Department of the Interior

U. S. Geological Survey

Coda duration magnitudes in central California:

An empirical approach

byCaryl A. Michaelson l

Open File Report 87-588

This report is preliminary and has not been reviewed for conformity

with U.S. Geological Survey editorial standards.

1 Menlo Park, California

1987

CODA DURATION MAGNITUDES IN CENTRAL CALIFORNIA:

Atf EMPIRICAL APPROACH

by

Caryl A. Michaelson

ABSTRACT.

A new empirical lapse time coda duration magnitude MD is presented to establish the continuity of dura­

tion magnitudes in the central California seismic network during the period beginning from mid-1977 through

1981. MD is modeled by relating Wood-Anderson or synthetic local magnitudes ML to a polynomial function of

log I (where t is the lapse time duration measured from the earthquake origin time), a correction for the instru­

ment attenuation setting of the seismograph station a, and a site correction 5 assumed to be related to the

attenuation and scattering properties of the local geology. Previously coda durations were measured from the P-

wave arrival time. The new formula for coda magnitude is based on data from 55 earthquakes in 5 source

regions with 0.9 < ML < 5.6, is MD = -0.43 (±0.068) + 0.84 (±0.074) log t + 0.56 (±0.020) log2 1 + a + 6, and

provides site corrections for 214 stations. The site corrections are spatially correlated. Stations overestimating

MD correspond to sites of lower density, and those underestimating MD correspond to higher density sites, as

indicated by the isostatic gravity field.

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INTRODUCTION.

The primary purpose of this paper is to define an empirical coda magnitude estimate for the central Cali­

fornia short-period seismic network (CALNET), by examining the relationship between coda durations and

Wood-Anderson magnitudes, ML . A uniform estimate of earthquake magnitudes is essential for comparisons

between different source regions and during different time periods. This is important for detecting and evaluating

whether or not there are significant spatial or temporal variations in seismicity rates and attenuation. The con­

tinuity of magnitudes, particularly for such a large region, is mack difficult by the sporadic nature of network

operations and seismic activity.

Bakun [1984b] conducted a pilot study to establish a preliminary empirical relationship of coda magnitude

with ML . Bakun [1984a] calculated Wood-Anderson magnitudes for the central California seismic network

(CALNET) from Wood-Anderson or synthetic Wood-Anderson seismograms. He selected 110 earthquakes in 5

source regions with 0.7 <*ML < 5.6, during the period from mid-1977 through 1981. Based on 55 of these earth­

quakes, Bakun [1984b] used observations of traditional coda duration T, epicentral distance A, and station correc­

tions 5, from 42 CALNET stations recorded on develocorder film to obtain the following empirical formula:

MD = 0.92 + 0.607(±0.005) log2 T + 0.00268(±0.00012) A + 8,

with the event magnitude being the mean of the individual estimates. The station corrections, 5, are listed in

Table 2 of Bakun [1984b].

The coda duration magnitude formulation presented in this study differs from Bakun's and other duration

magnitudes in several ways. Most importantly, the duration is redefined as the lapse time duration, following a

suggestion from Aid [personal communication, 1986], rather than the traditional coda duration. The lapse time

duration t, is the signal duration beginning with the event origin time, rather than the P-wave arrival time, as

used in the traditional coda duration T [Lee et al., 1972]. Thus, the two durations are related in the following

way, t = tp + T, where tp is the P-wave travel-time. Using the lapse time duration has two distinct advantages:

it relieves some of the problems associated with velocity model assumptions, and it inherently incorporates the

distance term but is simpler to calculate than the (epicentral or hypocentral) distance. Other differences in the

magnitude determination include the functional form of the magnitude relationship, and I applied corrections for

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the average site characteristics and for the instrument attenuation setting of the seismograph station. Finally, the

magnitude of an earthquake is represented by the weighted median of the individual estimates rather than their

mean. The new coda magnitude is based on a function of the lapse time duration, instrument attenuation and site

corrections, MD A// (log 1, a, 6).

DATA.

The data included in this analysis are local Wood-Anderson or synthetic local magnitudes ML , duration

measurements and phase data from CALNET stations recorded on develocorder film for 110 earthquakes in cen­

tral California. The hypocenters and ML magnitudes for these earthquakes were obtained from Tables 1-5 in

Bakun [1984a]. Figure 1 is a map of the epicenters and the CALNET station locations used in this study. The

insert in Figure 1 shows the depth distribution in each of the 5 source regions. For this paper I selected half of

the earthquakes listed in Table 2, and systematically read from the develocorder film the P-wave arrival times

and coda cutoff times at every CALNET station that recorded the events. In order to be consistent with the

CALNET phase data base, I used the same coda cutoff criteria prescribed by Lee et al. [1972], whereby the end

of the coda is the time when the coda envelope decreases to 10 mm peak-to-peak amplitude at a specific viewer

magnification of 10 mm = 1 sec. (There are alternatives to this criteria, but the goal is to provide a magnitude

formulation consistent with the CALNET coda readings during this time period.)

More than 5300 durations were measured initially; this is as complete a compilation as possible for these

stations and set of events. Some of these data have been rejected based on a few simple rules. Durations read

from traces where the P-wave travel-time residual is larger than ±2.0 seconds are deleted because there is a high

probability that the seismic signal is not from the station associated with that channel (e.g. from cross-talk on

the discriminators or misidentified channels). Durations whose measured lapse times are less than the expected

S-wave travel-time ts are also deleted because the coda is considered to be dominated primarily by scattered S-

waves [Aki and Chouet, 1975]. The routine CALNET practice has been to reject coda durations with T< 10 sec

because of the high probability that the signal is dominated by direct arrivals rather than scattered waves. By

adopting the minimum travel-time criteria t> ts , even codas of very short duration may be used. For typical

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California crustal velocities, the S-wave travel-time is t$ = 1.7 tp. Figure 2 is a plot of log t versus the P-wave

travel-time with a curve corresponding to the minimum lapse time criteria I = ts . A total of 5130 observations

from 210 stations comprise the resulting data set henceforth referred to as the independent set.

The independent set is used to establish an empirical relationship between lapse time duration t and local

magnitude ML through a weighted least-squares regression analysis. I restrict the observations in the regression

analysis to a subset of the independent set that reflects the data distribution in the CALNET catalog.

Specifically, the coda durations i available from the CALNET data base are largely from stations mat are within

a radius of 100 km from the epicenter. Therefore, in this study the regression is restricted to observations from

stations located within a P-wave travel-time radius of tp = 17.5 sec (~ 100 km), and have errors that are less

than the median absolute deviation, described later in this report. The resulting data set used in the regression

include durations from 156 CALNET stations within a radius of tP = 17.5 sec, with ten of them having less than

5 readings for the 55 shocks considered. The ML for an additional 50 earthquakes obtained from Bakun

[1984a,b] along with phase data and coda durations obtained directly from the CALNET catalog data base are

referred to as the test set. The test set is used to help evaluate the new relationship determined from regression

analysis, and is described later in mis report.

ATTENUATION CORRECTION.

The coda duration formulations of Lee et al. [1972] and Bakun [1984a, 1984b] do not explicitly accommo­

date variations in seismograph magnification. In fact, for every change of 6 dB the signal amplitude changes by

a factor of 2. Lee et al. [1972] considered the seismograph attenuation insignificant to the resultant magnitude,

probably because most of their data were from a small range of attenuation settings. However, Bakun [1984b]

noted a systematic correlation between the attenuation and the station corrections. In this study, the independent

set has observations over a wide range of instrument attenuation settings from 6 dB to 42 dB. Hence the signal

amplitude may vary by as much as a factor of 26, affecting the cutoff time of the duration significantly. Thus,

the apparent magnitude may vary by a factor of log 26 = 1.8, due to different instrument attenuation settings

alone. In most cases, the instrument attenuation is set according to the observed seismic background noise at

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each site, so that recorded background levels are relatively uniform across the network. The seismic background

noise is usually related to the local geology except at locations near the sea coast, or where cultural or atmos­

pheric noise levels are high.

I isolated the instrument attenuation as a separate correction term a, in the magnitude formula so that the

site corrections 8 reflect local geological site characteristics as much as possible. According to Richter [1935],

the amplitude of an earthquake signal decays at a constant rate, A^/vAo f', where A^ is the amplitude at time t

from signal origin, AO is related to the source function, and q is a constant Johnson [1979] suggested that the

amplitude decay rate is dependent on the site geology and the attenuation factor Q, calculating 0.8 < q < 2.2 for

most southern California stations. Unfortunately, Johnson did not distinguish the seismograph instrument attenua­

tion from site characteristics. The magnitudes of Johnson's earthquakes were limited to 2.0 < ML < 4.5, so that

q may be more complicated over a wider magnitude range. Lindh [personal communication, 1987] has found a

range of q=2-3 for the Parkfield, California region.

Varying the instrument attenuation affects the time required for the signal amplitude to decay by a factor

of 2 for each 6 dB setting. The difference in time is related to A log t^ 2£ _ °j? _ 0.15 per 6 dB,(£ ^--.U

assuming q=2.0. Geometrically, this is illustrated in Figure 3, where plots of log A versus log t are straight lines

with slope -q = -r* . While the difference in the amplitude magnitude estimate would change by a factor of

A A/L/v A log A, the duration magnitude changes by a factor of A MD^ A log t = ** , Consequently, vari-q

ations in signal duration and apparent duration magnitude due to a change in the instrument attenuation setting is

A MD/VA log t = 0.0250 per dB. Eaton [1984] noted that the majority of CALNET stations have attenuation set­

tings of 12 dB and 18 dB, and suggested that the average for the network be considered 15 dB, although this is

not an actual instrument setting. Assuming the attenuation correction is zero at 15 dB, I adopt the following

linear relationship:

-0.375, (4)

for the y* station at the time of the /* earthquake, with q=2.Q. (For q=3.0, cty = 0.017 attni} - 0.255.) Because

I use a quadratic form of t in the estimate of MD , a may be better estimated by a quadratic, but the difference

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between the two is small. The attenuation settings may be obtained from the CALNET station maintenance his­

tory files that are described by Eaton [1986]. The stations used in this study are of the same instrument type. If

any other type were to be included, differences in the instrument response may require a further magnitude

adjustment.

REGRESSION ANALYSIS.

Model. The coda magnitude relationship presented in mis paper is derived from the results of a standard

procedure of stepwise, linear, weighted least-squares regression and exploratory data analysis [Mosteller and

Tukey, 1977]. The fundamental goal is to relate lapse time coda durations t to Wood-Anderson magnitudes.

Obtaining the "best" fit involves a number of competing criteria, and the first problem is choosing an appropriate

model. I tested several classes of models mat included parameters other than the lapse duration, attenuation and

5, specifically distance, focal depth, and azimuth. I monitored the data variance and other statistical measures

while systematically introducing the predictor variables of varying order. In the end, I concluded mat MD is ade­

quately modeled by a quadratic polynomial of log t, with the site and instrument attenuation corrections as addi­

tive constants. If the traditional coda duration, i, had been used instead of the lapse duration, t, then it would

be essential to include P-wave travel-time or some measure of distance (e.g. ray-path, hypocentral or epicentral

distance and depth) as explicit predictor variables.

MD requires a polynomial function of log t because a linear function is not adequate over the large range

of ML values. As previously described, the independent set has magnitudes in the range from 0.9 <ML < 5.6. If

MD is constrained to be linear in log t, it can adequately fit ML over a limited range, approximately

2.0 < ML < 3.5. On the other hand, if MD is constrained to be linear in log2 t, it fits ML over a larger range,

approximately 1.5 < ML < 4.0. However, by including both log2 t and log t terms, MD fits ML quite well over

the full range of magnitudes in the independent set. Table 1 summarizes the analysis of variance after regression

of several classes of models in which increasing orders of log t are introduced While all of the models yield

similar magnitudes and fit about 89-97% of the data variance, the simplest model to "adequately" accomplish the

job is desired. A few points should be noted that helped direct the final choice of model. Models of class B,

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), have smaller standard errors and fits the data better than models of class A, Af/)/\//(log t).

However, models of class C, MD ~f (log t, log2 t), fit the data better than either models of class A or B. Higher

orders of A/a^/flog* t), with n > 3, do not increase the overall fit of the data, or reduce either the data vari­

ance or the standard errors significantly. This can be seen in the class D model, which does not improve the fit

significantly over the equivalent class C model. Within each class, both the attenuation and site corrections

enhance the solutions approximately 1% and 4% respectively. Using these criteria, I adopted the following for­

mula:

MD .. = a0 + a i log ty + a 2 log2 fy + Ofy + 8; , (5)

where t,-; is the total lapse time in seconds observed at the j* station for the i* earthquake, o;-; is the instru­

ment attenuation correction and 6; is the site correction.

Weighting. The independent set does not have uniform distribution in terms of source magnitude, depth,

source-station distance, azimuth, and site geology. Nor does it have the same data distribution as the CALNET

catalog. The majority of earthquakes in the CALNET catalog have magnitudes less than 2, therefore it is impor­

tant to estimate them as well as possible without sacrificing the fit to large magnitude events. By comparison,

the independent set is relatively depleted in small magnitude earthquakes, and has observations from stations at

distances up to 4-5 times greater than are normally included in the catalog.

Considering these differences, weights are assigned to each observation in the following manner. The

weighting vector is inversely proportional to the sum of the individually assigned weights, W~^w~l (ML , tp \

Note that this is different from the standard statistical approach where weights are inversely proportional to the

variance, which is known from the whole population distribution, and the sample population has the same distri­

bution. I assigned individual weights according to the number of observations in small ranges of magnitude NM/L

and travel-time Ntp . The magnitude weight is WML = £NW^ for the magnitude range AA/L = P, +1 - P, = 0.2.P,-

This mitigates the problem that earthquakes of small magnitudes have fewer observations than larger events, and

balances the total number of earthquakes in each magnitude range. The weight assigned to the travel-time obser-

T(+ivations is done in a similar manner: wtp = £N<f in the travel-time range A//. = y.+i - Y« = 2.5 sec for

Y,-

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tp < 17.5 sec, and w, = <*> for tp > 17.5 sec. In practice, observational data at distant stations tp > 17.5 sec and

with large standard errors are excluded from the regression analysis for reasons mentioned earlier. The weights

may be augmented according to other observations if their distribution significantly biases the problem. Thus,

the weights chosen provide uniform weighting over the magnitude range 0.9 < ML < 5.6 and the P-wave travel-

time range 0.0 < tp < 17.5 sec.

Results. The final formula is the result of an iterative process whereby site corrections are calculated from

the average station misfit from an initial magnitude formula, and are then included as a constant in the regres­

sion to obtain a better fitting solution. After 3 iterations, the ratio of the fit variance to the data variance R 2 ,

converged to a stable maximum, and the variance and standard errors converged to stable minima. The constant

coefficients are: a<p-0.4259 (±0.0681), ^=0.8442 (±0.0743), 32=0.5572 (±0.0199), and

Oij = (0.025 attriij - 0.375), so that Equation (5) becomes:

MD .. = -0.43 (±0.068) + 0.84 (±0.074) log fy + 0.56 (±0.020) log2 TJ7 + o^ + S,, (6)

This relationship accounts for 97.0% of the data variance, compared to 93.4% claimed by Lee et al. [1977] and

91.5% by Bakun [1984b].

Appendix A contains histograms of MD .. for all of the data for each earthquake to compare the mean,

median and mode as estimates of central tendency. The weighted median <MD >, and the median absolute devia­

tion MAD, are chosen as the measures of central tendency and spread, rather than the mean and standard error.

MAD is the median value of the absolute deviations between the individual estimates and the event median,

MAD = median I MD - <MD >i I [Mosteller and Tukey, 1977]. Alternatively, a more robust estimate of the

MAD may be selected. The median is chosen because it is not as sensitive as the mean to individual outliers. By

inspection of the MD histograms, there is not much difference between the measures of central tendency. How­

ever, for earthquakes with few or a skewed distribution of observations, the median is closer to an intuitive esti­

mate of the desired central tendency than the mean. The MAD also gives a better estimate of spread or uncer­

tainty under these circumstances than the standard deviation or confidence limits. Also, the median and MAD

are easily determined. Figure 4 is a plot of <MD > ± MAD including all of the observations, versus ML ±95%

confidence limits from Bakun [1984a]. All of the MD estimates are within the error MAD of the ML estimates.

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Table 2 lists the magnitude estimates where Equation (6) is applied to all of the observations with (a)

tP < 17.5 sec, and (b) all f/>. The modal value is also an acceptable measure of central tendency, but the max­

imum of a continuous function representing the distribution, or the maximum likelihood, must be found first, and

while this is simple, it is cumbersome to calculate for large numbers of earthquakes. The three measures of cen­

tral tendency yield consistent estimates when there are numerous observations per event. The estimates are also

consistent when including stations from the entire range of tP even though Equation (6) was based on stations in

a limited range of ?/>. Only in 2 cases do the magnitude estimates based on tP < 17.5 sec and all ?/> differ by

more than 0.05, and for these 2 instances, the difference is 0.08 MD . For virtually all but one, the difference is

less than the error estimated by the MAD . Thus, it is reasonable to suggest that including all tp in the median

does not bias the estimate of MD .

MAGNITUDE MISFIT.

The distribution of error in estimating MD is another indication of how well the relationship fits the data.

The magnitude misfit, e,;, is defined as the difference between the magnitude calculated from a single station

and the true magnitude. I estimate the misfit as the deviation from the median, £^ = MD .. - <MD >i. In Figure 5,

the misfit is plotted against the following parameters: log 1, observed P-wave travel-time, epicentral distance,

and azimuth. The data included in these plots are not restricted in range of tp . As can be seen in Figure 5, about

90-95% of the data are within 1/4 of a magnitude unit of the median represented by t = 0.0. In Figure 5(a), t is

plotted versus log t. Most of the data lie in the range log t = 1.25-2.60. The scatter is fairly uniform, although

slightly less at log t = 1.75-2.25. In general, the misfit is uncorrelated over the range of 10 < t < 550 seconds.

In Figure 5(b), t is plotted versus P-wave travel-time, tp . While only data with r/> < 17.5 sec were used for the

regression, the data from stations beyond this radius are fit equally well. The scatter actually decreases for

tP > 25.0 sec, although this may be attributed in part to the fewer data beyond this radius. Likewise, the scatter

of t decreases with increasing epicentral distance beyond about 150 km, as shown in Figure 5(c). Thus, I con­

clude that Equation (6) may be extrapolated to t over the full range of f/> without systematically biasing the

magnitude. In Figure 5(d), t is plotted versus the azimuth from the epicenter to the station location. The cluster­

ing of data in the NW and SE directions reflects the distribution of stations in northern California and events in

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the independent set. In addition, by inspection of Figure 4, neither the MAD nor the deviation of the median

from ML arc related to increasing ML . The difference between <MD > and ML are plotted versus depth in Figure

6. While there are not enough earthquakes in the independent set to infer anything about a depth dependence,

there is a hint of a pattern. The difference tends to be slightly negative at depths of 7-10.5 km and at 12-15 km,

indicating that MD slightly underestimates ML in these depth ranges. At depths shallower than 7 km, the coda

magnitudes are slightly greater than ML . In summary, the data misfit is small and uncorrelated as a function of

log t, observed P-wave travel-time, epicentral distance, source-receiver azimuth and ML . The misfit is uniformly

distributed, and does not appear to be attributable to systematic biases in the data, the choice of weighting in the

regression analysis, or by the formula for MD given in Equation (6). There appears to be a weak correlation with

depth, but this may be related to the material properties in the upper crust as a function of depth.

SITE CORRECTIONS.

The site correction, 8, is the mean of the difference between the event magnitude and individual station

estimates:

where K is the number of events station j has observed. Site corrections for stations outside the P-wave travel-

time radius of 17.5 seconds were assigned the negative of the mean magnitude misfit, -eiy -»5y . These site

corrections are preliminary and are denoted by asterisks in Table 3. Similarly, additional site corrections may be

assigned on a tentative basis to this list as stations are added in future applications. There are observations at

156 stations within the tp < 17.5 sec. Ten of the 156 stations arc represented by fewer than 5 earthquakes. In the

entire independent set, there are observations at 214 stations, with 34 of them recording fewer than 5 earth­

quakes.

As the seismograph characteristics are not incorporated in the site corrections, it may be possible to infer

geological and geophysical relationships from the spatial and temporal patterns apparent in the site corrections.

The magnitude misfit £;y and the site corrections 8y are plotted versus the average of the attenuation settings per

station in Figure 7. Negative and positive corrections represent sites that typically over- and underestimate

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earthquake magnitudes respectively. Site corrections are shown in map view in Figure 8. Open symbols

represent sites that typically overestimate the average magnitude of earthquakes and have negative 8. Solid sym­

bols represent sites with positive 8 that typically underestimate the magnitude of earthquakes.

The site correction is spatially correlated with local geology. Sites that are located on hard rock sites (e.g.

granites, ultramafics, metamorphosed Mesozoic sediments) and fast P-wave crustal velocities, tend to underesti­

mate MD and have positive 5. Sites located on Cenozoic volcanics and unmetamorphosed Mesozoic sediments

do not have clear affinities. I adopted the geologic code of Evernden, Kohler and Clow [1981], in an attempt to

quantify the correlation between the site correction and local geology. Evemden, Kohler and Clow [1981] divide

the surficial geology in California into 10 geologic units. Granitic and metamorphic rocks are represented as (A).

Paleozoic to Quaternary age sedimentary rocks are represented by (B) through (F) and (J). Tertiary and Quater­

nary volcanic rocks are (H) and (I) respectively. I denote rocks of unknown type by the letter (U). The site

corrections are plotted against the code for the mapped surficial geology in Figure 9 (top). Granitic and

metamorphic rocks typically have positive corrections, 8 = 0.15±0.30. Early Mesozoic sediments have

8 = 0.00±0.35. Early Tertiary sediments have S = 0.20±0.20. Oligocene-Pliocene sediments have S = 0.05±0.50.

Quaternary sediments have a large range of values, roughly 8 = 0.00±0.75. Tertiary and Quaternary volcanic

rocks tend to have negative values, 8 = -0.2QtO.45 and 1> = -0.3Q±0.40. The older Paleozoic and early Mesozoic

sediments (B) and (C), tend to overestimate MD compared to the younger early Tertiary through Pliocene sedi­

ments (E) and (F), while the youngest Quaternary sediments (J), have the greatest range of values. Conversely,

the older Tertiary volcanics (H) tend to underestimate MD compared to the younger Quaternary volcanics (I),

although their range of values overlap quite a bit A correlation of 8 with age of the rocks might be inferred, but

the relation is weak, and is opposite in sediments and volcanic rocks.

The site correction is spatially correlated with rock density in the upper crust. In Figure 9 (bottom), the

site correction is plotted versus the isostatic gravity field interpolated for that location, obtained from Jachens

and Griscom [1985]. Stations over sites with relatively low gravity anomalies tend to overestimate earthquake

magnitudes, while sites with relatively high gravity anomalies tend to underestimate MD . This suggests that

rocks of low density material tend to ring longer than the high density rocks when excited by seismic frequen-

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cies.

TEST SET.

The coda magnitude relationship may be further evaluated by applying the formula to a different set of

data in which the local magnitudes are known a priori. I used 50 of Bakun's [1984a,b] earthquakes not already

included in the independent set for which ML has already been established, and applied Equation (6) and the site

corrections from Table 3 to the duration measurements available from the CALNET catalog. Hereafter these

events are referred to as the test set. To obtain the lapse time duration t, I simply added the observed P-wave

travel-time tPt to the catalog of CALNET coda durations i, such that the new lapse durations are the linear

combination t = T + tp . The magnitudes for the test set are listed in Table 4, and in Figure 10, <MD > is plotted

against ML . The magnitude relationship represented by Equation (6) accounts for about 90-95% of the data vari­

ance in the test set, with the MAD generally less than 0.15 MD .

The test set may also be used to evaluate how the distribution of the duration readings in the CALNET

data base influences the magnitude estimates during the period from mid-1977 to 1981. It is important to note

that the lapse time coda durations for the test set of earthquakes were obtained directly from the readings of the

CALNET data base, relying on the routine processing of these earthquakes done by the U.S.G.S. staff. No

attempt was made to expand the number of data available or to evaluate individual readings. The test set con­

sists of few t per event because the CALNET catalog is relatively sparse in duration measurements. There are a

total of 1016 observations of t at 144 stations included in the test events. These include all observations of tp

because of the few total number of data available. There are few data (33) in the radius between tp > 17.5 sec

and tp < 25.0 sec, and none beyond. Thus, the magnitudes are not biased due to the inclusion of these data.

The magnitude misfit for the test set is plotted in Figure 11 versus (a) log t, (b) tp and (c) azimuth. I omit

the plot of the misfit versus epicentral distance because it is redundant of the plot versus P-wave travel-time. As

can be seen in Figure 11, about 90-95% of the data are within 1/4 of a magnitude unit of the median represented

by t = 0.0. As with the misfit for the independent data, the data misfit is small and uncorrelated as a function of

log t, observed P-wave travel-time, or source-receiver azimuth. The magnitudes for the test set tend to overesti-

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mate the Wood-Anderson magnitudes by approximately 0.10-0.15 MD units (see Figure 10). This is partly due to

the higher proportion of events at depths shallower than 7 km in the test set than are in the independent set.

Also, because the CALNET database tended to exclude coda durations less than 10 sec, the event magnitude

would be biased to a larger estimate, perceptible only at small magnitudes. As with the independent set, there

appears to be a weak correlation of the difference <MD > - ML with depth (Figure 11 (d), but this is probably

related to the properties in the upper crust. As observed with the independent set, earthquakes at 7-10 km depth

have MD magnitudes that tend to underestimate ML , and there are fewer of these proportionately in the test set.

In summary, the misfit of the test set is small and uniformly distributed. Equation (6) estimates the magnitude of

the test set of earthquakes almost equally as well as for the independent set despite the difference in the number

of data available for the test set There do not appear to be any systematic biases in the CALNET data base that

are unaccounted for in the weighting assigned in the regression analysis. The only exception to this is the weak

correlation with depth. Because this cannot be modeled as a smooth function, a large number of earthquakes

should be examined carefully before attempting to interpret it any further.

SUMMARY.

A new empirical coda duration magnitude relationship is presented to help establish the continuity of

earthquake magnitudes throughout the central California seismic network during the period from mid-1977

through 1981. MD is based on a quadratic polynomial function of log t (where t is the lapse time duration), a

correction for the attenuation setting of the seismograph instrument, and a site correction assumed to be related

to the characteristic attenuation properties of the local geology. MD has been modeled against Wood-Anderson

and synthetic local magnitudes, so that any discontinuities or systematic biases in the ML scale will be incor­

porated into MD . The new formula for MD appears to work well when applied to the CALNET data base,

despite the relatively few number of coda duration measurements in the catalog per earthquake. Considering the

limited number of durations in the CALNET data base, a large number of events should be examined to deter­

mine whether there are more complex spatial (or temporal) patterns than briefly mentioned in this study. How­

ever, extrapolation of MD to other stations and earthquakes outside these 5 source regions should be approached

cautiously.

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REFERENCES.

Aki, KM and B. Chouet, Origin of coda waves: source, attenuation and scattering effects, J. Geophys. Res. 80,

3322-3342, 1975.

Bakun, W. H., Seismic moments, local magnitudes and coda-duration magnitudes for earthquakes in central Cal­

ifornia, Bull. Seismol. Soc. Am. 74, no. 2, 439-458, 1984.

Bakun, W. H., Magnitudes and moments of duration, Bull. Seismol. Soc. Am. 74, no. 6, 2335-2356, 1984.

Draper, N. and H. Smith, Applied regression analysis, 2nd edition, John Wiley and Sons, 709pp., 1981.

Eaton, J. P., Content and structure of the CALNET location history file, LOCHST, and the CALNET mainte­

nance history file, MNHST, U.S.G.S. Administrative Report, 15pp., 1986.

Eaton, J. P., Noise analysis of the seismic system employed in the northern and southern California seismic nets,

Open-file Report 84-657, 23pp., 1984.

Evernden, J. F., W. M. Kolher, and G. D. Clow, Seismic intensities of earthquakes of conterminous United

States - Their prediction and interpretation, Geol. Surv. Prof. Paper 1223, 56pp., 1981.

Jachens, R. C, and A. Griscom, An isostatic residual gravity anomaly map of California - A residual map for

interpretation of anomalies from intracrustal sources, in Hinze, W. J., ed., The utility of regional gravity and

magnetic anomaly maps, Soc. of Explor. Geophys., Tulsa Oklahoma, 347-360, 1985.

Johnson, C. E., I. CEDAR - An approach to the computer automation of short-period local seismic networks, II.

Seismotectonics of the Imperial Valley of southern California, Ph.D. Dissertation California Institute of

Technology, 332pp., 1979.

Lee, W. H. K., R. E. Bennett and K. L. Meagher, A method of estimating magnitude of local earthquakes from

signal duration, Open-file Report, 28pp., 1972.

Mosteller, F. and J. W. Tukey, Data analysis and regression, Addison-Wesley, 588pp., 1977.

Richter, C. F., An instrumental earthquake magnitude scale, Bull. Seismol. Soc. Am. 25, 1-32, 1935.

-15-

ACKNOWLEDGEMENTS.

I would like to express my appreciation to Bill Bakun for his support and critical comments throughout

this project. Choosing the best fitting model requires intimate knowledge of the network operations in CALNET,

detection thresholds, and a thorough familiarity with the seismicity distribution in space and time. Because of

the massive volume of data and the complexity of the problem, I relied on the considerable knowledge of Kei

Aki, Bill Bakun, Jerry Eaton, Bill Ellsworth, Fred Klein, Rick Lester, Al Lindh, Shirley Marks, and Dave

Oppenheimer. Bob Simpson provided the gravity data and geologic codes used in the figures.

-16-

TABLES.

Table 1. Analysis of variance. The standard error of the residuals, SE; the data variance, £(res)2; the ratio of

the fit variance to the data variance, /? 2; improvement over a model with no variables, F-test; and the number of

degrees of freedom, NDF [Draper and Smith, 1981; Mosteller and Tukey, 1977] are reported for each model.

Table 2. Magnitude estimates for earthquakes in the independent set. Refer to Tables 1-5 in Bakun [1984] for

the source parameters. Regions (1) Parkfield, (2) San Juan Bautista, (3) Sargeant Fault, (4) Coyote Lake, and (5)

Livermore are the same as in Figure 4.

Table 3. Site corrections. An asterisk indicates that the estimate for this station comes from earthquakes at dis­

tances greater than the P-wave travel-time of tp > 17.5 sec. Stations denoted with asterisks or those with fewer

than 5 observations are suspect, and should be used with caution. A standard error listed as a question mark

indicates that the quantity is undefined because this station is represented by only 1 observation.

Table 4. Magnitude estimates for earthquakes in the test set Refer to Tables 1-5 in Bakun [1984] for the

source parameters. Regions are the same as in Table 2.

-17-

FIGURE CAPTIONS.

Figure 1. Epicenters and CALNET stations used in this study. The earthquakes occured between mid-1977

through 1981. The independent set of earthquakes are denoted by squares, the test set are denoted by circles, and

stations are noted as triangles. Wood-Anderson magnitudes are taken from Bakun [1984a]. The insert shows the

depth distribution in each of the 5 source regions.

Figure 2. Log 1 versus observed P-wave travel-time measured for the independent set of earthquakes. The solid

curve represents the minimum 1 = ts criteria, where t$ is the expected S-wave travel-time. The symbol type

indicates the source region (1) circle = Parkfield, (2) triangle = San Juan Bautista, (3) cross = Sargeant Fault, (4)

X = Coyote Lake, and (5) diamond = Livermore, and are adopted in subsequent figures.

Figure 3. Signal amplitude as a function of time, in linear (top) and log space (bottom). Decreasing the instru­

ment attenuation of the seismograph by 6 dB increases the signal amplitude by a factor of 2. The associated

A IOK A difference in duration of the signal is obtained through the relationship A log t^ 6 .q

Figure 4. <MD > versus Wood-Anderson and synthetic local magnitude ML for the 55 earthquakes in the

independent set. Vertical and horizontal bars represent the median absolute deviation MAD, and the 95%

confidence limits of <MD > and ML respectively. <MD > for the 5 earthquakes with ML < 1.5 slightly overesti­

mate ML , but the differences <MD >- ML are well within the error estimate, MAD.

Figure 5. Magnitude misfit £v = MD .. - <MD >; versus (a) log Tv , (b) P-wave travel-time */>.., (c) distance Ay,

and (d) azimuth. Symbol types are the same as in Figure 4. Large (small) symbols represent data that are within

(exceed) ± MAD of that individual event

Figure 6. Magnitude misfit per event <MD >f - ML . versus source depth. Symbols are the same as Figure 4.

-18-

Figure 7. Top: Magnitude misfit £iy versus the instrument attenuation setting attriij at the time of the I th earth­

quake and at the j* station. Bottom: Site correction 8; versus the average of the attenuation settings at the j*

station. (For example, if station XXX was set at 6 dB through 1980 and recorded 4 earthquakes in this time, but

was then changed to 12 dB and recorded 2 earthquakes since 1981, then the average attenuation setting of sta­

tion XXX for these 6 earthquakes is 8 dB.) Negative and positive corrections indicate sites that typically overes­

timate and underestimate earthquake magnitudes respectively.

Figure 8. Site corrections 6, in map view. Negative corrections (open symbols) represent sites that typically

overestimate earthquake magnitudes. Positive corrections (filled symbols) represent sites that typically underesti­

mate earthquake magnitudes. The symbol size is proportional to the absolute value of the station correction, the

larger symbols have greater corrections. Stations with standard errors less than 0.25 or that recorded more than 5

events are denoted as squares, all others are denoted as circles.

Figure 9. Top: Site corrections ^ versus geologic code of Evernden, et. al [1981]. A = granitic and

metamorphic rocks; B = Paleozoic sediments; C = Early Mesozoic sediments; D = Cretaceous-Eocene sediments;

E = Early Tertiary sediments; F = Oligocene-Pliocene sediments; J = Quaternary sediments; H = Tertiary vol-

canics; I = Quaternary volcanics; U - rocks of unknown affinities. Bottom: Site corrections 8, versus the isos-

tatic residual gravity field in milligalls taken from Jachens and Griscom [1985]. Symbols refer to the geologic

code in the top diagram.

Figure 10. <MD > versus Wood-Anderson and synthetic local magnitude ML for the test set. Symbols are the

same as Figure 4.

Figure 11. Magnitude misfit 6,, = MD .. - <M/>>, for the test set versus (a) log 1,-,, (b) P-wave travel-time tp ..,

(c) azimuth and (d) depth. Symbols are the same as in Figure 4.

Appendix A. Frequency of magnitude estimates MD for each earthquake in the independent set. ML ±95%

confidence intervals obtained from Bakun [1984b] are plotted as inverted arrows and horizontal bars at the top

-19-

of each histogram. Beneath ML are plotted the 3 measures of central tendency and error of MD calculated in this

study: the mode, the median <MD > ± MAD, and the mean MD ± 95% confidence intervals. The number of

duration measurements, N, are also listed. The event numbers (same as in Table 2) are printed in the upper right

comer of each diagram. The width of the MD window is 0.2 if N is less than 30, otherwise 0.1 is set as the

width of the window. The + symbols represents a weighted 3-point running average of the frequency distribution

of MD estimates used to estimate the mode.

Appendix B. Frequency of magnitude estimates MD for each earthquake in the test set The event numbers

correspond to those in Table 4. See Appendix A for explanation of the diagrams.

-20-

Table 1. Analysis of variance. The standard error of the residuals, SE; the data variance, £(res)2; the ratio of the fit variance to the data variance, R 2; improvement over a model with no variables, F-test; and the number of degrees of freedom, NDF [Draper and Smith, 1981; Mosteller and Tukey, 1977] are reported for each model.

CLASS MOTEL

1

2

A3

4

5

6

B7

8

9

10

c11

1 fr 12

T) u

VARIABLES

LOG* TAU , n - 123

/

y

'

/

'

'

/ *

s /

' *, s *

*

// /

v//

/

"

ANALYSIS OF VARIANCE

SE R1 S1023 F-TEST NDF

.01403 0.8935 0.6098 2.5989 3097

.01322 0.9036 0.5415 2.9023 3097

.01030 0.9426 0.3285 2.5441 3096

.008293 0.9621 0.2129 3.9285 3096

.01341 0.9028 0.5567 2.8766 3097

.01253 0.9134 0.4866 3.2651 3097

.009728 0.9488 0.2930 2.8713 3096

.007560 0.9685 0.1769 4.7587 3096

.01338 0.9032 0.5546 1.4437 3096

.01252 0.9137 0.4849 1.6383 3096

.009608 0.9501 0.2857 1.9647 3095

.007408 0.9698 0.1699 3.3081 3095

.007409 0.9698 0.1698 2.4807 3094

-21-

Table 2. Magnitude estimates for earthquakes in the independent set. Refer to Tables 1-5 in Bakun [1984] for the source parameters. Regions (1) Parkfield, (2) San Juan Bautista, (3) Sargeant Fault, (4) Coyote Lake, and (5) Livermore are the same as in Figure 4.

IV

1234567e9

10111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455

D&TZ770621770622770623700921790111790218790807790807790807790807790807790809790810790819790819790914791004791004791114791203800125800125800125800125800125800127800413800413800413800413800413800419800421800428800510800519800612800613800618810117810127810325810411810523810523810527810528810530810530810603810603810606810606810612811120

0243161419360318195701380155023205250556073112490025020604420104180118050613210503140521052405290629023306150620151821512308124519351821223003030927095604520009221016582347002616221526001314221817145115040731154100160653

RXG555333

3113155555522222212211321255223555333323

fOBS7113567462836982488372788356468217157515616973656980737367676271106967293472683263624666376939

38696936206555

MEDXAN+-M&D4122321212233113222123432543223313232243333112111221121

.474

.600

.137

.828

.219

.706

.982

.879

.609

.903

.424

.354

.608

.807

.547

.001

.174

.185

.410

.708

.622

.278

.671

.411

.783

.565

.756

.215

.430

.764

.253

.012

.025

.291

.774

.349

.597

.660

.085

.454

.987

.023

.226

.863

.475

.108

.049

.306

.925

.495

.268

.463

.197

.221

.856

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

Ill247078087090066107069141053044075068096091064063072076095067059081070075128073072042041058060081073070097066111111094129071061138132083205239102092085109108084122

4.1.2.2.3.2.li2.1.2.2.3.3.1.1.2.2.2.2.1.2.3.4.3.2.5.4.3.2.2.3.3.1.3.2.3.2.2.4.3.4.3.3.1.1.2.1.1.1.2.2.1.1.2.1.

MULN+- 95%479 0625 0152 0841 0202 0708 0991 0888 0598 0914 0413 0344 0598 0817 0550 0996 0163 0177 0414 0684 0615 0289 0679 0405 0774 0562 0748 0214 0434 0773 0251 0020 0029 0299 0778 0375 0604 0660 0092 0441 0004 0019 0230 0866 0497 0107 0076 0284 0926 0486 0275 0479 0248 0208 0846 0

.042

.159

.032

.033

.028

.021

.031

.025

.051

.017

.017

.024

.024

.032

.043

.019

.045

.064

.020

.057

.022

.022

.033

.023

.024

.036

.028

.023

.016

.015

.018

.021

.101

.021

.023

.049

.028

.035

.042

.041

.041

.028

.026

.038

.062

.030

.613

.214

.040

.026

.029

.054

.081

.027

.046

MODE4122321212233113222123432543223313232243333112111221121

.459

.441

.118

.793

.264

.709

.965

.869

.482

.891

.428

.391

.630

.797

.534

.017

.166

.232

.404

.643

.630

.272

.675

.420

.816

.557

.759

.241

.448

.769

.250

.032

.109

.272

.753

.370

.606

.586

.068

.412

.934

.020

.236

.775

.421

.105

.000

.138

.872

.515

.308

.474

.148

.218

.838

4123322213233113222123432543223303232243323112012221121

ML+-95*.600 0.670 0.200 0.000 0.100 0.500 0.180 0.900 0.610 0.000 0.400 0.400 0.600 0.650 0.290 0.200 0.240 0.280 0.400 0.610 0.700 0.400 0.600 0.500 0.900 0.600 0.800 0.200 0.300 0.700 0.200 0.000 0.910 0.300 0.700 0.200 0.540 0.800 0.000 0.300 0.900 0.900 0.500 0.910 0.500 0.100 0.790 0.500 0.100 0.450 0.150 0.310 0.030 0.100 0.990 0

.000

.210

.090

.090

.050

.050

.100

.050

.010

.060

.040

.020

.040

.070

.070

.070

.020

.020

.110

.080

.050

.080

.100

.140

.030

.000

.000

.030

.030

.030

.030

.050

.030

.020

.050

.020

.010

.050

.040

.030

.040

.100

.080

.040

.060

.070

.080

.030

.340

.040

.060

.060

.110

.040

.050

fOBS1491375

11511012580

12948

1291041471516350

1343534

10921

10714316214311117414912792

10611213211

1191109064

10614592

10912811481408739

42989139218468

MCDIAN+-MAD4122322212233113222123432543223313232243333112111221121

506619171862235738015910660939456.387643.830.575.024.089.129.446.630.618.320.674.424.800.590.777.245.477.790.285.052.015.334.809.354.577.651.092.433.996.054.258.890.515.135.068.306.943.514.299.495.210.251.864

0.1180.1420.0540.0970.1030.0670.1240.0880.1590.0690.0480.0830.0660.1040.1030.0750.0500.0800.0740.0780.0760.0680.0960.0750.0860.1440.0860.0740.0510.0520.0610.0670.1170.0790.0680.0700.0730.1260.1330.0860.1260.0770.0720.1430.1410.0980.1860.2440.0670.0880.1110.1150.1130.0940.150

3099 ftp £ ITS 5130 tp)

22-

Table 3. Site corrections. An asterisk indicates that the estimate for this station comes from earthquakes at dis­ tances greater than the P-wave travel-time of r/> > 17.5 sec. Stations denoted with asterisks or those with fewer than 5 observations are suspect, and should be used with caution. A standard error listed as a question mark indicates that the quantity is undefined because this station is represented by only 1 observation.

STA A SK f OBS

**

******

ABRARJBAYBBSBBNBCGBEEBEMBHRBBSBJCBJOBLRBMCBMHBMSBPCBPFBPIBPPBRMBRVBSBBSCBSGBSLBSRBVLBVTCACCADCAICALCAOCBRCBWCCNCCOCCYCDOCDSCDUCDVCLCCMCCKBCMJCMMCMOCMPCMRCPLCRACRPCSCCSBCTLCVLOAFGAX<3BDGBG<SBOGCB

0.1690.0960.031-0.219-0.255-0.026-0.225-0.098-0 . 3010.0210.1570.010-0.3090.091o.iee-0.068-0.0100.1050.009-0.102-0.146-0.122-0.491-0.0060.231-0.6620.027

-0.395-0.201-0.1300.2450.1750.0790.0030.243-0.054-0.1370.0580.357-0.190-0.202-0.2090.005-0.1060.2090.2200.1040.2560.2710.2280.2930.188-0.2020.012-0.1600.239

-0 . 120-0.2450.4070.2280.240-0.0130.1830.384

??

0.0650.0400.1860.0280.0330.0450.0800.0990.0610.0650.0370.0350.0660.0440.0650.1050.0410.1450.0640.0440.0470.0390.1050.1040.0380.0490.0400.0650.0710.0560.0440.0430.0400.0790.0610.0380.0620.1000.1120.097

?0.0870.0710.0400.0490.0540.1750.0490.2230.0480.0400.0620.0700.0650.052

70.1920.0790.1820.0270.1580.1?«

11

3423223130186

333326293030313228172025152130291733323212271140461311124335231191

251341202219232833141440361416

144

1654

-23-

************************

GCHOCRGCVGCWGDCGTTGGLGGPCTCGHGCTLGEMCMCGMKGMOCTMCRNCRT6S66SMGSN6SSGMKGHRH&ZHBTHCAHCBHCOHOPHCRBCZHDLHFEHFBBITHGSHOWHJGHJSHKRHLTHMOHORBPHHPLBPRHQRHSFHSLJAX.JBCJBGJBLJBMJBZJCBJECJBGJHLJOTJLTJLXJMGJPLJPPJPRJPSJRGJRRJRXJSAJSCJSFJSG

0.0750.2340.00?0.1220.1220.1550.081

-0.143-0.1230.1780.077

-0.1380.122

-0.154

-0.0430.249

-0.1830.064

-0.3330.0630.1220.118

-0.1520.164

-0.0400.041

-0.008-0.100-0.4360.0670.131

-0.2460.0790.102

-0 . 6310.3400.2330.3130.189

-0.087-0.631-0.0040.302

-0.587-0.3240.456

-0.4030.017

-0.430-0.0640.238

-0.026-0.3070.3390.125

-0.374-0.062-0.1580.2570.218

-0.244-0.0940.2850.314

-0.283-0.2130.4290.018

-0.2580.3010.5620.1320.229

-0.053-0.102

0.070

0.5610.0680.0680.1350.2010.1530.0770.1530.2340.2650.2880.0670.1170.2030.108

?0.3230.0590.0400.1850.1380.1700.2100.0900.0380.0450.0360.0860.0670.0300.0870.0320.0590.0620.0400.0530.0420.0400.0470.0950.0530.0460.0500.0850.0620.0810.0550.0960.1520.0430.0290.0490.0370.0360.1130.0260.0520.1030.1370.0890.0720.0520.1420.0470.0380.2810.0460.1230.0710.0700.0680.0520.0390.044

1522674

1218

87

123

10775126

211111

65

3635413925204123314332322744373231322840274025353324413737374011433825

87

383415213310341316

620153637

-24-

*************

It**

It

It**

**

*

*

*It

J8JJSMJSSJSTJTGJUCJWSKBBKBNKBRKBSKCPKCTKFPKGMKM?KRKLSLMCUMRFNBPNBRMCDNCFNDBNFIHTRNGVNBBHRMNLBNLNNMHNMTNMWNMXNOLSPRMSBNSPNTMNWROGOPADPAGPANPAPPARPBRPBWPBYPCAPCGPCRPGBPHAPBCPBGPBRPIVPJLPLOPMCPMGPMPPPFPPTPRCPSAPSEPSMPITPKKWJPWKT

-0.028-0.1040.1760.196-0.2960.254-0.1370.6140.0600.056-0.2680.1880.0860.4210.3860.165-0.1070.1180.1641.0640.061-0.142-0 . 122-0.018-0 . 5020.328-0.007-0.068-0 . 012-0.391-0 . 012-0.0130.0710.209-0.058-0.1500.3270.225-0.059-0.179-0.1880.195-0.073-0.145-0.019-0.3900.0950.0740.186-0.2100.1090.1400.3290.2460.392-0.413-0.021-0.331-0.069-0.559-0.199-0.354-0.2920.042-0.161-0.2970.0180.008

-0.398-0.128-0.026-0 . 001-0.246-0.104-0.023

0.0450.0630.1150.0420.0500.0^00.060

?0.030

?7??

0.64677??

0.054?

0.2020.4180.2110.1570.1490.0750.0660.2730.0910.1190.2020.0710.0480.1090.0650.1530.3130.2070.1540.0920.0620.103

??

0.1790.1260.0560.1200.1540.0830.3040.303

?0.1650.1550.4810.1130.0850.3340.3290.0680.0760.2420.2240.0720.0750.0680.1010.0930.2250.0950.1670.158

??

39209

43

3532

2113111131111

10188956

10229

23108

102321208845

117

14115

131043

1135155344

195

183157

1359

115577611

-25-

Table 4. Magnitude estimates for earthquakes in the test set Refer to Tables 1-5 in Bakun [1984] for the source parameters. Regions are the same as in Table 2.

EV DATE61 770619 142462 770621 044464 770623 182265 780324 194266 780625 080167 780709 051869 780709 052070 781107 130071 781214 071572 790119 211573 790127 005274 790404 074975 790511 225276 790802 141677 790802 204178 790802 205279 790802 214380 790803 024281 790806 222183 790807 051284 790807 141585 790927 061486 791004 185987 791108 180688 791128 225189 791210 141191 800218 081093 800331 101694 800408 133695 800413 075096 800413 075897 800413 153998 800413 170299 800414 0049

100 800414 0155101 800414 0345102 800520 1521103 800521 1927104 800522 0440105 800523 0910106 810211 0847107 810506 0916108 810524 0344109 810529 1112110 810531 1238111 810531 1635112 810601 1544113 810614 0750114 810614 0755115 810615 1429

REG55531121322222222444421222232222222211115233552222

fOBS566

15555

256

46172445332225192531131757

24152114222317217

241816123943

444045233

1138496835

MEDIAN+-MAD1.508 0.0681.408 0.1411.638 0.0642.492 0.0661.820 0.0391.309 0.1441.212 0.0842.631 0.1021.352 0.0232.806 0.0532.729 0.0742.952 0.0762.791 0.1212.699 0.0763.527 0.0593.096 0.0794.178 0.0862.802 0.0743.457 0.0831.588 0.1152.220 0.0782.871 0.0140.877 0.0552.791 0.1002.638 0.0882.944 0.0492.745 0.1152.708 0.0582.503 0.0372.539 0.0833.492 0.0782.813 0.0732.892 0.0342.734 0.0481.944 0.0652.567 0.0890.918 0.0712.311 0.1221.327 0.1211.156 0.0803.160 0.0722.726 0.1192.202 0.0701.050 0.2811.009 0.1691.638 0.1531.631 0.1172.968 0.0702.824 0.0971.785 0.107

MEAN-1-95%1.550 0.3171.415 0.2221.689 0.1422.480 0.0781.792 0.1531.303 0.2051.155 0.2252.673 0.0601.416 0.1612.799 0.0292.696 0.0642.941 0.0522.809 0.0422.721 0.0333.537 0.0513.105 0.0394.176 0.0572.780 0.0403.470 0.0451.554 0.0922.217 0.0772.824 0.2020.990 0.1862.762 0.0602.633 0.0672.948 0.0302.728 0.0832.723 0.0342.512 0.0742.540 0.0653.494 0.0562.860 0.1302.885 0.0342.735 0.0481.962 0.0482.569 0.0760.900 0.2482.346 0.1191.418 0.5021.182 0.3013.185 0.0492.734 0.0422.175 0.0441.123 0.1591.053 0.5901.619 0.1131.677 0.0552.982 0.0302.788 0.0621.775 0.075

MODE1.5001.4001.7572.4711.8661.1591.2662.6381.3282.8392.6272.9672.9222.6703.5073.1114.1492.8093.4561.6032.2632.8690.9322.8442.6742.9352.7242.7222.4962.5123.4892.7802.9002.7081.9462.5630.8502.2001.3001.1503.1672.8342.2300.9381.0001.5821.5652.9682.8161.764

MM-95% 1.230 0.110 1.490 0.090 1.960 0.100 2.500 0.050 1.580 0.000 1.190 0.190 1.120 0.000 2.600 0.040 1.220 0.050 2.700 0.100 2.600 0.180 3.000 0.050 2.800 0.100 2.900 0.040 3.100 0.050 2.600 0.050 3.900 0.040 2.800 0.040 3.400 0.030 1.970 0.050 2.260 0.070 2.900 0.030 0.760 0.060 2.540 0.060 2.500 0.030 2.700 0.040 2.400 0.040 2.700 0.110 2.300 0.070 2.500 0.040 3.200 0.050 2.800 0.040 2.800 0.020 2.600 0.030 1.900 0.140 2.500 0.060 0.650 0.050 2.200 0.040 0.980 0.010 1.060 0.040 3.100 0.070 2.600 0.050 2.250 0.060 0.680 0.010 1.380 0.000 1.460 0.160 1.630 0.060 2.700 0.050 2.900 0.070 1.740 0.080

1016

-26-

Figure 1. Epicenters and CALNET stations used in this study. The earthquakes occured between mid-1977 through 1981. The independent set of earthquakes are denoted by squares, the test set are denoted by circles, and stations are noted as triangles. Wood-Anderson magnitudes are taken from Bakun [1984a]. The insert shows the depth distribution in each of the 5 source regions.

EPICENTERS AND STATION LOCATIONS*1° I ' ' I I I I I I I I | I ! I , I . I , | , | , t , , , | , | , | , | , | , | , , , | , | , | , | , | , | , I . I l I I I

40

REGION_ 1 2345^E.,

V >

noK CLLU

a ao dg g

° S P SrtB o * |BB ° O

8 § J

Sargent Fault

EPICENTERS

a INDEPENDENT

CALNET STATIONS

Livermore

>Coyote Lake

Parkfield

124< 123'I I i | I I I I I ! I I I I I | I 1 I T |' I I I I i I i f

122° 121° 120"

-27-

Figure 2. Log t versus observed P-wave travel-time measured for the independent set of earthquakes. The solid curve represents the minimum t = ts criteria, where ts is the expected S-wave travel-time. The symbol type indicates the source region (1) circle = Parkfield, (2) triangle = San Juan Bautista, (3) cross = Sargeant Fault, (4) X = Coyote Lake, and (5) diamond = Livermore, and are adopted in subsequent figures.

3.0-

2.5-

2. 0-

.5-

i O

- *N

30. HC.

RRVEL- T IME IS

28 -

Figure 3. Signal amplitude as a function of time, in linear (top) and log space (bottom). Decreasing the instru­ ment attenuation of the seismograph by 6 dB increases the signal amplitude by a factor of 2. The associated

difference in duration of the signal is obtained through the relationship A log t'v « .

0 sec 20

0.3

.. . Alog A Alog t = *-

og t

-29-

Figure 4. <MD > versus Wood-Anderson and synthetic local magnitude ML for the 55 earthquakes in the independent set. Vertical and horizontal bars represent the median absolute deviation MAD, and the 95% confidence limits of <MD > and ML respectively. <MD > for the 5 earthquakes with ML < 1.5 slightly overesti­ mate ML , but the differences <MD > - ML are well within the error estimate, MAD.

5.-

i.H

o. r

3.2. 3. M

WGOD-fiNDERSCN

-30-

Figure 5. Magnitude misfit t^ = MD .. - <Af/>>, versus (a) log I;;, (b) P-wave travel-time tP .., (c) distance A,;, and (d) azimuth. Symbol types are the same as in Figure 4. Large (small) symbols represent data that are within (exceed) ± MAD of that individual event

.- "' '.'-.- '«.. ". ' t t ." . '.

20. 30. 140.

tp, P-NflVE TRflVEL-TIME (SEC50. 60,

100. 200. 300.

EPICENTRPL DISTflNCE (KM)

<vt» o.o

60. 120. 130. 240.

flZIMUTH (DEC FPQM NORTH]3CC.

31 -

Figure 6. Magnitude misfit per event <M^>, - Afj, versus source depth. Symbols are the same as Figure 4.

A

O

L.C

:-o.5 J

5. 1C.

DEPTH (KM,15. 2Q

-32-

Figure 7. Top: Magnitude misfit £,; versus the instrument attenuation setting aitn^ at the time of the i* earth­ quake and at the j* station. Bottom: Site correction 5y versus the average of the attenuation settings at the jA station. (For example, if station XXX was set at 6 dB through 1980 and recorded 4 earthquakes in this time, but was then changed to 12 dB and recorded 2 earthquakes since 1981, then the average attenuation setting of sta­ tion XXX for these 6 earthquakes is 8 dB.) Negative and positive corrections indicate sites that typically overes­ timate and underestimate earthquake magnitudes respectively.

l.O-i

0.5 -

0.0

-0.5H

-1.0

12. 18.

RTTN

-33-

Figure 8. Site corrections o^ in map view. Negative corrections (open symbols) represent sites that typically overestimate earthquake magnitudes. Positive corrections (filled symbols) represent sites that typically underesti­ mate earthquake magnitudes. The symbol size is proportional to the absolute value of the station correction, the larger symbols have greater corrections. Stations with standard errors less than 0.25 or that recorded more than 5 events are denoted as squares, all others are denoted as circles.

SITE CORRECTIONS, 8;41

PLANATION

- 0 (open) and

8 > 0 (solid) sites typically over- and under- estimate

has 2o- < 0.25 and N > 5 8 has 2cr > 0.25 or N < 5

124' 123 122'

-34

Figure 9. Top: Site corrections 6, versus geologic code of Evernden, et. al [1981]. A = granitic and metamorphic rocks; B = Paleozoic sediments; C = Early Mesozoic sediments; D = Cretaceous-Eocene sediments; E = Early Tertiary sediments; F = Oligocene-Pliocene sediments; J = Quaternary1 sediments;_H = Tertiary vol- canics; I = Quaternary volcanics; U = rocKs of unknown affinities. Bottom: Site corrections 6. versus the isos- tatic residual gravity field in milligalls taken from Jachens and Griscom [1985]. Symbols refer to the geologic code in the top diagram.

GRAN.,METAM.ROCKS

U

OLDSEDIMENTS

- -YOUNGVOLCANICS

OLD-^YOUNG

B D E FGEOLOGIC CODE

H

C.

-35-

Figure 10. <MD > versus Wood-Anderson and synthetic local magnitude ML for the test set. Symbols are the same as Figure 4.

5.-

u. -

2. -

ML

-36

Figure 11. Magnitude misfit £,y = MD .. - <MD >i for the test set versus (a) log t,y , (b) P-wave travel-time tp> ., (c) azimuth and (d) depth. Symbols are the same as in Figure 4.

-i.oO.E

tp = 17.5

20. 30. 40.

t n , P-HflVE TRflVEL-TIME (SEC)50.

bo. 120. 180. 2UO.

flZIMUTH (DEC FROM NORTH)300. 35C,

i.G - d

10.

DEPTH (KM]20.

-37-

Appendix A. Frequency of magnitude estimates MD for each earthquake in the independent set ML ± 95% confidence intervals obtained^ from Bakun [1984b] are plotted as inverted arrows and horizontal bars at the top of each histogram. Beneath ML are plotted the 3 measures of central tendency and error of MD calculated in this study: the mode, the median <MD >±MAD, and the mean MD ±95% confidence intervals. The number of duration measurements, N, are also listed. The event numbers (same as in Table 2) are printed in the upper right comer of each diagram. The width of the MD window is 02 if N is less than 30, otherwise 0.1 is set as the width of the window. The + symbols represents a weighted 3-point running average of the frequency distribution of MD estimates used to estimate the mode.

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-47-

Appendix B. Frequency of magnitude estimates MD for each earthquake in the test set The event numbers correspond to those in Table 4. See Appendix A for explanation of the diagrams.

0.

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