometrical spreading accounts
for almost all of the decrease of MMI at these distances. The
decay of MMI with D in the B&R is not very different from
that in southern California (Fig. 11).
2212
W. H. Bakun
Figure 5. The 21 July 1959 earthquake near the
Arizona–Utah border (event 12). See legend to Figure
3 for definition of symbols and contours.
M and the locations of SN earthquakes along the west
margin of the B&R can be estimated if a combination model
(Combo), where the SN model (9), rather than B&R model
(2), is used in (4) for MMI site azimuths ranging from 145⬚
through 330⬚. The solution for the 1966 Truckee earthquake
(event 14 in Table 1) using the Combo model is shown in
Figure 12. MI is 5.9 and the intensity center is 6 km west of
the epicenter. The mean epicenter-to-intensity-center distance for the five SN events using the Combo model is
22 km. The mean and standard deviation of (MI ⳮ M) are
ⳮ0.08 and 0.18, respectively.
Large Historical Earthquakes
The MMI attenuation models can be used to estimate the
magnitude and location of large historical earthquakes in and
near the B&R. The 1872 Owens Valley, California, earthquake occurred in the eastern SN near the west margin of
the B&R; the Combo MMI attenuation model is appropriate
for the analysis of MMI assignments for the Owens Valley
earthquake. It will be shown that the source location and
M 7.4–7.5 estimated using intensity assignments are consistent with the location of surface rupture and the M estimated
from geologic field observations by Beanland and Clark
(1994). The 1887 Sonora, Mexico, earthquake occurred in
the B&R near the U.S.–Mexico border; the B&R MMI attenuation model is appropriate for MMI assignments for the
Figure 6.
The 30 August 1962 Cache Valley,
Utah, earthquake (event 13). See legend to Figure 3
for definition of symbols and contours.
Sonora earthquake. It will be shown that the source location
is poorly constrained by the intensity data, but M 7.5 estimated from intensity data for locations along the surface
rupture is consistent with M estimated from geologic field
observations by Natali and Sbar (1982) and by Suter (2006).
The 1872 Owens Valley, California, Earthquake
The 26 March 1872 earthquake ruptured about 100 km
of the Owens Valley fault with predominantly right-lateral
strike-slip motion; the average horizontal displacement was
6 m (Beanland and Clark, 1994). The felt area and maximum
fault displacement are comparable to those of the M 7.8
1906 San Francisco and M 7.9 1857 Fort Tejon strike-slip
earthquakes, but the 1906 and 1857 rupture lengths were
significantly larger (Ellsworth, 1990).
Previous estimates of M for the 1872 event have been
based on isoseismal areas and on geologic studies of the fault
rupture. Comparisons of 1872 isoseismal areas with those of
other large earthquakes led Oakeshott et al. (1972) to conclude that the 1872 earthquake was a magnitude 8 event.
Hanks et al. (1975) used the MMI VI isoseismal area to estimate an M0 of 5 ⳯ 1027 dyne cm; Hanks and Kanamori
(1979) used Hanks et al.’s (1975) M0 to estimate M 7.8.
Toppozada et al. (1981) used isoseismal areas for MMI V,
VI, and VII to estimate magnitudes of 7.1, 7.1, and 7.7.
MMI Attenuation and Historical Earthquakes in the Basin and Range Province of Western North America
2213
Figure 7. The 28 March 1975 Pocatello Valley,
Idaho, earthquake (event 15). See legend to Figure 3
for definition of symbols and contours.
Figure 9. MI (circles) using (2) for SN events versus the epicenter-to-site azimuth (⬚ measured clockwise from north ⳱ 0⬚). (a) 1966 Truckee; (b) to (e)
Mammoth Lakes events. The dashed red lines are the
MI ⳱ mean (Mi) for B&R paths (330⬚ clockwise to
145⬚) and for paths through the SN (other azimuths).
The MI values are given as red numbers.
Figure 8. The 4 February 1976 Chino Valley, Arizona, earthquake (event 16). See legend to Figure 3
for definition of symbols and contours.
Ignoring the MI obtained for the offshore MMI V isoseismal,
Toppozada et al.’s (1981) MI would be 7.4. Toppozada and
Branum’s (2004) MI 7.4 is a misprint (Toppozada, written
comm. 2005); their MI is 7.1 for the 1872 event. Beanland
and Clark (1994) used measurements of fault offsets and
rupture length to obtain an M0 1.8–4.4 ⳯ 1027 dyne cm, and
an M of 7.5 to 7.7. Finally, Stein and Hanks (1998) adopted
Beanland and Clark’s (1994) geologic measurements to es-
2214
W. H. Bakun
Figure 11.
The B&R model, the SN model, and
Bakun’s (2006) MMI attenuation model for southern
California (SoCalif) for an M 6.0 source.
(a) dMMI ⳱ (MMI ⳮ MMIB&R) for SN
paths for the five SN events located near the west margin of the B&R are black dots. The red dotted line is
the output of a Stineman (1980) smoothing filter applied to the dMMI. The green dashed line is a linear
trend along the red dotted line. (b) The smoothed
dMMI ⳱ (MMI ⳮ MMISN) for the MMI assignments
in a.
Figure 10.
timate an M0 2 ⳯ 1027 dyne cm, which corresponds to M
7.5, rather than the M 7.4 listed by Stein and Hanks (1998).
I used Toppozada et al.’s (1981) summary descriptions
of the effects of the 1872 event. There are almost no MMI
⬍V assignments because most people were asleep when the
2:30 a.m. event occurred. Toppozada et al.’s (1981) MMI V
isoseismal is in the Pacific Ocean from San Francisco to San
Diego. The truncation of the MMI V assignments at the California coast would bias estimates of MI if the MMI V assignments in California were included. Estimating MI using
intensity assignments for only those intensity levels with apparently complete sampling of the D distribution is a better
strategy (Bakun and Scotti, 2006). MMI assignments are
truncated at the California coast at about D ⳱ 450 km; the
sampling of MMI is apparently complete at the MMI V 1⁄2
level (Fig. 13a), but MMI V assignments that would normally
be expected at D greater than about 450 km are missing.
Mi for the MMI ⱖ V 1⁄2 assignments are not sensitive to
epicenter-to-MMI site azimuth if the Combo MMI attenuation model is used (Fig. 13b).
The intensity center is located at the south end of the
1872 rupture (Fig. 14), where the maximum slip of about
10 m occurred (Beanland and Clark, 1994). MI is 7.44 at the
intensity center and about 7.45 along the 100- to 110-km
rupture length. M is 7.1 to 7.6 at the 95% confidence level.
My preferred M is 7.4–7.5 and Beanland and Clark’s (1994)
preferred M is 7.6, and there is considerable overlap in the
95% confidence range of M from intensity data and Beanland and Clark’s (1994) permissible M 7.5–7.7 range. For a
110-km-long strike-slip rupture length on a continental fault,
the expected M is 7.2 (Wells and Coppersmith, 1994) to 7.3
(Hanks and Bakun, 2002), suggesting that the 1872 Owens
Valley earthquake was a high stress drop source.
1887 Sonora, Mexico, Earthquake
The 3 May 1887 earthquake that ruptured the east side
of the San Bernardino Valley in northeastern Sonora, Mexico, was one of the largest historic normal faulting earthquakes in North America (Fig. 15). Field measurements suggest an average displacement of 3 m over a rupture length
of 80 km with a maximum displacement of 4.5 m (Natali
and Sbar, 1982). Assuming a rupture depth of 0 to 16 km,
Natali and Sbar (1982) estimated M0 ⳱ 1.27 ⳯ 1027 dynecm (M 7.4). Suter (2006) used postearthquake field observations by Goodfellow (1887a, 1887b, 1888) and Aguilera
(1888, 1920) to estimate a rupture length of 101.8 km. Suter
(2006) used this rupture length and Wells and Coppersmith
(1994) normal fault regression relation to estimate M 7.5.
DuBois and Smith (1980) compiled descriptions of the
MMI Attenuation and Historical Earthquakes in the Basin and Range Province of Western North America
2215
Figure 13. (a) MMI assignments for the 1872
Owens Valley, California, earthquake for B&R paths
(open circles) and SN paths (dots). MMI V assignments are generally not available at D ⬎450 km, the
epicentral distance from San Diego. (b) Mi estimate
from MMI ⬎V using the Combo MMI model. MI ⳱
mean (Mi) ⳱ 7.46.
Figure 12.
The 12 September 1966, Truckee,
California, earthquake (event 14). (a) See legend to
Figure 3 for definition of symbols and contours. (b)
Mi (circles) using the B&R model for azimuths from
330⬚ clockwise through 145⬚ and the SN model for
other azimuths. The red line is MI ⳱ mean (Mi) ⳱
5.9 for all Mi values.
nardino Valley leaves little doubt of the source location. I
assume Stover and Coffman’s (1993) epicenter location
(30.8⬚ N, 109.25⬚ W). MI is 7.5, in close agreement with
Natali and Sbar’s (1982) M 7.4 and Suter’s (2006) M 7.5,
both estimated from geologic field observations. M is 7.2 to
7.7 at the 95% confidence level.
Discussion
effects of the 1887 event and assigned MMI for 214 sites in
the United States and Mexico. Sbar and DuBois (1984) listed
coordinates for 171 of DuBois and Smith’s (1980) 214 sites.
Many of DuBois and Smith’s (1980) MMI values were assigned by using descriptions of ground failures and/or damage to adobe structures of unknown resistance to shaking.
Ground failure and damage to adobe structures can occur
over a wide range of input ground shaking, so DuBois and
Smith’s (1980) listed ranges of MMI for many sites. I used
DuBois and Smith’s (1980) descriptions of effects to assign
unambiguous MMI at 27 sites; MMI IV at 2 sites, MMI V at
10 sites, and MMI VI at 15 sites (Table 4). The MMI V and
VI assignments are sufficient to estimate MI, but not to adequately constrain the epicenter (Fig. 15). Fortunately, the
mapped surface rupture along the east side of the San Ber-
MMI Attenuation in the Western Rocky Mountains
and in the Colorado Plateau
Five of the six test events (4, 5, 13, 15, and 16 in Table
1) lie near the boundary of the B&R, and the 1959 Arizona–
Utah border event (event 12) occurred in the Colorado Plateau (Fig. 1). If the B&R model were not appropriate for
these events, then Mi would change with the azimuth of the
MMI site from the epicenter. There are no systematic
changes of Mi with azimuth for the B&R test events (Fig. 16),
in contrast with the variations of Mi obtained for the SN
events (Fig. 9). The patterns of Mi for the Utah events
(Fig. 16a, b, and d) suggest that the attenuation of MMI in
the western Rocky Mountains is not significantly different
from that in the B&R. The pattern of Mi for the 1976 Chino
2216
W. H. Bakun
Figure 14. The 1872 Owens Valley, California,
earthquake for MMI ⬎V assignments. See legend to
Figure 3 for definition of symbols and contours. The
blue line is Beanland and Clark’s (1994) zone of surface rupture.
Valley event (Fig. 16f) suggests that the attenuation of MMI
in the Colorado Plateau is not significantly different from
that in the B&R. The consistency of MI and ML and the
pattern of Mi for the 1959 Arizona–Utah border event
(Fig. 16c) support this inference.
Figure 15.
The 1887 Sonora, Mexico, earthquake
for MMI V (smaller circles) and VI (larger circles)
assignments (Table 4). See legend to Figure 3 for definition of symbols and contours. The blue line is the
extent of surface displacement on the Pitaycachi fault
(Natali and Sbar, 1982). Coffman and Stover’s (1993)
location (red star) is the preferred location. The intensity center is the green triangle.
central California relative to Pakiser and Brune’s (1980)
50 km depth of the base of the SN.
The SN Model and the Root of the Sierra Nevada
The slow rate of decrease of MMI for D ⬎100 km in
the SN model (Fig. 11) can be explained by critical reflections from layers near the base of the SN. Similar reflections
from the crustal layers and the Moho influenced damage
patterns in and near San Francisco (D ⳱ 100 km) during the
1989 Loma Prieta earthquake (e.g., Somerville and Yoshimura, 1990; Catchings and Kohler, 1996). Pakiser and
Brune’s (1980) preferred model for the root of the SN implies low-velocity crustal rocks beneath a subducted ophiolite sequence (slab) dipping eastward at about 50 km depth
beneath the western margin of the SN. The “bump” in MMI
at 105 km ⬍ D ⬍ 130 km in the SN model is also reminiscent
of the “bump” in ML residuals at 75 km ⬍ D ⬍ 125 km for
earthquakes in central California that was interpreted by
Bakun and Joyner (1984) as the result of Moho reflections.
Bakun and Joyner’s (1984) ML bump and the damage effects
in the 1989 Loma Prieta earthquake occurred at somewhat
smaller D, consistent with a shallow Moho (25–30 km) in
The Root of the SN and Earthquakes in Nevada
How does the SN affect strong shaking from Nevada
earthquakes? Tests using the nine CNSZ calibration events
(three of the nine events are shown in Fig. 17a–c) show a
consistent pattern of Mi with azimuth that is different from
that of the SN earthquakes shown in Figure 9. The MI obtained using the Combo model (Fig. 17a–c, left column) are
significantly smaller than the MI obtained for B&R paths.
Moreover, the Mi for the nine CNSZ earthquakes using the
B&R model are not systematically greater for SN paths
(Fig. 17a–c, right column). The smoothed dMMI for the nine
CNSZ events for SN paths show only a small increase with
D and there is no “bump” in MMI that can be associated with
reflections from layering near the base of the SN (Fig. 18).
The most notable aspect is the bay (negative values) in the
smoothed dMMI at 40 km ⬍ D ⬍ 90 km. A decrease in
crustal phase amplitudes at sites within and adjacent to the
2217
MMI Attenuation and Historical Earthquakes in the Basin and Range Province of Western North America
Table 4
MMI Assignments Used for the 1887 Sonora, Mexico,
Earthquake
Place
Albuquerque
Altar
Benson
Bisbee
Chihuahua City
Crittenden
El Paso
Elgin
Ft. Apache
Ft. Thomas
Gila Crossing
Globe
Guaymas
Harshaw
Kingston
Las Cruces
Nogales
Oro Blanco
Pantano
Phoenix
Pinal
San Simon
Solomonville
Tombstone
Tucson
Washington Camp
Yuma
MMI*
VI
VII
VIII
VII–VIII
V
VI
VII–VIII
VI–VII
VII–VIII
V
V
VI–VII
IV
VI–VII
V
VI–VII
VI–VII
VI
VII–VIII
VI
VI
VII
VII
VII–VIII
VII–VIII
VI–VII
IV–V
MMI†
V
V
VI
VI
V
VI
VI
VI
VI
V
IV
V
V
VI
V
V
VI
V
VI
V
VI
VI
VI
VI
VI
VI
IV
Lat (⬚ N)‡
Long (⬚ W)‡
35.08
30.72
31.96
31.44
28.63
31.65
31.76
31.66
33.78
33.03
33.41
33.4
27.93
31.47
32.92
32.31
31.34
31.48
32
33.45
33.3
32.27
32.81
31.71
32.22
31.42
32.72
106.65
111.73
110.3
109.92
106.08
110.7
106.48
110.52
109.98
109.95
112.34
110.78
110.9
110.7
107.7
106.78
110.94
111.28
110.58
112.07
111.08
109.23
109.63
110.07
110.97
110.55
114.72
*MMI assigned by DuBois and Smith (1980).
†
MMI assigned here using descriptions in DuBois and Smith (1980). I
do not consider ground failure or damage to buildings of unknown (presumably poor) construction.
‡
Taken from Sbar and DuBois (1984).
SN is expected if there is a root to the SN (Bolt and Gutdeutsch, 1982). That is, the shadow zone in MMI is independent evidence for a root of the SN.
The 1986 Chalfant Valley, California, Earthquake
Figure 16. Mi (circles) using (2) for B&R test
events versus the epicenter-to-site azimuth (⬚ measured clockwise from north ⳱ 0⬚). The dashed lines
are MI.
The 21 July 1986 M 6.2 Chalfant Valley event occurred
in the B&R about 35 km east of the four 1978–1981 Mammoth Lakes events (Fig. 1). Although the pattern of MMI
variation with azimuth (Fig. 17d, right column) is similar to
that for the five SN events (Fig. 9), MI is 5.7 using the Combo
model. On the other hand, MI is 6.2, equal to the instrumental
M if the B&R model is used for all azimuths (Fig. 17d, right
column). The discrepancy of M and MI using the Combo
model for Nevada earthquakes (Fig. 17a–c) is similar to that
of the Chalfant Valley earthquake. The influence of the SN
on MMI assignments at California sites is apparently that of
the earthquakes in the Nevada B&R and not that of the
nearby Mammoth Lakes, California, SN earthquakes. MI
should be estimated using the B&R model. That is, MI is 6.2
for the Chalfant Valley earthquake.
2218
W. H. Bakun
Figure 17. Mi (circles) versus azimuth for: (a) 1954 Rainbow Mountain 1, Nevada
(event 7); (b) 1954 Rainbow Mountain 2, Nevada (event 8); (c) 1954 Fairview Peak
and Dixie Valley, Nevada (event 9); (d) 1986 Chalfant Valley, California (event 21),
events using the Combo model (left column) and the B&R (right column) models. The
red dashed lines are the MI. MMI assignments in (d) are taken from Stover and Brewer
(1994).
MMI Attenuation and Historical Earthquakes in the Basin and Range Province of Western North America
2219
close agreement with Natali and Sbar’s (1982) M 7.4 and
Suter’s (2006) M 7.5, both estimated from geologic field
observations. M is 7.2 to 7.7 at the 95% confidence level.
Acknowledgments
The comments and suggestions of Tom Brocher and Woody Savage
greatly improved the manuscript. The Generic Mapping Tools software
package by Wessel and Smith (1991) was used to generate many of the
figures.
dMMI ⳱ (MMI ⳮ MMIB&R) for SN
paths (225⬚ clockwise through 315⬚) for the nine
CNSZ calibration events. The red dotted line is the
output of a Stineman (1980) smoothing filter. The
dotted green line is a linear trend, dMMI ⳱
0.00038Dh, along the red line. The deviation of red
and green lines for 40 km ⬍ Dh ⬍ 90 km is consistent
with a shadow zone associated with the root of the
SN.
Figure 18.
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MMIB&R ⳱ (0.44 Ⳳ 2.34)
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(10)
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U.S. Geological Survey
Menlo Park, California 94025
Manuscript received 24 February 2006.