ALBERT

Notes: P seismograms recorded in Europe from some of the earthquakes that occur at depths of around 100 km in northern Chile show three prominent arrivals P, bP and pP; bP being interpreted as a conversion of downward radiated S to P at a discontinuity in wavespeed beneath the source. On broad-band seismograms the duration of the P pulse is around 5s, that of bP around 2s and that of pP around 12s. These differences in duration have been interpreted as Doppler effects due to the motion of the source of seismic radiation, this being assumed to be a near-unilateral fracture propagating downwards on a steeply-dipping fault-plane. For the downward radiated pulses (P and bP) the source is travelling towards the observer whereas for the upward radiated pulse (pP) the source is receding from the observer.The near-unilateral fracture interpretation of the differences in pulse duration is based on data from the earthquake of 1976 November 30 recorded on effectively one azimuth (∼30-40°), which is towards Europe. To give further support to the interpretation requires data from a wider range of azimuths but this is not available for the 1976 earthquake. However, data from the northern Chile earthquake of 1980 May 26 are available from four stations covering an azimuthal range of 180°: Eskdalemuir, Scotland (EKA, azimuth 31.6°); Blacknest, England (BNA, azimuth 35.6°); Gauribidanur, India (GBA, azimuth 95.2°) and Warramunga, Australia (WRA, azimuth 212.0°). The 1980 earthquake, which appears to have a very similar mechanism to that of the 1976 earthquake, is investigated here to see if the observations are consistent with the near-unilateral fracture mechanism.The first motion of P and pP where these can be observed and the general form of the broad-band seismograms are consistent with the presence of a nodal plane dipping steeply towards the east. P is observed to be small relative to the surface reflection pP at EKA, BNA and GBA where P leaves the source close to a node, and P is large relative to pP at WRA where P leaves the source away from the node and the take-off of pP is close to a node.Taking the steeply-dipping nodal plane to be the fault plane, the fault dimensions and fracture speeds compatible with the pulse durations are estimated. Using one of the compatible solutions (fault length 40 km, maximum width, 18 km, fracture speed 0.5P wavespeed, maximum dimension oriented downdip) seismograms are computed and compared to the observed. The computed seismograms simulate the pulse durations and relative amplitudes of most of the main pulses. The detailed form of the main pulses is not modelled possibly because the fault model used is oversimplified. The complexity of the observed pulses presumably indicates that the distribution of slip on the fault plane varies less smoothly than assumed in the model.To determine the detailed distribution and time history of slip on the fault requires data from a larger number of well-distributed stations than is available here. However, if it is accepted that the pulse durations of P, bP and pP given are reliable and that hP is an S-to-P conversion at a boundary below the source then the conclusion seems to be inescapable that the source was a near-unilateral fracture propagating downwards on a steeply-dipping fault-plane.

Notes: Theory predicts that pulses that propagate on stationary non-minimum time paths, such as the PP path, undergo phase shifts such that the onset is emergent and the observed pulse is non-causal relative to the arrival time predicted by ray theory. The phase shift isπ/2 radians, at least at high frequencies, so that the observed pulses should approximate to the Hilbert transform of the pulse recorded over a minimum time path. Although onsets of phases that follow non-minimum time paths (usually called mini-max phases) are predicted to be emergent, those observed often seem clear and no more difficult to read than those of arrivals that follow minimum time paths. An example of a PP seismogram which is clearly emergent is shown here. Simulations obtained by Hilbert transforming the impulse responses of conventional long-period and short-period seismographs convolved with attenuation operators. show that the first half-cycle of mini-max phases which should have the emergent onset will usually be of low amplitude relative to the second half-cycle. This suggests that on observed seismograms the first half-cycle of mini-max phases may be obscured by earlier arrivals. The second half-cycle will then be taken as the first motion and could appear to have a well-defined onset. The effects of phase shifts that result in emergent onsets can be corrected for to some extent, and ideally onset times of mini-max phases would be read from such corrected records. However. onset times of PP read directly from conventional seismograms are reported in bulletins and these times have been assumed by some to be reliable enough to be used to determine anomalies in wavespeed in the upper mantle in the vicinity of the reflection point. Perhaps surprisingly the assumption appears to be justified in that the apparent onset time of a mini-max phase on a conventional short-period seismograph may be little different from the onset time read after correction for the π/2 phase shifts.