Broadband Seismology and 

Small Regional Seismic Networks

U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1538-S

KENTUCKYf 

PS. ::».f*:«F^ kam V" r§ ,W'«. MISSOURI TENNESS

ARKANSAS
Cover. Gray, shaded-relief map of magnetic anomaly data. Map area includes parts of 

Missouri, Illinois, Indiana, Kentucky, Tennessee, and Arkansas. Illumination is from the 

west. Figure is from Geophysical setting of the Reelfoot rift and relations between rift 

structures and the New Madrid seismic zone, by Thomas G. Hildenbrand and John D. 

Hendricks (chapter E in this series).
Broadband Seismology and 

Small Regional Seismic Networks

By R.B. Hermann

INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE 

Edited by Kaye M. Shedlock and Arch C. Johnston

U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1538-S

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1995
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY 

Gordon P. Eaton, Director

For sale by U.S. Geological Survey, Information Services

Box 25286, Federal Center

Denver, CO 80225

Any use of trade, product, or firm names in this publication is for descriptive purposes only and 

does not imply endorsement by the U.S. Government

Library of Congress Cataloging-in-Publication Data

Herrmann, Robert B.

Broadband seismology and small regional seismic networks / by R.B. Herrmann.

p. cm.—(Investigations of the New Madrid seismic zone ; S) 

(U.S. Geological Survey professional paper, 1538-S)

Includes bibliographical references.

Supt.ofDocs.no.: 119.16:15388

1. Earthquakes—Missouri—New Madrid Region. 2. Seismology—Missouri— 

New Madrid Region. I. Title. II. Series. HI. Series: U.S. Geological Survey professional paper; 1538. 

QE535.2.U6I59 1995 vol. S 

551.2'2'09778985 s—dc20

[551.2'2'0978985] 95-5245

CIP
CONTENTS

Abstract........................................................................................................................... SI

Introduction..................................................................................................................... 1

Earthquake of September 26, 1990................................................................................. 2

Earthquake of May 4, 1991............................................................................................. 5

Discussion....................................................................................................................... 7

Acknowledgments........................................................................................................... 10

References Cited............................................................................................................. 10

Appendix......................................................................................................................... 12

Grid Search ............................................................................................................. 12

Single-Station Phase-Velocity Estimate ................................................................. 13

FIGURES

1. Location of the September 26, 1990, and May 4, 1991, earthquakes in the New Madrid seismic zone

in relation to seismicity from 1975-92.................................................................................................................... S2

2. Comparison of observed and synthetic time histories for the September 26, 1990, earthquake recorded

at IRIS station CCM................................................................................................................................................ 3

3. Comparison of observed traces to synthetics for different source depths in CUS Earth model for the

September 26, 1990, earthquake ............................................................................................................................. 4

4. Comparison of observed and synthetic time histories for the May 4, 1991, earthquake recorded at

IRIS station CCM.................................................................................................................................................... 6

5. Comparison of observed traces to synthetics for different source depths in CUS Earth model for the

May 4, 1991, earthquake......................................................................................................................................... 7

6. Comparison of observed and synthetic time histories for the May 4, 1991, earthquake recorded at

IRIS station CCM using the MALDEN Earth model.............................................................................................. 8

7. Comparison of observed traces to synthetics for different source depths in the MALDEN Earth model for the

May 4, 1991, earthquake......................................................................................................................................... 9

8. Surface-wave focal mechanisms in the New Madrid region superimposed on

regional-seismic-network epicenters....................................................................................................................... 10

9. Comparison of observed and CUS model synthetic time histories for the September 26, 1990,

earthquake in different filter bands to illustrate waveform modeling ability .......................................................... 11

10. Graphic example of mathematical operations used in determination of goodness-of-fit in

grid search technique............................................................................................................................................... 13

11. Demonstration of the cross-correlation technique to revise dispersion between the May 4, 1991,

earthquake and CCM station................................................................................................................................... 15

TABLES

1. Event information for earthquakes in the New Madrid seismic zone on September 26, 1990,

and May 4, 1991..................................................................^ S2

2. Parameters of layered elastic halfspace for CUS and MALDEN models used in generation of

synthetic seismograms............................................................................................................................................. 2

III

BROADBAND SEISMOLOGY AND 

SMALL REGIONAL SEISMIC NETWORKS

By R.B. Herrmann1

ABSTRACT

The New Madrid seismic zone earthquakes of September 26, 1990, and May 4, 1991, are analyzed from the 

point of view of demonstrating how broadband digital 

recordings at regional distances can be used together with 

regional-seismic-network data to define source parameters 

and Earth structure. Regional-seismic-network data provide 

excellent epicenter information, and broadband data provide seismic moment values. In addition, the broadband 

data can provide strong constraints on both the focal mechanism, when focal-sphere coverage of regional network 

data is sparse, and the source depth, when the epicenter is 

not well situated with respect to network geometry.

The September 26,1990, earthquake has a source depth 

of 15 km and a seismic moment of 3.5xl022 dyne-cm. The 

focal mechanism is primarily one of thrust faulting, with the 

pressure axes aligned roughly east-west. One nodal plane 

strikes 145° and dips 75° SW., and the other strikes 20° and 

dips 25° SE. The broadband-waveform-fit depth agrees well 

with aftershock monitoring.

The May 4, 1991, earthquake near Risco, Mo., had a 

source depth of 8 km, which was well constrained by the 

PANDA (portable array for numerical data acquisition) 

(Chiu and others, 1991) deployment. The seismic 

moment is estimated to be 1.7xl022 dyne-cm. The focal 

mechanism indicates predominantly strike-slip faulting, 

with the P-axis trending northeast-southwest. One nodal 

plane strikes 353° and dips 66° E., and the other strikes 

90° and dips 75° S.

Both focal mechanisms obtained are compatible with 

previous solutions in the seismic zone. In addition, there is 

evidence of 3 percent variation in crustal velocities over 

slightly different paths.

'Department of Earth and Atmospheric Sciences, Saint Louis University, 3507 Laclede Avenue, St. Louis, MO 63103.

INTRODUCTION

The New Madrid seismic zone includes the locations of 

three very large earthquakes (rap>7.0) that occurred during 

the winter of 1811-12. Most of the larger earthquakes 

(rap>5.2) in the Central United States since then have 

occurred in this zone (Mitchell and others, 1991). Focal 

mechanisms have been obtained for a number of the modem 

earthquakes. When combined with other crustal-stress data, 

earthquake focal mechanisms in the region are consistent 

with E.-W. or ENE.-WSW. orientations of maximum compressive stress (Zoback and Zoback, 1991; Zoback, 1992). 

Some previously inconsistent focal mechanisms were 

revised by Herrmann (in press) and are now consistent with 

this overall trend. Given this agreement, the object of 

focal-mechanism studies now is on the relation of nodal 

planes to spatial seismicity patterns and on the dependence 

of strong ground motion on the particular mechanism.

Regional seismic activity has been monitored by a variety of seismographs since the installation of the 80-kg 

Wiechert seismograph at Saint Louis University in 1909. 

Significant milestones in instrumentation were the installations of the WWSSN (World Wide Standard Seismograph 

Network) long-period instrument in the 1960's, the regional 

seismic network in 1975, the broadband digital IRIS (Incorporated Research Institutions for Seismology) station at 

CCM (Cathedral Cave, Mo.) in 1989, and the local deployment of the dense PANDA array in 1989-92 (Yang and others, in press).

The object of this paper is to derive source parameters 

for two large earthquakes that occurred in the zone during 

1990-91 and to assess how regional network data can complement broadband digital data. The two earthquakes are 

those of September 26, 1990, and May 4, 1991. The origin 

times and locations of these events are given in table 1. Figure 1 shows the location of these two events with respect to 

the regional network seismicity. In addition, the location of 

the IRIS station CCM is indicated. The May 4, 1991, earthquake is close to the dense linear patterns of seismicity near 

New Madrid, Mo., whereas the September 26, 1990, earthquake is on the periphery of the very active zone (fig. 1). The

si
S2 INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE

Table 1. Event information for earthquakes in the New Madrid seismic zone on September 26, 1990, and May 4, 1991.

[UT, Coordinated Universal Time. CUS crustal model derived from Nuttli and others (1969). MALDEN crustal model is the result of modeling Rayleigh- and Love-wave signals 

as a single-mode surface wave]

Date

09/26/90 

05/04/91

Origin time 

(UT)

13:18 

01:18

Latitude

37°09.6'N. 

36°33.6'N.

Longitude

89°34.8'W. 

89°49.8'W.

Depth 

(km)

15 

8 

8

Strike 

(degrees)

145 

90 

90

Dip 

(degrees)

75 

75 

75

Rake 

(degrees)

70 

20 

25

Moment 

(dyne-cm)

3.5xl022 

2.0xl022 

1.7xl022

Model

CUS 

CUS 

MALDEN

Table 2. Parameters of layered elastic halfspace for CUS and MALDEN models used in generation 

of synthetic seismograms.

[H, layer thickness; VP, P-wave velocity; Vs. S-wave velocity; p, density; Qp~\ inverse P-wave quality factor; 2s"1 . inverse 

S-wave quality factor]

H VP VS 

(km) (km/s) (km/s)

P Qp'1

(g/cm3)

&-'

CUS crustal model

1.00 5.0 2.89 

9.00 6.1 3.52 

10.00 6.4 3.70 

20.00 6.7 3.87 

8.15 4.70

2.5 0.005 

2.7 0.0005 

2.9 0.0005 

3.0 0.0005 

3.4 0.0005

0.01 

0.001 

0.001 

0.001 

0.001

MALDEN crustal model

1.00 4.89 2.83 

9.00 5.98 3.44 

10.00 6.21 3.59 

10.00 6.44 3.72 

10.00 6.47 3.74 

20.00 7.97 4.60 

8.05 4.65

seismograph-station distribution of the regional network 

roughly parallels the density of the seismicity.

EARTHQUAKE OF 

SEPTEMBER 26, 1990

This earthquake is interesting for a number of reasons. 

First, its location is along a diffuse northwest seismicity 

trend to the north of the strong linear seismicity trends of the 

central portion of the New Madrid seismic zone (fig. 1). In 

addition, the m^=4.5 earthquake occurred at the edge of the 

regional seismic network, 31 km away from the nearest seismograph station. Thus, depth control is poor because it 

depends on sensitivity to first-arrival-cross-over distances of 

the particular crustal model used rather than to the curvature 

of the travel-time curve and good S-P arrival-time differences at short distances. Finally, because of the lack of seismograph stations directly above the source, the focal-sphere 

coverage of P-wave first-motion data is not sufficient to 

completely define the nodal planes of the focal mechanism.

The broadband signal at CCM, a distance of 175 km 

at an azimuth of 305°, was passed through a WWSSN

2.5 0.005 

2.7 0.0005 

2.8 0.0005 

2.8 0.0005 

2.8 0.0005 

3.3 0.0005 

3.3 0.0005

92° 91°

*» n ::. ...

I \J>

o o 

o c

38 ° - ° £i

a0TM 0% 

MO 0

o °

o f ° _ fK _ O 3 1 u 0 ,

3 6 <3Hto> A oif O °9^ r\Kl\

O o

° cf *

O . 35" m 1 m m

0.01 

0.001 

0.001 

0.001 

0.001 

0.001 

0.001

90° 89° 88° 87°

^r>' so ' o!J °(

J o o ° o * 2 IN° 

>/ o°° /o ILL o°° o/o

**•? *»*•*» *00 7 ^o0 , B^\« 1°®°°° p^>v

^JL} 0 ° \

ji o"S|^9iyj> _ 0 ,-^ o 

F° o ° °j!<jfcp"X"^ KY °

mSBrSB^ r~" °~~ >3r^

H^BK*^^ o TENN Far • ' ••

ef o ° 

J\ 1 I

Figure 1. Location of the September 26, 1990, (092690), and 

May 4, 1991, (050491), earthquakes in the New Madrid seismic 

zone in relation to the seismicity contained in the 

regional-seismic-network catalog from 1975-92. The location of 

IRIS station CCM is indicated.
BROADBAND SEISMOLOGY AND SMALL REGIONAL SEISMIC NETWORKS S3

R

3.354X10' 04

Rayleigh

9.288X10' 04

10 SECONDS 

I

Figure 2. Comparison of observed and synthetic (upper and lower traces, respectively, for each component) time histories for the 

September 26, 1990, earthquake recorded at IRIS station CCM. 

Both sets are filtered using a 15-100 WWSSN LP instrument response with a peak gain of 1. Peak amplitudes have units of centimeters. A total of 50 s of displacement time history is displayed, 

starting 20 s after the event origin time. Each pair of observed and 

synthetic traces is plotted using the same linear scale to emphasize 

similarity of modeled phases. The source parameters used in

15-100 instrument response with a peak gain of 1.0 to 

make equivalent seismograms. These observed three-component seismograms are shown as the upper traces in each 

part of figure 2. Shown in the upper-right-hand corner of 

figure 2 are the observed P-wave first-motion data for the 

earthquake plotted in a lower-hemisphere equal-area projection. As can be seen, a number of focal mechanisms can 

be placed through these observations, depending on the 

number of inconsistencies permitted.

To use the broadband signal to constrain the focal 

mechanism, synthetic seismograms were generated using

making the synthetics are given in table 1 for this earthquake. The 

lower-hemisphere equal-area projections to the right show the observed P-wave first-motion data from the main event (upper) and 

the main and aftershock first-motion data (lower). The mechanism 

plotted is that required by the waveform fit. A circle or plus sign indicates a compression, and a triangle or minus sign indicates a dilatation. Positive Z, R, and T component values represent motion up, 

away from the source, and in a direction clockwise around the 

source.

the CUS model of table 2. This model is derived from the 

simple crustal model given by Nuttli and others (1969) and 

used for synthetic seismogram modeling (Herrmann, 

1979a) and focal mechanism determination from surface 

waves (Herrmann, 1979b). The model does a reasonable 

job in explaining surface-wave group velocity dispersion in 

the 5- to 50-s period range in the Midcontinent. Wavenumber integration code was used to generate synthetic seismograms. Rather than attempt a true waveform inversion for 

source parameters and structure, synthetic seismograms 

were generated for a suite of strike, dip, and rake values for
S4 INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE

4.12X10'04

DEPTH

05

10

11

12

13

4.33x10'04

15

16

17

18

19

20

R

OBSERVED TRACES 

2.00X10'04 . 1.01x10-°i

SYNTHETIC TRACES 

3.20X10'04 H 7.93X10'04

1.04x10'03

8.36X10'04

9.53X10'04

9.24X10'04

9.82x10'04

9.28X10'04

9.41X10'04

1.06X10' 03

9.95X10'04

9.81X10'04

9.86X10'04

RB

0.520

0.730

0.752

0.768

0.777

0.773

0.777

0.774

0.772

0.758

0.743

0.703

FOCAL 

MECHANISM

9

Figure 3. Comparison of observed and synthetic 

seismogram time histories for different source depths 

(shown in kilometers) in CUS Earth model for the September 26, 1990, earthquake. All time histories are filtered with the WWSSN LP instrument response as in 

figure 2. Observed traces are plotted in the top row. 

Other rows are the best solutions using the grid search 

method for focal depths of 5 to 20 km. The grid search 

goodness-of-fit value, RB, is given to the right of the

50 SECONDS

synthetic traces. The corresponding lower-hemisphere-projection focal mechanism, in which the compressional quadrant is shaded, for each depth is plotted 

to the right of RB values. All traces present 50 s of time 

history, starting 20 s after the origin time. Positive Z, R, 

and T component values represent motion up, away 

from the source, and in a direction clockwise around 

the source.
BROADBAND SEISMOLOGY AND SMALL REGIONAL SEISMIC NETWORKS S5

a double-couple source at different depths. The choice of the 

strike, dip, and rake angles was initially based on visual 

examination of P-wave first-motion data in figure 2.

A visual goodness-of-fit criteria is based on several 

observations of the observed signals. First, the P-wave 

first-motion is a dilatation. Second, the phase approximately 

5 s after P (identified as "sP" by Langston, 1994) is also a dilatation. Third, the first motion on the tangential component is 

positive. Fourth, the ratio of peak amplitudes on the Z, R, and 

T components is roughly 1,1, and 5, respectively (ignoring 

the high-frequency spike on the Z component, which depends 

on the fine detail of the velocity structure in the lower crust 

and upper mantle). Finally, the shape of the Rayleigh-wave 

pulse on the Z and R components must agree. Even though 

this qualitative set of criteria is difficult to quantify, the final 

solution is very sensitive to changes in strike, dip, and rake 

angles of 10°.

After finding a good visual fit, the grid search technique 

(described in the Appendix) is used to strictly obtain the best 

fit. In doing this, a computationally intensive grid search uses 

a restricted range of focal-mechanism parameters that were 

chosen on the basis of the initial visual search. The search grid 

included dip angles every 5° in the inclusive range of 

60°-90°, strike angles every 5° in the range 135°-180°, rake 

angles every 5° in the range 55°-110°, and source depths 

from 5-20 km in increments of 1 km.

Figure 3 shows the best fit at each source depth between 

observed and predicted time histories. The goodness-of-fit 

parameter, RB (see Appendix), is indicated to the left of the 

lower-hemisphere focal-mechanism diagram. The RB 

reaches a maximum at depths of 13 and 15 km. This sequence 

of computations highlights those features of the waveforms 

that are sensitive to depth. First, the separation between P and 

sP increases with depth on the Z and R components. Second, 

the high-frequency spike in the vertical-component synthetics 

(component Z) is depth sensitive in arrival time and must be 

due to an initial upward-propagating S wave from the source. 

Next, the width of the Rayleigh-wave pulse increases with 

depth. The 5-km depth trace in figure 3 is visually rejected 

from being the best fit to the observed time histories because 

of these observations. It is also rejected by the low RB value. 

The Earth model used is not capable of accounting for the 

high-frequency spike on the vertical component, but grid 

searches using other Earth-structure models do not yield very 

different focal mechanism and depth selections.

The accepted focal-mechanism solution for the September 26, 1990, earthquake is listed in table 1 and plotted in the 

lower right of figure 2. This solution has only seven P-wave 

first motion inconsistencies for the main shock. It is also consistent with aftershock data, indicated by the focal mechanism 

displayed at the lower right part of figure 2 (of course, this 

assumes that the aftershocks and the main event have the 

same focal mechanisms). The first-motion inconsistencies 

may be due to an imperfect Earth model, which is evidenced 

by the mismatch of the S-wave pulses on the vertical (Z)

component. The other feature of the solution is that the focal 

depth is in the 13- to 15-km range rather than at 10 or 20 km. 

This is consistent with focal depths of 10-16 km for aftershocks located using regional network data as well as readings from portable instruments deployed above the 

hypocenter (Taylor and Wuenscher, 1990).

The Langston (1994) focal mechanism for this event 

had about the same seismic moment and had one nodal plane 

striking 50° and dipping 60° SE. and the other nodal plane 

striking 153° and dipping 68° SW. The solution given in 

table 1 has one nodal plane striking 20° and dipping 25° SE. 

and the other striking 145° and dipping 75° SW. Both solutions have approximately east-west pressure axes. The Langston (1994) Earth model provides a better fit to the 

high-frequency S pulse on the Z component, but his model 

predicts an sP/P ratio on the R component that is greater than 

that observed. Although the focal mechanisms are very similar, the differences are due to the Earth model used and also 

to the complexity of the search technique used, the search 

technique of this paper being computationally more 

intensive.

EARTHQUAKE OF MAY 4,1991

This earthquake occurred near the towns of Risco and 

Maiden, Mo., and occurred well within the station distribution of the New Madrid regional seismic network and also 

within the dense PANDA deployment (Yang and others, in 

press). Because of this location relative to the two seismic 

networks, the focal depth of the event is well defined and is 

given as 6.9 km by Yang and others (in press). In addition, 

the focal mechanism is relatively well constrained.

Figure 4 presents the observed P-wave first-motion 

data, the observed seismograms, and the synthetic seismograms for CCM that fit the data well. The dip of the east-west 

nodal plane of figure 4 is not well constrained from the 

first-motion data, and can vary in dip from south to north, but 

is constrained by the waveform data. For this event, the 

distance to CCM is 209 km along an azimuth of 323°.

The grid search technique was again applied, with dip 

angles varying from 60° to 75° in increments of 5°, the strike 

varying from 70° to 110° in increments of 5°, and the rake 

angle varying from -20° to 40° in increments of 5°. Depths 

were sampled in the range of 5 to 20 km. Figure 5 shows the 

results of the grid search, plotting the synthetic time history 

for the best fitting focal mechanism at each depth. The RB 

values indicate that the best fit to the observed waveforms is 

obtained at a source depth of 8 km. Because the sP phase is 

not as prominent as in the previous example (fig. 3) because 

of focal mechanism, the major constraint on source depth is 

the pulse width of the Rayleigh-wave pulse on the Z and R 

components. Figure 5 shows the sensitivity of the synthetic 

time histories to focal depth, which is permitted to vary from 

5 to 20 km. The 8-km depth chosen for this earthquake is
S6 INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE

R

5.097X10' 04

5.281X10' 04

Rayleigh

3.163X10' 04

-A,_

3.130xlO' 04

5.197X10' 04

S.OTOxlO' 04

10 SECONDS 

I

Figure 4. Comparison of observed and synthetic (upper and lower traces, respectively, for each component) time histories for the 

May 4, 1991, earthquake recorded at IRIS station CCM. Both sets 

are filtered using a 15-100 WWSSN LP instrument response with a 

peak gain of 1. Peak amplitudes have units of centimeters. A total 

of 50 s of time history is displayed, starting 30 s after the event origin time. Each pair of traces is plotted using the same scale for comparison of individual features. The source parameters used in

seen to provide a reasonable agreement in the duration of the 

Rayleigh wave.

The selected best solution is given in table 1, and the 

corresponding synthetic traces are plotted in figure 4. Several observations can be made by comparing the traces. The 

Rayleigh and S arrivals are predicted too early by the model, 

even though the shape and amplitudes of the prominent 

arrivals are in agreement. Additionally, the shape of the Rayleigh pulse on the Z component is slightly out of phase with 

the synthetic time history.

making the synthetics are given in table 1 for this earthquake and 

the CUS structure. The lower-hemisphere equal-area projections to 

the right show the observed P-wave first-motion data from the event 

with (upper) and without (lower) the focal mechanism superimposed. Circles and triangles indicate compressional or dilatational 

P-wave first-motion, respectively. The CUS model is used. Positive 

Z, R, and T component values represent motion up, away from the 

source, and in a direction clockwise around the source.

To reconcile the problems with the Rayleigh- and 

S-wave arrival times, the arrivals were modeled as a 

single-mode surface wave, and the phase difference in the 

complex signal was used to define an improved phase-velocity dispersion between the source and receiver, and thus lead 

to a better Earth model (see Appendix). The result is the 

MALDEN model of table 2. The difference between this 

model and the CUS model is that the shear-wave velocity is 

lower throughout the entire crust by about 0.1 km/s, or about 

3 percent (Langston, 1994, also noted the need for a slower 

model but, instead of defining a new model, simply
BROADBAND SEISMOLOGY AND SMALL REGIONAL SEISMIC NETWORKS S7

R

5.10x10-° 4

DEPTH

05

06

07

08

09

10

15

20

OBSERVED TRACES

3.16X10'04

4.86X10'04

5.20x10' 04

SYNTHETIC TRACES

RB

0.830

0.854

0.864

0.871

0.870

0.860

0.746

0.589

FOCAL 

MECHANISM

Figure 5. Comparison of observed and synthetic seismogram 

time histories for different source depths in CUS Earth model for 

the May 4, 1991, earthquake. The observed traces are given in the 

top row, with the other rows giving the solution for different 

source depths (shown in kilometers). The grid search

constructed synthetics at a distance of 220 km to improve 

phase alignment). The best fitting synthetic time histories for 

the MALDEN model are shown in figure 6. Note the better 

agreement in the arrival time of the large positive amplitudes 

on the three components as well as the phase of the Rayleigh-wave pulse on the Z component. Figure 7 shows the 

results of the grid search for a limited selection of source 

depths. The best focal mechanism and corresponding

goodness-of-fit parameter (RB) and focal mechanism are also indicated. All traces start 30 s after the origin time and consist of 50-s 

segments. Positive Z, R, and T component values represent motion 

up, away from the source, and in a direction clockwise around the 

source.

seismic moment differ slightly from that obtained using the 

CUS model (table 2).

DISCUSSION

The focal mechanisms obtained here are similar to 

those found in Langston (1994) but differ somewhat because
S8 INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE

R

5.097X10' 04

5.130X10' 04

3.422X10' 04

5.197X10' 04

Rayleigh

4.734xlO' 04

10 SECONDS 

I

Figure 6. Comparison of observed and synthetic (upper and lower 

traces, respectively, for each component) time histories for the May 

4,1991, earthquake recorded at IRIS station CCM. Both sets are filtered using a 15-100 WWSSN LP instrument response with a peak 

gain of 1. Peak amplitudes have units of centimeters. The source parameters used in making the synthetics are given in table 1 for this

earthquake and the M ALDEN structure derived from these observed 

waveforms. The first-motion information is described in figure 4. The 

MALDEN model is used. Note the better agreement in arrival time 

and phase of the surface waves compared with that shown in figure 

4. Positive Z, R, and T component values represent motion up, away 

from the source, and in a direction clockwise around the source.

of the nature of his shear-wave velocities in the lower crust. 

This study was not a direct attempt at waveform linear inversion, but rather it is an initial study to understand the salient 

features of the waveform to be fit. A numerical 

goodness-of-fit procedure was implemented in order to 

quantify a good fit. Regional-seismic-network data were 

necessary to provide a first-order constraint on focal mechanisms through P-wave first-motion data and through depth 

estimates. Even though the waveforms themselves are capable of defining depth, an initial estimate of values is required 

to generate the Green's functions used for constructing 

synthetic seismograms.

To see how these focal mechanisms agree with other 

solutions in the region, they are plotted together with seismicity in figure 8. The other focal mechanisms, including 

corrected mechanisms for the July 21,1967, earthquake at 

the upper left corner of the figure, and the March 3, 1963, 

earthquake just west of the May 4, 1991, earthquake are 

taken from Herrmann (1979b, in press). The May 4,1991, 

earthquake lies on an east-west seismicity trend, and, on 

the basis of this, the east-west-striking nodal plane can be 

assumed to be the fault plane. The September 26, 1990, 

earthquake is plotted at the top center of the figure. It is 

associated with a diffuse pattern of seismicity. However,
BROADBAND SEISMOLOGY AND SMALL REGIONAL SEISMIC NETWORKS S9

5.10X10'04

DEPTH

05

08

10

15

20

5.32X10' 04

R

OBSERVED TRACES

3.16x10' 04

SYNTHETIC TRACES

5.20X10'04

4.75X10' 04

4.73x10-° 4

4.82X10' 04

4.99X10' 04

6.00x10-° 4

RB

0.838

0.867

0.850

0.723

0.582

FOCAL 

MECHANISM

50 SECONDS

Figure 7. Comparison of observed traces to synthetics for different source depths in the MALDEN Earth model for the May 4, 1991, 

earthquake. The presentation is identical to that of figure 5.

the east-west-trending P-axis is consistent with the other 

mechanisms in the area and also with compressive stress patterns in the Midcontinent (Zoback and Zoback, 1991; 

Zoback, 1992).

An interesting feature of the study is the sensitivity of 

the long-period portion of broadband data to Earth structure. 

The CUS model was adequate for describing most features 

of the observed waveform of the September 26, 1990, earthquake. However, it was not able to describe the high-frequency arrival following S on the R component and the 

large-amplitude S pulse on the Z component. To illustrate 

this, figure 9 compares the observed and synthesized ground 

velocities after being low-pass-filtered with different corner 

frequencies. The source parameters of table 1 were used 

together with the CUS Earth model. As higher frequencies 

are introduced by increasing the filter corner frequency, the 

agreement between the observed and synthetic waveforms 

decreases in terms of shape, frequency content, and peak 

amplitude. This is not unexpected because the Earth model 

used is a very simple, plane-layered structure. Preliminary 

attempts at waveform inversion for velocity structure

indicates that changes are required in both the entire crust 

and in the upper mantle to better explain the high-frequency 

character of the waveforms.

The problem of an appropriate velocity model is interesting. This paper has shown evidence that the Earth models required to fit waveforms recorded at the same 

seismograph station from two earthquakes, separated by 

only 70 km, must vary by 2-4 percent in velocity (comparison of CUS and MALDEN models in table 2). This difference in structure along two neighboring paths is not 

unexpected, given that the May 4, 1991, earthquake 

occurred near the edge of the Reelfoot graben and intrusive 

plutons (Hildenbrand and others, 1992). In the future, data 

from additional stations will make it possible to determine 

whether this velocity change is uniform over the entire path 

or if it is spatially variable. Information on the lateral variation of the crustal-velocity model may provide crucial 

information to explain the occurrence of earthquakes in the 

region. Finally, the difference in high-frequency-waveform 

detail indicates the need to refine the models in order to 

improve predictions of high-frequency ground motion for 

hazard mitigation.
S10 INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE

ACKNOWLEDGMENTS

This research was sponsored in part by the U.S. Geological Survey under grants 14-08-0001-G2138 and 

14-08-0001-G2142 and by Phillips Laboratory, Hanscom 

AFB under contract F19628-90-K-0040. This paper benefited from the suggestions of H. Kanamori, K. Shedlock, and 

an anonymous reviewer.

REFERENCES CITED

Chiu, J.M., Steiner, G., Smalley, R., Jr., and Johnston, A.C., 1991, 

PANDA: A simple, portable seismic array for local- to regional-scale seismic experiments: Bulletin of the Seismological 

Society of America, v. 81, no. 3, p. 1000-1014.

Herrmann, R.B., 1979a, SH-wave generation by dislocation sources—A numerical study: Bulletin of the Seismological Society 

of America, v. 69, no. 1, p. 1-15.

————1979b, Surface wave focal mechanisms for eastern North 

American earthquakes with tectonic implications: Journal of 

Geophysical Research, v. 84, no. B7, p. 3543-3552. 

-in press, Broadband modeling of regional seismic events:

37°30

90°30' 9CT00 1

89°30' 89°00'

Bulletin of the Seismological Society of America, v. 85.

Hildenbrand, T.G., Rosenbaum, J.G., and Reynolds, R.L., 1992, 

High-resolution aeromagnetic study of the New Madrid seismic zone: A preliminary report: Seismological Research Letters, v. 63, no. 3, p. 209-232.

Jenkins, G.M., and Watts, D.G., 1968, Spectral Analysis and its 

Applications: San Francisco, Holden-Day, 525 p.

Langston, C.A., 1994, An integrated study of crustal structure and 

regional wave propagation for southeastern Missouri: Bulletin 

of the Seismological Society of America, v. 84, no. 1, p. 

105-118.

Mitchell, B.J., Nuttli, O.W., Herrmann, R.B., and Stauder, W., 

1991, Seismotectonics of the Central United States, in Slemmons, D.B., Engdahl, E.R., Zoback, M.D., and Blackwell, 

D.D., eds., Neotectonics of North America: Boulder, Colo., 

Geological Society of America, p. 245-260.

Nuttli, O.W., Stauder, W., and Kisslinger, C., 1969, Travel time 

tables for earthquakes in the Central United States: Earthquake 

Notes, v. 40, no. 4, p. 19-28.

Shumway, R.H., 1988, Applied Statistical Time Series Analysis: 

Englewood Cliffs, N.J., Prentice-Hall, 379 p.

Taylor, K.B., and Wuenscher, M.E., 1990, Special investigations 

of seismic activity: The Ripley, Tenn. earthquake of 29 Aug. 

1990 and the New Hamburg, Missouri earthquake of 26 Sept. 

1990, in Central Mississippi Valley Earthquake Bulletin: 

Quarterly Bulletin 66, Third Quarter 1990, Saint Louis University.

Yang, Y.T., Chiu, J.M., Chen, K.C., Liaw, Z.S., Chiu, S.C., and 

Johnston, A.C., in press, Single-event, first motion, focal 

mechanism studies in the central NMSZ using PANDA data: 

Bulletin of the Seismological Society of America, v. 85.

Zhao, L.-S., and Helmberger, D.V., 1994, Source estimation from 

broadband regional seismograms: Bulletin of the Seismological Society of America, v. 84, no. 1, p. 91-104.

36°30

Figure 8. Surface-wave focal mechanisms from this study and 

Herrmann (1979b, in press) in the New Madrid region superimposed on regional-seismic-network epicenters. Dates of occurrence 

are shown with focal-mechanism plots (i.e., 050491 indicates May 

4, 1991).

Zoback, M.D., and Zoback, M.L., 1991, Tectonics stress field of 

North America and relative plate motions, in Slemmons, D.B., 

Engdahl, E.R., Zoback, M.D., and Blackwell, D.D., eds., Neotectonics of North America: Boulder, Colo., Geological 

Society of America, p. 339-366.

Zoback, M.L., 1992, Stress field constraints on intraplate seismicity 

in eastern North America: Journal of Geophysical Research, v. 

97, no. B8, p. 11761-11782.

Published in the Central Region, Denver, Colorado 

Manuscript approved for publication December 21, 1994 

Edited by Richard W. Scott, Jr. 

Graphics prepared by Carol Quesenberry 

Photocomposition by Patricia L. Wilber
BROADBAND SEISMOLOGY AND SMALL REGIONAL SEISMIC NETWORKS Sll

R

1.84x10-° 4

6.15X10' 04

4.43x10-° 4

4.13X10' 03

3.43X10' 04 L U

-^^\/\^^^l^

4.57x1(T04

4.42x10' 04

1.28x1(T03

FILTER 

0.10 Hz

2.27X10' 04

1.90x1(T03 I

———\W^rU~«JI^

2.45x1(T03 6.13X10' 04 

——^————Mjv,———

1.11x10' 02

6.24X10- 03

5.77x10' 03

1.36X10' 03

1.21x1(T03

7.80X10' 03

4.39X10' 03

2.00x10' 02

J I J\wV^**>^*.

^

1.03X10' 02

OBS

SYN

OBS 0.20 Hz

SYN

OBS 0.50 Hz

SYN

OBS 1.00 Hz

SYN

50 SECONDS

Figure 9. Comparison of filtered observed (OB S) and CUS mod- component and each filter frequency, the same plotting scale is used

el synthetic (SYN) three component ground-velocity time histories to emphasize differences in peak values. All traces start 20 s after

for the September 26, 1990, earthquake. The broadband velocity the origin time and consist of 50-s segments. Positive Z, R, and T

time histories, in units of cm/s, are low-pass-filtered at 0.10, 0.20, component values represent motion up, away from the source, and

0.50 and 1.00 Hz with a second-order Butterworth filter. For each in a direction clockwise around the source.
S12 INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE

APPENDIX r=(rz> rR, rT\ M=(M0Z, M0*, M0r), and 1=(1, 1, 1), and the 

numbers

GRID SEARCH

For focal-mechanism determination, a grid search is 

used with goodness-of-fit criteria designed to quantify a 

good visual fit between observed and modeled time histories. Let the N-sample synthetic and observed three-component time histories for the Z, R, and T components be sz, SR, 

ST and QZ, OR, o-p, respectively, where the synthetic time histories are generated for a unit seismic moment and a given 

combination of strike, dip, and rake angles and source depth. 

Because the waveforms may not agree in time due to either 

the Earth model used for synthetics or seismograph timing, 

the first step is to determine the time shift required to align 

the prominent features of the two time series.

Construct theoretical and observed vectors of time 

histories by concatenating the respective components:

r = M-1/(|1||M|)

s —

and

o = (oz, OR, O T)

(1)

(2)

Note that these are equivalently 3N-dimensional vectors. A 

cross correlation of the two time series is used to define the 

required time shift. Next, the synthetic time series are 

shifted, and the shifted time series for each component 

defined by sz, SR, and ST- The goodness of fit of each individual component is given by the vector dot product of the 

unit vectors:

(3)

for

c=Z, R, T

Following Zhao and Helmberger (1994), individual 

seismic-moment estimates are made for each component by 

using the relation

M0 C = Max(\oc\)/Max(\sc\)

Thus, for each choice of source depth and 

focal-mechanism parameters, six numbers are generated, 

MQC and rc, for c=Z, R, and T. To quantify the visual 

goodness-of-fit criteria, we require that the individual rc be 

as close to 1 as possible and that the individual seismic-moment estimates be equal. Mathematically, this can 

be expressed by defining the three-component vectors

and

r =

(5)

(6)

rg measures the similarity of moment estimates, and r^ measures the closeness of individual elements of r to unity.

The best fit is that which maximizes the product 

RB=fyg. The seismic-moment estimate is the weighted 

average

(7)

There are several advantages to the techniques proposed. First, even though the example considers a fit to a 

three-component time history, the mathematical steps will 

work for a single-trace comparison or for many traces from 

many stations. In this latter case, individual rc and MQC values are determined for each station, but the r, M, and 1 vectors would have a dimension greater than 3. The formulation 

for the goodness-of-fit parameter and the weighted seismic-moment estimate would remain the same. The second 

point is that the formalism permits the application of a 

time-dependent weighting function to each observed-synthetic trace pair for the purpose of enhancing low-amplitude, 

but significant, arrivals, such as P and sP relative to S and 

the surface wave. The only negative about this procedure is 

that it is very computationally intensive compared to the 

simple comparison of first-motion and amplitude-ratio data 

that Langston (1994) used as an initial inversion.

Figure 10 shows an example of graphical output of the 

program that implements the goodness-of-fit estimation. 

The top row shows the concatenated Z, R, and T theoretical 

traces for the source parameters and seismic moment of 

l.OxlO20 dyne-cm. The result is a time series 150 s long. The 

second row gives the corresponding observed time series. 

The vertical tick marks indicate the termination points of 

individual components. The bottom row shows the 

cross-correlation function, which indicates a 2.3-s time shift 

between the top two traces. The traces are not exactly 

identical in shape because the autocorrelation function is not 

perfectly symmetric about its maximum. The third row 

superimposes these traces after shifting the observed trace 

by -2.3 s. Above each component are the individual component goodness-of-fit values and seismic moment estimates, 

e.g., rz=0.906 and M0z=1.943xl022, respectively, for the Z 

component. The overall goodness-of-fit is RB=0.871, and 

the mean moment estimate is A/o=2.01xl022 dyne-cm.
BROADBAND SEISMOLOGY AND SMALL REGIONAL SEISMIC NETWORKS S13

DIP=75.0 STK=90.0 RA£E=20.0 H = 8.0 

Synthetic

z

RB=0.8712 M =20.1.39 SHIFT=2.30 DT=0.1000 N = 501

0.906 

1.943x10 +02

0.876 

2.038x10 +02

0.833 

2.066x10 +02

2.624X10' 06

5.197x10' 04

5.284x10-°4 

5.197X10" 04

0.872x10 +0°

Figure 10. Graphic example of mathematical operations used in 

the determination of goodness-of-fit in the grid search technique. 

The first and second rows show the concatenated Z, R, and T 

time histories of the synthetic and observed 15-100 WWSSN 

seismograms for the May 5, 1991, earthquake recorded at CCM. 

The synthetics were generated using the CUS model (table 2), a 

dip of 75°, a strike of 90°, a rake of 20°, a depth of 8 km, and a 

seismic moment of l.OxlO20 dyne-cm. The bottom row shows 

the cross-correlation function. The third row shows the superposition of the observed (gray) and synthetic (solid) traces after

time shifting and peak-amplitude normalization. Annotations on 

the third row indicate: the individual component correlation coefficient and moment estimate (e.g., 0.906 and 194.3 for the Z component); the overall goodness-of-fit, RB; the moment estimate 

relative to that used to generate the synthetic, MQ; the required 

time shift; the data sampling interval; and the number of points 

sampled for each component. Vertical ticks are used to separate 

individual components. Positive Z, R, and T component values 

represent motion up, away from the source, and in a direction 

clockwise around the source.

SINGLE-STATION PHASE-VELOCITY 

ESTIMATE

Given a known seismic source defined in terms of its 

moment tensor and distribution of point forces, synthetic 

seismograms can easily be generated for plane-layered, isotropic media. If the observed signal and the synthetic consist

of a well-defined fundamental-mode surface wave, then the 

difference in the complex phase of the signals can be used to 

define the phase velocity of the observed surface wave, 

which in turn can be inverted for an improved velocity model. 

This section describes a cross-correlation technique to estimate the phase velocity and, more importantly, to provide a 

qualitative estimate of the confidence in the dispersion.
S14 INVESTIGATIONS OF THE NEW MADRID SEISMIC ZONE

For simplicity, let the synthetic fundamental-mode signal have a Fourier transform X(f) expressed as

X(f) = (8)

where

r is the source-receiver distance,

A(f) and </>(/) includes the effect of source time function

and surface-wave excitation, and 

k(f) is related to the phase velocity, c(f), by k(f)=2nf/c(f). 

Let the observed signal be given by

Y(f) = A0 (f)el (9)

If the observed signal only consists of the fundamental-mode 

surface wave, which is possible through appropriate 

time-domain windowing or phase-match filtering, then

Y(f) =

('*(/) -iK(f)r (10)

If it is assumed that the source is known, e.g., O=<|), then 

the simple mathematical technique of cross-correlation can 

be used to define the difference in phase,

X(f)X*(f) A(f}

(11)

where

the * symbol represents a complex conjugate. 

The phase of the left-hand side can be interpreted in terms of 

the difference in wavenumber and, effectively, the phase 

velocity between the observed and synthetic traces.

If the assumptions of knowing the source phase and 

having only a single mode in the observed signal are not met, 

then the inferred phase-velocity correction cannot be 

accepted with confidence. This difficulty can be addressed 

by using smoothed spectra, and a statistical test (Jenkins and 

Watts, 1968; Shumway, 1988).

The time series x(t) and y(t) are windowed between a 

'min and fmax to isolate the surface-wave mode and then 

Fourier-transformed to provide windowed complex Fourier 

spectra, X(f) and Y(f). From these two spectra, the autocorrelation and cross-correlation spectra are defined from the 

relations

XY(f) = Y(f)X*(f)

XX (f) = X(f)X*(f)

YY(f) = Y(f)Y*(f)

(12)

(13)

(14)

The smoothed spectra XY, XX, and YY, at a frequency 

f=kAfaxe. defined by

XY(k) = i

the coherency squared,

K12 =

XY(k + n) (15)

XY /(XXYY)

and the estimated cross spectra

H(f) = = XY(f)/XX(f)

(16)

(17)

Because of the smoothing, there is redundant information 

that can be used to estimate the confidence on the cross 

spectra. The statistical test is whether the two spectra are 

significantly different. Defining a factor

1/2

(18)

then the 100(1-a) percent confidence bands on the 

amplitude and phase spectrum of the cross spectrum are

(19)

(20)

To estimate the phase velocity and error, let r be the distance between the two surface-wave observations, and let the 

theoretical phase velocity used to generate the synthetic be 

cm. The difference in the phase will be explained by a difference in phase velocities. The corrected phase-velocity 

estimate is obtained from

c cm cor 

and the error in the phase velocity is estimated to be

Ac = c sin (O)/cor

(21)

(22)

Experimentation shows that increasing the smoothing window will reduce the coherency, and, hence, increase the 

95-percent confidence limits on the phase velocity. A value 

of L=3 is adequate. In addition, a larger L will lead to rippling in the phase velocity at high frequencies, which may 

be due to the use of an essentially rectangular smoothing 

function.
BROADBAND SEISMOLOGY AND SMALL REGIONAL SEISMIC NETWORKS S15

RAYLEIGH LOVE

SYN

OBS

50.00 63.33 76.67 90.00 50.00 63.33 76.67 90.00 50.00 63.33 76.67 90.00 50.00 63.33 76.67 90.00

TIME, IN SECONDS TIME, IN SECONDS TIME, IN SECONDS TIME, IN SECONDS

CUS MODEL

0.00 0.08 0.17 0.25

FREQUENCY, IN HERTZ

MALDEN MODEL

0.00 0.08 0.17 0.25

FREQUENCY, IN HERTZ

CUS MODEL

0.00 0.08 0.17 0.25

FREQUENCY, IN HERTZ

MALDEN MODEL

"0.00 0.08 0.17 0.25

FREQUENCY, IN HERTZ

B D

Figure 11. Demonstration of the cross-correlation technique used 

to revise the initial Earth structure model between the May 4, 1991, 

earthquake and the CCM station. A and C illustrate the modification 

of the original dispersion computed using the CUS model for the 

Rayleigh and Love waves, respectively. The top traces are the synthetics predicted using the CUS model, and the second set of traces 

are the observed data. The dotted lines in the phase velocity versus 

frequency plots are the theoretical phase-velocity dispersions based

This technique was applied to the observed vertical (Z) 

and tangential (T) traces for the May 4, 1991, earthquake. 

Figure 11 shows the windowed WWSSN 15-100 

long-period instrument time histories. No attempt was made 

to isolate the fundamental mode using phase-match filters.

Consider Figure 1 1 A, which compares the theoretically 

predicted vertical-component Rayleigh-wave arrival for a 

depth of 8 km and the mechanism given in table 1 using the 

CUS model of table 2 to the observed signal at CCM. The 

model-predicted dispersion is given by the dotted curve, 

whereas the dispersion inferred using the cross-correlation 

analysis is given by the solid curve with error bars. As is 

obvious from the signals, the CUS model is too fast. In

on the CUS model, and the solid lines with error bars are the dispersions required to explain the signal differences in shape and arrival 

time. The new dispersion was inverted to yield the MALDEN model of table 2. B and D show the result of another iteration starting 

with the MALDEN model of table 2. The results indicate little need 

to change that portion of the model affecting dispersion between 

0.05 and 0.25 Hz. All traces have been passed through a WWSSN 

15-100 long-period instrument.

addition, the shape of the Rayleigh-wave pulse differs. Figure 11C is a similar display for the Love wave. The resulting 

dispersion curves were inverted by starting with the CUS 

model and keeping Poisson's ratio fixed. The Ac values are 

used as relative weights in the inversion. The new Earth 

model is given as the MALDEN model in table 2. Figures 

1 IB and 1 ID show the result of further processing with this 

newer model for the Rayleigh and Love arrivals, respectively. First note that the arrival times of the positive peaks 

of the waveforms now agree and that little additional change 

in the dispersion is required in the 0.04- to 0.25-Hz band. 

Because the improved fit yielded better waveform shapes, 

no further iterations were performed.

U.S. GOVERNMENT PRINTING OFFICE: 1995 - 673-046 / 20004 REGION NO. 8