George L. Choy

Global patterns of radiated seismic energy and apparent stress

Radiated energies from shallow earthquakes with magnitudes ≥5.8 that occurred between 1986 and 1991 are used to examine global patterns of energy release and apparent stress. In contrast to traditional methods which have relied upon empirical formulas, these energies are computed through direct spectral analysis of broadband seismic waveforms. Velocity-squared spectra of body waves are integrated after they have been corrected for effects arising from depth phases, frequency-dependent attenuation, and focal mechanism. The least squares regression fit of energy Es to surface wave magnitude Ms for a global set of 397 earthquakes yields log Es = 4.4 + 1.5Ms, which implies that the Gutenberg-Richter relationship overestimates the energies of earthquakes. The least squares fit between Es and seismic moment M0 is given by the relationship Es = 1.6 × 10−5 M0, which yields 0.47 MPa as the average global value of apparent stress. However, the regression lines of both Es–Ms and Es–M0 yield poor empirical predictors for the actual energy radiated by any given earthquake; the scatter of data is more than an order of magnitude about each of the regression lines. On the other hand, global variations between Es and Mo, while large, are not random. When subsets of Es–M0 are plotted as a function of seismic region and faulting type, the scatter in data is substantially reduced. The Es–M0 fits for many seismic regions and tectonic environments are very distinctive, and a characteristic apparent stress τc can be derived. The lowest apparent stresses ( 3.0 MPa) are associated with strike-slip earthquakes that occur at oceanic ridge-ridge transforms and in intraplate environments seaward of island arcs. Intermediate values of apparent stress (1.5 < τa < 3.0 MPa) are associated with strike-slip earthquakes at incipient or transitional plate boundaries. In general, the dominant mode of failure for a tectonic environment is associated with the faulting type that has the lowest apparent stress. An energy magnitude ME can complement moment magnitude Mw in describing the size of an earthquake. ME, being derived from velocity power spectra, is a measure of seismic potential for damage. Mw, being derived from the low-frequency asymptote of displacement spectra, is more physically related to the final static displacement of an earthquake. When earthquake size is ranked by moment, a list of the largest events is dominated by earthquakes with thrust mechanisms. When earthquake size is ranked by energy, the list of the largest events is dominated by strike-slip earthquakes.

Seismic attenuation of the inner core : Viscoelastic or stratigraphic?

Broadband velocity waveforms of PKIKP in the distance range 150° to 180° are inverted for inner core attenuation. A mean Qα of 244 is determined at 1 Hz from 8 polar and 9 equatorial paths. The scatter in measured Q−1 exceeds individual error estimates, suggesting significant variation in attenuation with path. These results are interpreted by (1) viscoelasticity, in which the relaxation spectrum has a low-frequency corner near or slightly above the frequency band of short-period body waves, and by (2) stratigraphic (scattering) attenuation, in which attenuation and pulse broadening are caused by the interference of scattered multiples in a velocity structure having rapid fluctuations along a PKIKP path. In the scattering interpretation, PKIKP attenuation is only weakly affected by the intrinsic shear attenuation measured in the free-oscillation band. Instead, its frequency dependence, path variations, and fluctuations are all explained by scattering attenuation in a heterogeneous fabric resulting from solidification texturing of intrinsically anisotropic iron. The requisite fabric may consist of either single or ordered groups of crystals with P velocity differences of at least 5% and as much as 12% between two crystallographic axes at scale lengths of 0.5 to 2 km in the direction parallel to the axis of rotation and longer in the cylindrically radial direction, perpendicular to the axis of rotation.

Regional Estimates of Radiated Seismic Energy

We revise the spectral technique for estimating radiated energy from recordings of large earthquakes at regional distances (Δ 27.5 km from the source, we model the geometrical spreading of the regional wavefield as r – γ where γ = 0.5 for f ≤ 0.2 Hz and γ = 0.7 for f ≥ 0.25 Hz. We fit the spectral falloff with distance using a frequency-dependent attenuation Q = 400( f /1.5)0.6, where Q = 400 for f ≤ 1.5 Hz. There is little directivity apparent in the corrected velocity spectra: the velocity spectra observed to the northwest along strike are amplified by a factor of 2.5 from 0.3 to 1.0 Hz and those to the southeast are amplified by a factor of 1.6 from 0.3 to 0.7 Hz. We group the stations in NEHRP site classes, using average 1-D velocity structures to estimate site amplification as a function of frequency and assuming 0.40 ≤ κ ≤ 0.55 sec for the near-surface attenuation. We increase the amplification of the soft-soil sites from 0.1 to 1.0 Hz by a factor that reaches 1.7 at 0.3 Hz because they are more strongly amplified than the NEHRP-D velocity structure predicts. We combine the 65 single-station estimates of radiated energy using an equal-azimuth weighting scheme that compensates for station distribution and incorporates the observed directivity, yielding a regional estimate of E s = 3.4 ± 0.7 × 1022 dyne cm. This regional estimate of radiated energy corresponds closely to the teleseismic estimate of E s = 3.2 × 1022 dyne cm.

Seismicity associated with the Sumatra-Andaman Islands earthquake of 26 December 2004

The U.S. Geological Survey/National Earthquake Information Center (usgs/neic) had computed origins for 5000 earthquakes in the Sumatra–Andaman Islands region in the first 36 weeks after the Sumatra–Andaman Islands mainshock of 26 December 2004. The cataloging of earthquakes of m b (usgs) 5.1 and larger is essentially complete for the time period except for the first half-day following the 26 December mainshock, a period of about two hours following the Nias earthquake of 28 March 2005, and occasionally during the Andaman Sea swarm of 26–30 January 2005. Moderate and larger ( m b ≥5.5) aftershocks are absent from most of the deep interplate thrust faults of the segments of the Sumatra–Andaman Islands subduction zone on which the 26 December mainshock occurred, which probably reflects nearly complete release of elastic strain on the seismogenic interplate-thrust during the mainshock. An exceptional thrust-fault source offshore of Banda Aceh may represent a segment of the interplate thrust that was bypassed during the mainshock. The 26 December mainshock triggered a high level of aftershock activity near the axis of the Sunda trench and the leading edge of the overthrust Burma plate. Much near-trench activity is intraplate activity within the subducting plate, but some shallow-focus, near-trench, reverse-fault earthquakes may represent an unusual seismogenic release of interplate compressional stress near the tip of the overriding plate. The interplate-thrust Nias earthquake of 28 March 2005, in contrast to the 26 December aftershock sequence, was followed by many interplate-thrust aftershocks along the length of its inferred rupture zone.

An Overview of the Global Variability in Radiated Energy and Apparent Stress

A global study of radiated seismic energies E R and apparent stresses T a reveals systematic patterns. Earthquakes with the highest apparent stress occur in regions of intense deformation and rupture strong lithosphere. In oceanic settings, these are strike-slip earthquakes (T a up to 27 MPa) occurring intraplate or at evolving ends of transform faults. At subduction zones and intracontinental settings, these are strike-slip earthquakes with T a up to 7 MPa. Normal-fault earthquakes exhibit a more complex pattern. Higher T a s (up to 5 MPa) are found for intraslab events at depths from 35 to 70 km that occur near zones of intense deformation such as a sharp slab bend or the juncture of colliding slabs. Lower T a s (< 1 MPa) are found for normal-fault earthquakes at the outer rise and outer trench wall or deep in flat warm slabs. The lowest average τ a (0.3 MPa) is found for thrust-fault earthquakes at subduction zones. The variation of average apparent stress with tectonics suggests a relationship with lithospheric strength and fault maturity. Mature faults, such as plate boundaries that have experienced large cumulative slip, appear to have low strength and tend to yield earthquakes with low apparent stresses. Immature faults, in contrast, are stronger and yield high apparent stresses because either they are the result of fresh-rock fracture or at least their cumulative fault slip is quite small. These results have implications of use to the seismic engineering community because E R and its magnitude counterpart M e are reliable indicators of the potential for damaging ground motion.

Modeling and validation of a 3D velocity structure for the Santa Clara Valley, California, for seismic-wave simulations

A 3D seismic velocity and attenuation model is developed for Santa Clara Valley, California, and its surrounding uplands to predict ground motions from scenario earthquakes. The model is developed using a variety of geologic and geophysical data. Our starting point is a 3D geologic model developed primarily from geologic mapping and gravity and magnetic surveys. An initial velocity model is constructed by using seismic velocities from boreholes, reflection/refraction lines, and spatial autocorrelation microtremor surveys. This model is further refined and the seismic attenuation is estimated through waveform modeling of weak motions from small local events and strong-ground motion from the 1989 Loma Prieta earthquake. Waveforms are calculated to an upper frequency of 1 Hz using a parallelized finite-difference code that utilizes two regions with a factor of 3 difference in grid spacing to reduce memory requirements. Cenozoic basins trap and strongly amplify ground motions. This effect is particularly strong in the Evergreen Basin on the northeastern side of the Santa Clara Valley, where the steeply dipping Silver Creek fault forms the southwestern boundary of the basin. In comparison, the Cupertino Basin on the southwestern side of the valley has a more moderate response, which is attributed to a greater age and velocity of the Cenozoic fill. Surface waves play a major role in the ground motion of sedimentary basins, and they are seen to strongly develop along the western margins of the Santa Clara Valley for our simulation of the Loma Prieta earthquake.

The Energy Radiated by the 26 December 2004 Sumatra–Andaman Earthquake Estimated from 10-Minute P-Wave Windows

The rupture process of the M W 9.1 Sumatra–Andaman earthquake lasted for approximately 500 sec, nearly twice as long as the teleseismic time windows between the P and PP arrival times generally used to compute radiated energy. In order to measure the P waves radiated by the entire earthquake, we analyze records that extend from the P -wave to the S -wave arrival times from stations at distances Δ >60°. These 8- to 10-min windows contain the PP, PPP , and ScP arrivals, along with other multiply reflected phases. To gauge the effect of including these additional phases, we form the spectral ratio of the source spectrum estimated from extended windows (between TP and TS ) to the source spectrum estimated from normal windows (between TP and TPP ). The extended windows are analyzed as though they contained only the P-pP-sP wave group. We analyze four smaller earthquakes that occurred in the vicinity of the M W 9.1 mainshock, with similar depths and focal mechanisms. These smaller events range in magnitude from an M W 6.0 aftershock of 9 January 2005 to the M W 8.6 Nias earthquake that occurred to the south of the Sumatra– Andaman earthquake on 28 March 2005. We average the spectral ratios for these four events to obtain a frequency-dependent operator for the extended windows. We then correct the source spectrum estimated from the extended records of the 26 December 2004 mainshock to obtain a complete or corrected source spectrum for the entire rupture process (∼600 sec) of the great Sumatra–Andaman earthquake. Our estimate of the total seismic energy radiated by this earthquake is 1.4 × 1017 J. When we compare the corrected source spectrum for the entire earthquake to the source spectrum from the first ∼250 sec of the rupture process (obtained from normal teleseismic windows), we find that the mainshock radiated much more seismic energy in the first half of the rupture process than in the second half, especially over the period range from 3 sec to 40 sec.

Radiated Energy and the Rupture Process of the Denali Fault Earthquake Sequence of 2002 from Broadband Teleseismic Body Waves

Displacement, velocity, and velocity-squared records of P and SH body waves recorded at teleseismic distances are analyzed to determine the rupture characteristics of the Denali fault, Alaska, earthquake of 3 November 2002 ( M W 7.9, M e 8.1). Three episodes of rupture can be identified from broadband (∼0.1–5.0 Hz) waveforms. The Denali fault earthquake started as a M W 7.3 thrust event. Subsequent right-lateral strike-slip rupture events with centroid depths of 9 km occurred about 22 and 49 sec later. The teleseismic P waves are dominated by energy at intermediate frequencies (0.1–1 Hz) radiated by the thrust event, while the SH waves are dominated by energy at lower frequencies (0.05–0.2 Hz) radiated by the strike-slip events. The strike-slip events exhibit strong directivity in the teleseismic SH waves. Correcting the recorded P -wave acceleration spectra for the effect of the free surface yields an estimate of 2.8 × 10 15 N m for the energy radiated by the thrust event. Correcting the recorded SH -wave acceleration spectra similarly yields an estimate of 3.3 × 10 16 N m for the energy radiated by the two strike-slip events. The average rupture velocity for the strike-slip rupture process is 1.1 β –1.2 β . The strike-slip events were located 90 and 188 km east of the epicenter. The rupture length over which significant or resolvable energy is radiated is, thus, far shorter than the 340-km fault length over which surface displacements were observed. However, the seismic moment released by these three events, 4 × 10 20 N m, was approximately half the seismic moment determined from very low-frequency analyses of the earthquake. The difference in seismic moment can be reasonably attributed to slip on fault segments that did not radiate significant or coherent seismic energy. These results suggest that very large and great strike-slip earthquakes can generate stress pulses that rapidly produce substantial slip with negligible stress drop and little discernible radiated energy on fault segments distant from the initial point of nucleation. The existence of this energy-deficient rupture mode has important implications for the evaluation of the seismic hazard of very large strike-slip earthquakes.

The Rupture Process of the Manjil, Iran Earthquake of 20 June 1990 and Implications for Intraplate Strike-Slip Earthquakes

In terms of seismically radiated energy or moment release, the earthquake of 20 January 1990 in the Manjil Basin-Alborz Mountain region of Iran is the second largest strike-slip earthquake to have occurred in an intracontinental setting in the past decade. It caused enormous loss of life and the virtual destruction of several cities. Despite a very large meizoseismal area, the identification of the causative faults has been hampered by the lack of reliable earthquake locations and conflicting field reports of surface displacement. Using broadband data from global networks of digitally recording seismographs, we analyse broadband seismic waveforms to derive characteristics of the rupture process. Complexities in waveforms generated by the earthquake indicate that the main shock consisted of a tiny precursory subevent followed in the next 20 seconds by a series of four major subevents with depths ranging from 10 to 15 km. The focal mechanisms of the major subevents, which are predominantly strike-slip, have a common nodal plane striking about 285°–295°. Based on the coincidence of this strike with the dominant tectonic fabric of the region we presume that the EW striking planes are the fault planes. The first major subevent nucleated slightly south of the initial precursor. The second subevent occurred northwest of the initial precursor. The last two subevents moved progressively southeastward of the first subevent in a direction collinear with the predominant strike of the fault planes. The offsets in the relative locations and the temporal delays of the rupture subevents indicate heterogeneous distribution of fracture strength and the involvement of multiple faults. The spatial distribution of teleseismic aftershocks, which at first appears uncorrelated with meizoseismal contours, can be decomposed into stages. The initial activity, being within and on the periphery of the rupture zone, correlates in shape and length with meizoseismal lines. In the second stage of activity the aftershock zone expands and appears to cluster about the geomorphic and geologic features several tens of kilometres from the rupture zone. The activity is interpreted as a regional response to quasistatic stress migration along zones of tectonic weakness. The radiated energy of the main shock and the estimate of seismic moment yields an apparent stress of 20 bars. High apparent stress may be typical of strike slip earthquakes occurring in intracontinental environments undergoing continental collision.