Page 14 - Winter 2008

Fig. 9. Nonlinear imaging of cracks in solids. The TREND image (a) shows the extent of the damage region of a highly complex surface crack resulting from a hammer impact onto a glass sample. The difference frequency (sideband) is used to create the scan. The image in (b) illustrates the focusing of elastic energy (again using the dif- ference frequency) onto a fatigue crack. The white line approximates the crack while the black curve is the edge of the sample (a steel bearing cap).
sophisticated triangulation methods. TR was suggested as an
alternative method for earthquake localization and imaging
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beginning in the 1980s. Sources of earthquakes are
described physically using what is known as double couple. A double couple source generates a displacement wavefield that contains complex radiation patterns for the shear, compres- sional, and surface waves, making the source localization problem additionally challenging.
By applying a TRM, earthquake source locations can be found by taking the recorded seismograms, time-reversing them, and back propagating them through a numerical velocity model. In the example described here, seismograms were recorded worldwide from a well-known earthquake in central California, known as the 2004 Parkfield Earthquake. Figure 10 shows progressive snapshots of the back propaga- tion of the velocity wavefield. Note the energy observed at the focal time located elsewhere is due, primarily, to an insuffi- cient distribution of receivers and is due, secondarily, to mode conversion (for example, conversion of body waves to surface waves).
The accuracy of reconstructing an earthquake source
using TR relies upon the accuracy of the numerical model-
ing. The first attempts of seismic source localization using TR
were conducted by McMechan and were limited to simple
velocity models70,72 or restricted to the acoustic case73 (using
only compression waves). With the development of efficient
wave-propagation methods which can handle complex geo-
logic models, the TR method is now an alternative to other
source location methods as demonstrated numerically by
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Gajewski. The first global scale TR reconstruction of an
earthquake using surface waves was performed by Larmat et al. to image the rupture of the 2004 great Sumatra earth-
Summary
This article presents a brief overview of Time Reversal (TR), an extremely active area of acoustics. We described TR and the mechanics of how it works. We also described bene- fits and limitations inherent in TR, relative to standard meth-
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Globe and LOA.
quake.
This work first began at the Institute of Physics of the
shows a result of TREND in a glass sample with a highly complex surficial crack. The very bright red regions in the figure show the highest nonlinear response, corresponding to the regions of highest damage intensity.
TR and NEWS are also combined in another method potentially not restricted to detecting only surface/near-sur-
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In this method, the initial source signal(s) propagate to a crack in a sample, where new frequencies are produced (e.g., harmonics/sidebands). The crack acts as a nonlinear scattering source. The combined signals (linear and nonlinear) are detected at a TRM. Before performing TR one filters the signals, leaving only the nonlinear frequency content of the wave. The filtered signals are time reversed and rebroadcast from the TRM. These signals then focus back only on the nonlinear scattering source, i.e., the crack. The signals are back-propagated repeatedly as a detector (a laser) scans stepwise in a raster-type manner around the entire sample, or in a region of interest. In this manner, one can iso- late the nonlinear scatterer from the background. An advan- tage of this method is that only a single forward propagation step is required. Figure 9b shows an example of the method, in a steel bearing cap sample that has a narrow but deep, sur- face breaking crack. The interaction of the crack with the
face features.
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back propagating waves is extremely complex. While in
principle it is possible to focus the energy on buried features or surface features without a priori knowledge of their exis- tence/location, it is only possible to experimentally verify this
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a buried feature has been successfully demonstrated in 2-D
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source localization and study of earthquake source complex- ity. In earthquake source localization, identifying individual arrivals on seismograms is a challenging and time-consum- ing task, particularly when dealing with the large volume of data currently recorded on a daily basis by the stations which make up the Global Seismic Network (GSN) [http://www.iris.edu/about/GSN/]. The arrivals, comprised of a variety of body waves, both compressional and shear, as well as surface waves, are used to locate a seismic source via
with surface features, to date.
The back propagation to find
and 3-D numerical models.
The last topic we describe is TR applied to earthquake
12 Acoustics Today, January 2008