Observing supershear earthquakes in the far-field

Eric M. Dunham

Department of Earth and Planetary Sciences, Harvard Universityedunham@fas.harvard.edu

SCEC 2005

(a) Love waves at 400 km, cos(2φ) factor removed

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100 150 100 150Time (s)

Outside Mach cone (90 deg)

Inside Mach cone (0 deg)

(b) Superposition of subshear and supershear segments

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L=70 km3.5 km/s<c(ω)<4.5 km/s

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(a) Spectral Nodes (b) Displacement Spectra, Love Waves at 400 km

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Motivation and SummarySupershear rupture speeds have been claimed for several recent earthquakes. While near-source records provide the best opportunity for discerning details of the rupture process, they are often lacking for these events, leaving regional and teleseismic records as the only sources of information. This poster discusses the far-field signature of supershear earthquakes, essentially applying ideas about directivity discussed by Ben-Menahem and Singh [1981] to current dynamic source models. The main results can be summarized as:

1. S-wave radiation from a supershear rupture segment forms a Mach cone (MC) a. outside the MC, waves arrive in the order in which they were emitted b. inside the MC, waves arrive in the reverse order c. on the MC, all waves arrive simultaneously, producing a maximum in directivity (but at about 50 deg from forward)2. Teleseismic waves take off outside the MC (at least for stike-slip events), leaving surface waves as the best candidates for observing the MC 3. Radiation from multi-segment ruptures (specifically those having both a sub-Rayleigh and supershear segment, as suggested by dynamic models) is complex: a. Waves from multiple segments arrive simultaneously within the MC, often enhancing amplitudes in the forward direction (causing potential misinterpretation as a purely sub-Rayleigh event) b. Standard analysis methods for estimating rupture velocity (e.g., peak-to-peak amplitude vs. azimuth, inverting for average rupture velocity) might easily be fooled c. A Fourier-domain analysis could potentially be useful for estimating rupture velocity.

fault

hypocenter

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Mach cone

(~50 deg for V/cs=1.6)

hypocenter

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Ben-Menahem [1961], Ben-Menahem and Singh [1981]

Inside Mach cone, S waves trace the reverse of the source history

Outside Mach cone, S waves trace source history

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Denali Fault Earthquake, Model II snapshots of fault every 1.83 s

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Inside Mach coneazimuth=0 deg

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(a) Far-field Displacement Waveform Ω(t)

(b) Superposition of subshear and supershear segments

Take-off angle=90 deg

superpositionsub-Rayleigh supershear

Dynamic Source Model

To illustrate the ideas discussed above, synthetic far-field seismograms will be generated for the dynamic source model shown above [Dunham and Archuleta, 2004]. The model is characterized by1. an initial sub-Rayleigh segment followed by a supershear segment2. the simultaneous coexistence of a Rayleigh wave (on the fault) and the supershear rupture.

The source time function has the following properties:1. Increase during the initial bilateral propagation2. Decrease as the left-moving pulse dies3. Increase when the rupture becomes supershear (with an extra bump of moment release from the Rayleigh wave)4. An abrupt termination due to the artificial termination of the rupture (since only 110 km of the fault was modeled).

The model was developed for the 2002 Denali Fault earthquake to explain features of the near-source records at Pump Station 10. A 110 km segment of the Denali fault was modeled as a vertical fault extending 10 km down from the surface.

This figure shows far-field waveforms for direct S waves, with the radiation-pattern dependence removed. These are not intended as predictions of actual ground motion since many effects (attenuation, conversion/reflection at the surface, etc.) are not included. Instead, their purpose is to illustrate the main ideas in an idealized context. In this case, the waveform is simply given by the sum of the source time functions of the individual segments, appropriately compressed or expanded in time due to directivity.

In (a), waveforms are shown for three take-off angles (where 0 deg=vertically downward and 90 deg=horizontal) and many azimuths (forward direction is to right). The red line marks the Mach cone, although by the time the take-off angle drops into the teleseimic range, all waves are emitted outside the Mach cone. Amplitude is maximum around the Mach cone, although a strong concentration in the forward direction is also present.

Part (b) explains how waves from the sub-Rayleigh and supershear segments interfere with each other. Outside the Mach cone, waves arrive successively in the order in which they were released from the fault. Inside the Mach cone, waves from the supershear segment are reversed in time and overlap the earlier-released waves from the sub-Rayleigh segment. This effectively increases the amplitudes in the forward direction, potentially leading to misinterpretation as the directivity pattern due to a fast, but purely sub-Rayleigh, event.

Direct S Waves

Surface Waves

Fourier Spectra

This figure shows Fourier spectra from the Love-wave seismograms. The signature of a finite source is the presence of spectral nodes or holes, frequencies at which there is destructive interference of waves. These have been used in the past to estimate rupture velocity [e.g., Filson and McEvilly, 1967]. The period of the node decreases as the Mach cone is approached, corresponding to the compression of the signal. Part (a) shows how the period varies with azimuth for a purely sub-Rayleigh and purely supershear event. Note that the period is not precisely defined since the phase velocity of Love waves is frequency-dependent. Part (b) applies this idea to the Love-wave synthetics generated in the previous section.

This figure shows synthetic Love-wave seismograms, with the radiation-pattern dependence removed. The fundamental mode response is calculated for a layer-over-a-half-space crustal model (layer: cs=3.5 km/s, H=35 km; half-space: cs=4.5 km/s). Maximum amplitudes occur around the Mach cone, although a significant amplitude enhancement occurs in the forward direction due to constructive interference of waves from the sub-Rayleigh and supershear segments. The type of interference (constructive or destructive) depends on the velocities and lengths of the two segments, as well as wave propagation effects. Again, the main point is that these records could easily be misinterpreted as being generated by a sub-Rayleigh event.

Ben-Menahem, A. (1961), Radiation of seismic surface waves from finite moving sources, Bulletin of the Seismological Society of America, 51, 401-435.Ben-Menahem, A. and S. J. Singh (1981), Seismic Waves and Sources, Springer-Verlag, New York.Dunham, E. M. and R. J. Archuleta (2004), Evidence for a supershear transient during the 2002 Denali Fault earthquake, Bulletin of the Seismological Society of America, 94, S256-S268.Filson, J. and T. V. McEvilly (1967), Love wave spectra and the mechanism of the 1966 Parkfield sequence. Bulletin of the Seismological Society of America. 57, 1245-1259.

References

Directivity: Subshear vs. Supershear