Seismological Research Letters
 © 2008 by the Seismological Society of America
Abstract
Seismic waveform data, recorded by shortperiod instruments of the Cooperative New Madrid Seismic Network (CNMSN), and a temporary aftershock deployment for the 2001 Bhuj M_{W} 7.6 earthquake are corrected to the theoretical WoodAnderson response, and the horizontal peak amplitudes are used to determine local magnitude scales for the Mississippi embayment of the central United States and the Kachchh basin of western India, with a focus to understand the distance attenuation in these two regions. Results show that the distancecorrection function for the Mississippi embayment of the central United States is showing a weak distance attenuation within 17.0–100.0 km. The distancecorrection function for the Kachchh basin of western India is showing a relatively stronger distance attenuation within 17.0–100.0 km. Kachchh basin distance attenuation is closer to southern California than to the central United States suggesting fundamental differences in local wave propagation between these two intraplate regions.
INTRODUCTION
Large intraplate earthquakes have been characterized as having high stress drops and long recurrence intervals compared with large interplate earthquakes (Kanamori and Allen 1986). Consequently, it is difficult for seismologists to study strong ground motions excited by large earthquakes in an intraplate region because of their long recurrence times. Thus, ground motions from small earthquakes are usually studied to estimate strong ground motions for future, larger earthquakes in intraplate regions.
In the winter of 1811–12, a time period with no modern seismic instruments, three large earthquakes occurred in the New Madrid seismic zone (NMSZ) in the central United States (Johnston and Schweig 1996). The recurrence interval of such sequences of events is thought to be on the order of 500 years based on dating of paleoliquefaction features seen in the epicentral region (Tuttle et al. 2002; Tuttle et al. 2005).
The Bhuj 2001 M_{W} 7.6 earthquake occurred in the Kachchh basin of western India, which is also considered an intraplate region (Biswas 1982, 1987). The earthquake and its aftershocks were wellrecorded by modern digital seismic instruments (Bodin and Horton 2004). Several investigators have suggested that there are important similarities between the 1811–12 New Madrid earthquakes and the 2001 Bhuj M_{W} 7.6 earthquake (Johnston 2001; Ellis et al. 2001; Talwani and Gangopadhyay 2001; Hough et al. 2002), including the location of large intraplate earthquakes within an ancient rift zone, reactivation of rift structures through present regional tectonic compression, seismic wave propagation within consolidated and unconsolidated sediments of the rift, and even the felt area. Therefore, it is reasonable to compare the attenuation of peak ground motion amplitudes of seismic waves with distance in the NMSZ, where no strong ground motion records exist, with ground motions in Kachchh basin, where strong ground motion records do exist.
The goal of this study is to produce selfconsistent local magnitude scales for the Mississippi embayment of the central United States, using digital seismograms from the Cooperative New Madrid Seismic Network (CNMSN), and for the Kachchh basin of western India, using digital seismograms from a temporary seismograph network deployed to study aftershocks of the 2001 Bhuj M_{W} 7.6 earthquake (Bodin and Horton 2004). We wish to understand the distance attenuation in these two regions based on the distancecorrection functions found in the local magnitude scales. We are investigating the assertion that there are “analog” regions for the NMSZ based on geological or tectonic reasons.
For convenience, the Mississippi embayment of the central United States will be referred to as the “central U.S.” and the Kachchh basin of western India will be referred to as “western India,” except as otherwise specified.
Data and Data Processing
Figure 1 shows the earthquakes and stations used in this study. Figure 1(A) shows the distribution of earthquakes and seismic stations for the central U.S. that includes 444 earthquakes, occurring in 1999–2005 and with magnitudes between M_{D} 1.5 and M_{D} 4.1, and 34 stations with 53 horizontal components. The earthquake parameters are from the New Madrid earthquake catalog (http://folkworm.ceri.memphis.edu/catalogs/html/cat_nm.html). These earthquakes and stations were selected to have a consistent distance range for the central U.S. and western India data sets so that the results for the two regions can be compared directly. In other words, the central U.S. data set is a subset of the data used by Miao and Langston (2007) and may display different parameter values in subsequent inversions than previously obtained. In Miao and Langston (2007), we mainly consider the distance attenuation in the range up to 1,000 km, while we can only consider the distance attenuation in the range up to 100 km in this study because of the distance limitation for the western India data (Bodin and Horton 2004). Figure 1(B) shows the distribution of aftershocks for the 2001 Bhuj M_{W} 7.6 earthquake and the stations of the temporary network for western India, including 879 earthquakes with magnitude between M 0.3 and M 5.0 (the other 366 earthquakes with no magnitude data were not included in the figure) and 10 stations with 20 horizontal components (Bodin and Horton 2004).
The temporary network for the 2001 Bhuj earthquake aftershock observation was deployed by the Center for Earthquake Research and Information (CERI) at the University of Memphis, along with the MidAmerica Earthquake Center (MAEC) and the Institute of Science and Technology for Advanced Studies and Research (ISTAR) in India. The aftershocks were recorded by eight portable seismographs deployed for 18 days starting on 12 February 2001, 17 days after the mainshock. More than 2,000 aftershocks were recorded. Location parameters were determined for 1,245 events, and magnitude parameters were determined for 879 of these events. The aftershock depth distribution covered almost the entire crust, with concentrations at about 26 km in the lower crust and 10 km in the upper crust (Bodin and Horton 2004).
The seismic instruments used in both regions were L28 shortperiod seismometers (figure 2). The sampling rates used in both regions are 100 samples/sec, so the recorded seismic wave frequency content can be as high as 50 Hz. We recovered the gainranged data for the central U.S. and corrected the instrument response to a standard WoodAnderson response for all the seismogram data used in this study (Miao and Langston 2007; Uhrhammer and Collins 1990). Then we filtered these seismograms using a bandpass filter with corner frequencies at 0.5 and 10.0 Hz (Kanamori 1980). Figure 3 shows an example of a seismogram recorded at station ANJ of the temporary network for the 2001 Bhuj earthquake. The peak amplitudes on every horizontal component were read for inversion of the local magnitude scale, M_{L}.
Data Analysis
Following Richter (1935, 1958), the local magnitude M_{L} is based on peak amplitudes of horizontal seismograms recorded by a standard WoodAnderson instrument with free period T_{0} = 0.8 sec, magnification = 2800, and damping = 0.8 and is given by (1) where A is the maximum trace amplitude observed on the horizontal component, –log A_{0} is an empirically determined distancecorrection function with the assumption that when a maximum amplitude of 1 mm is observed at a distance of 100.0 km, M_{L} = 3.0, and S is an empirically determined station correction factor.
Following Hutton and Boore (1987), the distancecorrection function in equation 1 can be expressed as where n and K are parameters sometimes related to the geometrical spreading and anelastic attenuation, r is the hypocentral distance in kilometers, 100.0 is the reference distance in kilometers, and 3.0 is the reference event magnitude.
The distance range for the western India data set is only about ∼0–100 km. We chose to invert for distancecorrection functions using 17.0 km as the reference distance and 2.0 as the reference event magnitude as suggested by Hutton and Boore (1987). Presumably, this will minimize the effect of local wave propagation and anelastic attenuation on local magnitude estimates of the earthquakes, because a closer reference distance is employed.
Using the techniques developed in Miao and Langston (2007), we inverted for local magnitude scales for the central U.S. and western India. Figure 4(A) shows the residual distribution with distance for the central U.S. for 22,129 horizontal peak amplitudes. The residual distribution shows a symmetrical pattern, and most of the residuals are between –0.6 and +0.6. The residual frequency plot shows a normal distribution. The variance of the residual frequency plot was used for error estimation of the model parameters. In the same way, we used 14,020 horizontal peak amplitude data in the inversion for the local magnitude scale for western India (figure 4B).
Figure 5 (lines) shows the inverted distancecorrection functions –log A_{0} for the local magnitude scales of the central U.S. and western India and their variations with distance for predicted errors in n and K of ± one standard deviation. The distancecorrection function for the central U.S. is given by showing a weak distance attenuation within 17.0–100.0 km. The distancecorrection function for western India is given by showing a relatively strong distance attenuation within 17.0–100.0 km.
Figure 6 shows the error analysis for local magnitude in western India. It can be seen that the M_{L} standard deviation decreases only slightly with the number of peak amplitude data used in the inversion. The more data used, the smaller the standard deviation is. The error analysis for the central U.S. shows the same pattern as that for western India (Miao and Langston 2007).
Figure 7 shows the error analysis for the station corrections in western India. Again, the standard deviation of station corrections decreases only slightly with the number of peak amplitude data used in the inversion. Figure 8(A) shows the spatial distribution of station corrections for the central U.S. Most of the station corrections in the northwest are positive, while most station corrections in the southeast are negative.
Compared with the known Mississippi embayment distribution (Langston 2003a, b), the positive station corrections may represent a thin sedimentary pile, and the negative station corrections may represent a thicker sedimentary section. Figure 8(B) shows the spatial distribution of station corrections for western India. The smallest station correction, –0.2288 (the largest absolute value among the station corrections), corresponds to the station located at a liquefaction site (Bodin and Horton 2004).
DISCUSSION AND CONCLUSIONS
Figure 5 shows the comparison of local magnitude scales for the central U.S., western India, and some other regions. The local magnitude scales are based on the 17.0km reference distance and a reference event magnitude of 2.0. It can be seen from the figure that the distancecorrection function for the central U.S. is comparable to that of Tanzania (Langston et al. 1998), but that the distancecorrection function for western India is closer to southern California (Hutton and Boore 1987). It is well known that the distance attenuation in southern California is much stronger than that of the central U.S., and we expected that the distance attenuation pattern in western India should be somewhat like that in the central U.S. because of the similarities between the 1811–12 New Madrid earthquakes and the 2001 Bhuj M_{W} 7.6 earthquake (Johnston 2001; Ellis et al. 2001; Talwani and Gangopadhyay 2001; Hough et al. 2002). Yet, the results show that there are significantly different distance attenuation patterns for the two regions.
The local magnitude scale for western India shows another feature similar to southern California. The distancecorrection function remains the same no matter if the reference distance is 100.0 km with reference event magnitude 3.0 or 17.0 km with reference event magnitude 2.0. The local magnitude for the central U.S. is different in that the distancecorrection function changes if the reference distance and the reference event magnitude are changed (figure 9). Bodin and Horton (2004) determined magnitudes of the aftershocks using an approximate scale. The basic idea of their scale was to determine magnitudes of the aftershocks based on a linear relation between the log of the observed aftershock amplitudes and the corresponding magnitudes found in the National Earthquake Information Center catalog. Figure 9 shows that there is a bias of about half a magnitude unit at the high end of the data set where M_{L} is larger than found by Bodin and Horton (2004). The bias is greater for lower magnitudes.
Even though there exist some important similarities between the 1811–12 New Madrid earthquakes and the 2001 Bhuj M_{W} 7.6 earthquake (Johnston 2001; Ellis et al. 2001; Talwani and Gangopadhyay 2001; Hough et al. 2002), the distancecorrection functions found in this study show that the distance attenuation in the central U.S. is much weaker than that of western India even in the local distance range of 17–100 km. There are also some other differences that suggest the analogy should not be taken too far. For example, the distance between the epicenter and the nearest plate boundary is quite large for the central U.S. (more than 1,000 km) while the distance in western India is only 300–400 km (Bodin and Horton 2004). The earthquake depth distributions are also different. Most of the earthquakes in the central U.S. are located at depths of 15 km or less, while most of the aftershocks for the 2001 Bhuj M_{W} 7.6 earthquake occurred throughout the 40km thick crust (Bodin and Horton 2004).
The parameters n and K in the distancecorrection function of the local magnitude scale can be interpreted to represent geometric spreading and anelastic attenuation (Hutton and Boore 1987). Thus, changes in n and K with frequency may help us to understand the distance attenuation differences with frequency between these two regions. We apply narrow bandpass filters, with frequencies centered at 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, and 9.0 Hz, to the seismic data and invert for new distancecorrection functions to obtain frequencydependent parameters n and K for the two regions. Results (figure 10) show that the n parameter increases with frequency for both regions. The increasing rate for the central U.S. is larger than that of western India for the data below 5.0 Hz. Above 5.0 Hz, n increases relatively slowly for both regions. Parameter K generally decreases with frequency in both regions. However, and consistent with results in Miao and Langston (2007), K is negative, implying that there are wave propagation effects that allow waves to propagate farther without loss in the crust of the central U.S. The groundmotion parameters are a function of local seismic structure and the state of the crust, but it is difficult to make a judgment about groundmotion parameters from geological or tectonic interpretations. We conclude that the distance attenuation pattern for the Mississippi embayment of the central U.S. and the Kachchh basin of western India are quite different, which suggests that there are significant differences in wave propagation as well.
Acknowledgments
We thank Arch Johnston, Christine Powell, Eugene Schweig, and Mitch Withers for their valuable comments. An anonymous reviewer was helpful in improving this manuscript. Use of the Generic Mapping Tool (Wessel and Smith 1998) program for figure 1 is acknowledged. The Seismic Analysis Code (Goldstein and Minner 1996) was used for much of the analysis. We thank Paul Bodin for his help in accessing the 2001 Bhuj M_{W} 7.6 earthquake aftershock waveform database.
Footnotes

Center for Earthquake Research and Information, University of Memphis