# Broadband Source Parameters Computed at the NEIC

Since 1985, the NEIC has been actively incorporating methods of broadband seismogram analysis into its routine operations with two objectives: (1) to improve the accuracy of reported source parameters, such as depth and focal mechanism; and (2) to introduce new data services that were previously impractical without digital broadband data, such as estimating radiated energy. Some of the broadband digital operations in routine use by the NEIC are described below.

**Broadband depths.**

From
digitally recording networks and arrays, broadband seismograms of body waves
that are flat to displacement and velocity in at least the frequency range from
0.01 to 5.0 Hz are now routinely obtained for most earthquakes of magnitude
greater than about 5.5 by using the method of Harvey and Choy (1982).
The broad spectral content in displacement
and velocity records often permits identification and resolution of the source
functions of direct and surface reflected phases by direct inspection. The
advantages that accrue from analyzing such data can be seen in an example (Fig. 1)
that compares different representations of the same P wave.
The arrival times of direct and surface
reflected arrivals are most easily identified and measured in broadband
displacement and velocity.The
differential times can be used to infer source depth. Polarities and relative
amplitudes of various phases can be measured directly from the data and used to
constrain nodal planes of the focal mechanism.

**Figure 1.** Four representations of a P wave recorded at
station RSNY are shown. From top to
bottom: the long-period record, short-period record, broadband ground
displacement and broadband ground velocity. In the broadband records the
identification of the depth phases is unequivocal and the measurement of
differential travel times with respect to the direct P wave is accurate.

Since October 1985, estimates of depth determined from
inversion of differential times of depth phases identified on broadband
waveforms for earthquakes having *m _{b}* > 5.8 have been published
in the Monthly Listings of the Preliminary Determination of Epicenters
(PDE). Since January 1996, the
broadband depths for shallow earthquakes have been derived by modeling
broadband P and transversely polarized S waves using methods described by Choy
and Dewey (1985).

**Broadband fault-plane solutions and complexity of rupture.**

Beginning January 1996, a broadband fault
plane solution has been determined whenever possible for any earthquake having
a magnitude > 5.8 and published in the Monthly Listings of the PDE.
The broadband fault-plane solution is determined primarily from
least-squares fitting of synthetic waveforms to teleseismically recorded
broadband body waves that are flat to displacement between
approximately 0.01 to 5.0 Hz.
Additional constraints are sometimes
provided by polarities from P-waves at distances
< 30° from the epicenter,
from Hilbert-transformed body waves of
certain secondary arrivals (e.g., PP), and from transversely polarized S
waves. Prior to January 1996, fault
plane solutions were constrained primarily by using first motion data
from P, pP and PKP waves.
These solutions are "first motion" solutions
rather than "broadband" solutions.

Along with the depth and mechanism analyses, the NEIC examines the source-time functions of P-wave displacements for complexity of earthquake rupture. The identification of any multiple events is noted in the COMMENT section of the description of the earthquake in the Monthly Listings.

**Radiated Energy ( E _{S} )**.

The energy radiated by an earthquake is estimated from the energy spectral density of the broadband P-waves, using the method described by Boatwright and Choy (1986), where the energy flux in the P waves is obtained by direct integration of velocity-squared records.

Energy gives a physically different measure of earthquake size than moment. Energy is derived from high frequencies in the velocity power spectra, while moment is derived from the low-frequency asymptote of the displacement spectra. Thus, energy is a measure of seismic potential for damage, while moment is a measure of the area ruptured by an earthquake.

**Apparent stress**.

A source parameter that relates the amount of energy radiated per unit of moment is apparent stress,
which is defined as uE_{S}/M_{0} where u is the modulus of rigidity,
E_{S} is radiated energy and M_{0} is seismic moment.
Apparent stress is used as an indicator of fault maturity (Choy et al, 2002).
High apparent stresses (greater than about 1.0 MPa [megapascal]
are associated with immature faults.
Low apparent stresses (much less than 1.0 MPa) are associated with mature faults.

**Energy Magnitude ( M _{e} )**.

The energy magnitude,

*M*, is computed from the radiated energy using the Choy and Boatwright (1995) formula (eq. 6):

_{e}
*M _{e} = 2/3 log E_{S} - 2.9*

where energy is in Newton-meters.

**The relationship of M _{e} to
M_{W}**.

Although

*M*and

_{e}*M*are magnitudes that describe the size of an earthquake, they are not equivalent.

_{W}*M*, being derived from velocity power spectra, is a measure of seismic potential for damage to anthropogenic structures.

_{e}*M*, being derived from the low-frequency asymptote of displacement spectra, is physically related to the final static displacement of an earthquake. Because they measure different physical properties of an earthquake, there is no

_{W}*a priori*reason that they should numerically equal for any given seismic event. The energy magnitude,

*M*, is an essential complement to moment magnitude,

_{e}*M*, for describing the size and affect of an earthquake rather than an alternative.

_{W}
**Differential magnitude**.

The difference between energy magnitude and moment magnitude (M_{e} - M_{W})
is called the differential magnitude. Like apparent stress,
it is a measure of whether an earthquake rupture is rich or depleted in seismic energy per unit moment.

Starting with the November 1986 Monthly Listing, the NEIC
has published estimates of radiated energy computed directly from broadband
body waves.
*M _{e}*
has been published routinely beginning with the July 1995 Monthly
Listing.

**References**

Boatwright, J. and G. Choy, Teleseismic estimates of the
energy radiated by shallow earthquakes,
*J. Geophys. Res., 91*, 2095-2112, 1986.

Bormann, P., Baumbach, M., Bock, G., Choy, G., Seismic sources and
source parameters: New Manual of Seismological Observatory Practice, Chapter 3, *IASPEI Commission on Practice, 27 p.*, 2002.

Choy, G. L., and J. L. Boatwright, Global patterns of
radiated seismic energy and apparent stress,
*J. Geophys. Res.
100*, 18205-18228, 1995.

Choy, G. L.,
J. L. Boatwright, and Steve Kirby, The radiated seismic energy and
apparent stress of interplate and intraplate earthquakes at subduction zone
environments: Implications for seismic
hazard estimation, *U. S. Geol. Survey
Open-File Report 01-005*, 10 pages, 2001.

Choy, G. L. and J.W. Dewey, Rupture process of an extended
earthquake sequence: Teleseismic analysis of the Chilean earthquake of 3 March
1985, *J. Geophys. Res.,93,* 1103-111, 1988.

Choy, G. L., McGarr, A., Kirby, S. H., Boatwright, J.,
An overview of the global variability in radiated energy and apparent stress:
in Abercrombie, R., Kanamori H., McGarr, A., and Di Toro, G., eds.,
Radiated Energy and the Physics of Earthquake Faulting,
*AGU Geophysical Monograph Series 170, p. 43-57*, 2006.

Harvey, D. and G. L. Choy, Broadband deconvolution of GDSN
data, *Geophys. J. R. Astr. Soc., 69,*
659-668, 1982.