Reply to comment by J. R. Murphy on 'Q for short-period P waves: is it frequency dependent?' by A. Douglas

Using network averaged spectra Murphy (1989) demonstrates that if it is assumed that the source functions of explosions at Pahute Mesa, Nevada Test Site (NTS) are as predicted by the Mueller-Murphy (M-M) source model then the average t * at around 1 Hz for P waves radiated from the test site must be about 0.75 s. With this value of t * Murphy (1989) estimates the best fitting M-M spectrum for each explosion studied, by adjusting A, t _o & c ; A & t _o being the amplitude and delay time of pP relative to P and c the wave speed for the material in which the explosion was fired. The absolute amplitudes of the theoretical spectra are obtained using a calibration factor estimated from the data. Murphy (1993) extends the analysis to explosions in granite at the Nevada, French Sahara and E. Kazakh test sites. For the French Sahara explosion t * is assumed to be 0.75 s (Murphy's estimate for NTS explosions), and for the E. Kazakh explosion a t * of 0.55 s is used. For the French Sahara and E. Kazakh explosions Murphy (1993) shows that by using the same calibration factor as for the NTS it is possible by varying A & t _o to fit the estimated average network spectra using the M-M granite source. Murphy (1993) states that the amplitudes and spectra for the largest NTS explosion in granite (PILE DRIVER) can also be predicted using the M-M model but these results are not shown.     

A fault plane solution using theoretical P seismograms

We use the method of Hudson and Douglas, Hudson & Blarney to compute seismograms which simulate the codas of 10 short period P -wave seismograms from a shallow earthquake. The polarities and relative amplitudes of P and pP measured from seven of the observed seismograms are used to compute a fault plane solution with confidence limits, assuming that the source radiates as a double couple. This solution is in approximate agreement with that given for the same earthquake by Sykes & Sbar, who used only the onset polarities of short-period P waves. The small difference between the two solutions can be explained by interference between the true first motion of P and microseismic noise at two stations.
The results show that, for some shallow earthquakes, the relative amplitude method has the following advantages over the first motions method. First, a P/pP amplitude ratio (with appropriate confidence limits) can always be measured, even in seismograms which are so noisy that the first motion of P is uncertain. Second, the fault plane solutions obtained from relative amplitudes have known confidence limits. Finally, by using more information from each seismogram, the relative amplitude method requires considerably fewer seismograms than the first motions method.     

Deconvolution of teleseismic recordings for mantle structure

Delineation of detailed mantle structure frequently requires the separation of source signature and structural response from seismograms recorded at teleseismic distances. This deconvolution problem can be posed in a log-spectral domain where the operation of time-domain convolution is reduced to an additive form. The introduction of multiple events recorded at many stations leads to a system of consistency equations that must be honoured by both the source time functions and the impulse responses associated with propagation paths between sources and receivers. The system is inherently singular, and stabilization is accomplished through the supply of an initial estimate of the source time function. Although alternative choices exist, an effective estimate is derived from the eigenimage associated with the largest eigenvalue in a singular-value decomposition of the suite of aligned seismograms corresponding to a given event. The relation of the deconvolution scheme to simultaneous least-squares deconvolution is examined. Application of the methodology to broadband teleseismic P waveforms recorded on the Canadian National Seismograph Network demonstrates the retrieval of effective Green's functions including secondary phases associated with upper-mantle structure.     

Complex P waveforms from a Gulf of Aden earthquake

Summary. It is shown that complex teleseismic P waveforms from a shallow earthquake in a tectonic area can be interpreted using a simple source model embedded in a plane layer velocity structure (with sea layer) whose details are based upon independent evidence. This gives hope that structural complexity in tectonic regions may not always make distant P -wave seismograms impossible to interpret, and that, instead, source complexity may be responsible for some of the many complex waveforms observed, even for earthquakes below magnitude m _b 5.5.     

Shear-coupled PL

Summary. Observed teleseismic shear-coupled PL -waves ( SPL ) display a variety of waveforms depending on factors such as source depth, source type and velocity structure. Using a WKBJ spectral method for SV -wave propagation, synthetic seismograms of SPL are produced to examine the factors important in SV and SPL excitation. Results show that SPL is preferentially excited by shallow sources compared to deep sources. This is due to large source area reverberations which consequently leak as SV -waves into the mantle. Interaction at the receiver area then sets up the classic prograde elliptical motion by which SPL can be identified. This is in accordance with the teleseismic observations and indicates that most previous models for the propagation of SPL were not appropriate for shallow source since emphasis was placed on wave interactions occurring only near the receiver.     

Fault plane solutions using relative amplitudes of P and pP

Summary. One way of finding the fault plane orientations of small shallow earthquakes is by the generation of theoretical P -wave seismograms to match those observed at several distant stations. Here, a technique for determining the uniqueness of fault plane solutions computed using the modelling method of Douglas et al . is described. Relative amplitudes of P and pP , and their polarities if unambiguous, are measured on the observed seismograms to be modelled, and appropriate confidence limits are assigned to each measurement. A systematic search is then made for all fault plane orientations which satisfy these observations.
Examples show that if P and pP are not severely contaminated by other arrivals, a well-defined and unique fault plane orientation can often be computed using as few as three stations well distributed in azimuth. Further, even if pP is not identifiable on a particular seismogram, then an upper bound on its amplitude – deduced from the observed coda – still places a significantly greater constraint on the fault plane orientation than would be provided by a P onset polarity alone. Modelling takes account of all such information, and is able to further eliminate incompatible solutions (e.g. by the correct simulation of sP ). It follows that if solutions can be found which satisfy many observed seismograms, this places high significance on the validity of the assumed double-couple source mechanism.
This relative amplitude technique is contrasted with the familiar first motion method of fault plane determination which requires many polarity readings, whose reliabilities are difficult to quantify. It is also shown that fault plane orientations can be determined for earthquakes below the magnitude at which first motion solutions become unreliable or impossible.     

A near-regional explosion source model for tuff

Summary. A variety of near-regional (300 km) data, including spectral amplitudes of Pg , surface-wave forms, and close-in (5–10 km) accelerograms have been used to build an elastic seismic source model for a 1-Mton explosion in tuff at near-regional distances. The model consists of: (1) a pressure pulse which injects 3 × 10¹² cm³ of volume into the medium, (2) a vertical, upward force impulse that imparts 10¹⁸ dyn-s of momentum to the medium, each source component having a time duration of 0.6 s and a depth of 1.3 km. The force impulse appears to be required by two considerations: (a) the striking similarity, apart from sign, of explosion surface waves with those of their cavity collapses, (b) the observation of considerable SV energy leaving the source of the 1-Mton explosions JORUM and HANDLEY . Scaling curves have been constructed which fit the proposed source model. These scaling curves employ: very slow decrease, as (yield)^−0.10 of the primary corner frequency; decay as (frequency)⁴ or (frequency)³ to high frequency. While these scaling curves are unconventional, they appear to be the only ones which can satisfy the near-regional data. The slow scaling with yield of the spectral carner frequency suggests that it is caused by something other than the equivalent elastic radius, e.g. the time duration of motion at the source. The results, at odds with similar studies at teleseismic distances, suggest that significantly different equivalent elastic sources are required at near-regional (as compared with teleseismic) distances; therefore, the effect of the upward impulse might not be seen at teleseismic distances. Consequently, these results probably do not pertain to the seismic discrimination problem at teleseismic distances.     

Teleseismic body wave radiation from a seismic source in a layered medium

Summary. A simple method is presented which combines the reciprocity theorem and the flat layer theory to yield teleseismic body wave radiation from seismic sources embedded in the Earth's crust. The source is represented by its equivalent body forces and can be quite general. The effect of Yucca Flat geology on explosion signals is studied in detail. In particular, the m _b— M _s relation is shown to be dependent on detonation medium and source depth. Application to shallow earthquake faults demonstrates the strong influence of free surface and layering on the shape of P- and S-wave teleseismic spectra.     

Errors in focal depth determination and the depth of seismicity in Iran and Turkey

Summary. It is the supposed presence of intermediate depth earthquakes in areas of continental collision which supports the existence of subducting slabs in regions such as the Zagros mountains of Iran. Mounting field evidence from that region suggests that intermediate focal depths allocated by tele-seismic locations are wrong. No pP depth control exists for earthquakes in the Zagros and all teleseismic locations use P phases alone.
This paper examines the effect of random noise in arrival-time data on the variances calculated for origin time and hypocentral depth. These can be simply related to the distribution of recording stations and it can be shown that in any one region the smaller shocks will tend to have greater errors in depth than the larger. However, this effect cannot alone account for all the probable mislocation in depth of some small shocks in the Zagros. The discrepancy may, however, be explained by the difference in the quality of arrival-time data between large and small events. It is also shown that crustal earthquakes will have greater errors in depth than earthquakes of equivalent size in the mantle. If reliably read, PKP phases can help contribute to the accuracy of hypocentral depth. The conclusion is that although errors in origin time and depth are well correlated for teleseismic locations of all earthquakes, the value of the errors themselves may be small for the bigger shocks, and this may explain why standard bulletin locations seem to give very reasonable focal depths for the biggest events in Iran. Thus the focal depths of the smaller earthquakes (which include all the published deeper ones in the Zagros) are unreliable, while the focal depths for the largest events are likely to be much better.     

Seismic response characteristics of marine reflection profiling systems

Summary. Factors influencing the seismic response characteristics of marine profiling systems are reviewed. The single frequency case is used to illustrate the influence of different frequencies on the response, as well as the towing depths of the source and receiver, and the geometry of a linear receiving array. The more realistic case of band-limited source waveforms is considered, using frequency spectra calculated from theoretically derived airgun signals. The results show that the number and shape of sidelobes of the profiling system response, as well as the filtering characteristics for reflections arising from reflectors in the vertical plane perpendicular to the axis of the receiver array are determined by the depths of the source and receiver and the relative amplitudes of the frequencies in the source waveform. These factors, along with the configuration of the hydrophone elements in the receiver array, determine the frequency and amplitude attenuation of reflections in the vertical plane containing the receiver array.
The filtering characteristics of the system both in and out of the vertical plane containing the receiver array are discussed, with implications for discriminating between off-axis and in-plane reflections. A plan view of the response of the system is constructed in the time domain for various profiling configurations and sources of different frequency content at a given time. This example shows how useful the resulting pictures are for optimizing acquisition parameters in profiling experiments.     

Imaging crustal discontinuities and the downgoing slab beneath western Crete

The migration of teleseismic receiver functions yields high-resolution images of the crustal structure of western Crete. Data were collected during two field campaigns in 1996 and 1997 by networks of six and 47 short-period three-component seismic stations, respectively. A total of 1288 seismograms from 97 teleseismic events were restituted to true ground displacement within a period range from 0.5 to 7 s. The application of a noise-adaptive deconvolution filter and a new polarization analysis technique helped to overcome problems with local coda and noise conditions. The computation and migration of receiver functions results in images of local crustal structures with unprecedented spatial resolution for this region. The crust under Crete consists of a continental top layer of 15–20 km thickness above a 20–30 km thick subducted fossil accretionary wedge with a characteristic en echelon fault sequence. The downgoing oceanic Moho lies at a depth of 40–60 km and shows a topography or undulation with an amplitude of several kilometres. As a consequence of slab depth and distribution of local seismicity, the Mediterranean Ridge is interpreted as the recent accretionary wedge.     

t*— an unsuitable parameter to characterize anelastic attenuation in the Eastern Carpathians

Investigation of teleseismic P -wave recordings at a temporary network in the Eastern Carpathians, equipped with predominantly short-period sensors, is compared with synthetic modelling of anelastic attenuation of teleseismic waves in the upper mantle. Using the t * approach, we examine variations of amplitude decrease over frequency for teleseismic recordings in the frequency band 0.5–1.5 Hz. The results reveal a consistent pattern of increased t * values in the centre of the network, in the Vrancea region at the bend of the Carpathian Arc, although the magnitude of the observed variation in t * is much higher than expected. Synthetic t * parameter computations for the same event-receiver configurations reproduce the observed pattern in terms of relative variations. However, the amplitude of the synthetic t * values explains only 10–20 per cent of the observed variation in t *. t * is not a direct measure for anelastic attenuation but rather for a combination of anelastic and other attenuating effects such as scattering and amplitude fluctuation related to velocity inhomogeneities. If regional amplitude variations are solely attributed to anelastic attenuation, all other effects are mapped into Q . We discuss the role of anelastic attenuation and other effects in the case of the Eastern Carpathians and conclude that t * is an unsuitable parameter to characterize anelastic attenuation in the Eastern Carpathians.     

Lower-crustal rifting in the Rukwa Graben, East Africa

An M_w 5.9 earthquake occurred in the Lake Rukwa rift, Tanzania, on 1994 August 18, and was well recorded by 20 broad-band seismic stations at distances of 160 to 800 km and 21 broad-band stations at teleseismic distances. The regional and teleseismic waveforms have been used to investigate the source characteristics of the main shock, and also to locate aftershocks that occurred within three weeks of the main shock. Teleseismic body-wave modelling yields the following source parameters for the main shock: source depth of 25 ± 2 km, a normal fault orientation, with a horizontal tension axis striking NE-SW and an almost vertical pressure axis (Nodal Plane I: strike 126°–142°, dip 63°–66°, and rake 280°–290°; Nodal Plane II: strike 273°–289°, dip 28°–31°, and rake 235°–245°), a scalar moment of 4.1 times 10¹⁷ N m, and a 2 s impulsive source time function. Four of the largest aftershocks also nucleated at depths of 25 km, as deduced from regional sPmp–Pmp times. The nodal planes are broadly consistent with the orientation of both the Lupa and Ufipa faults, which bound the Rukwa rift to the northeast and southwest, respectively. The rupture radius of the main shock, assuming a circular fault, is estimated to be 4 km with a corresponding stress drop of 6.5 MPa. Published estimates of crustal thickness beneath the Rukwa rift indicate that the foci of the main shock and aftershocks lie at least 10 km above the Moho. The presence of lower-crustal seismicity beneath the Rukwa rift suggests that the pre-rift thermal structure of the rifted crust has not been strongly modified by the rifting, at least to depths of 25 km.     

Receiver functions at the stations of the German Regional Seismic Network (GRSN)

Several years of broad-band teleseismic data from the GRSN stations have been analysed for crustal structure using P -to- S converted waves at the crustal discontinuities. An inversion technique was developed which applies the Thomson-Haskell formalism for plane waves without slowness integration. The main phases observed are Moho conversions, their multiples in the crust, and conversions at the base of the sediments. The crustal thickness derived from these data is in good agreement with results from other studies. For the Gräfenberg stations, we have made a more detailed comparison of our model with a previously published model obtained from refraction seismic experiments. The refraction seismic model contains boundaries with strong velocity contrasts and a significant low-velocity zone, resulting in teleseismic waveforms that are too complicated as compared to the observed simple waveforms. The comparison suggests that a significant low-velocity zone is not required and that internal crustal boundaries are rather smooth.     

Matrix and Stokes vector representations of detectors for polarized waveforms: theory, with some applications to teleseismic waves

This paper deals with the problem of detecting polarized waveforms in multivariate time series. Detectors are designed in the frequency domain using the spectral matrix and matrix-algebra, and also a Stokes vector-algebra. All the detectors are expressed as functions of inner products in real vector spaces, and consequently are extremely easy to program for digital computers, and are computationally very efficient. Several suggestions for the application of the detectors to the interpretation of teleseismic waveforms are given.     

A Teleseismic Delay Time Study Across the Central African Shear Zone In the Adamawa Region of Cameroon, West Africa

Summary. P -wave relative teleseismic residuals were measured for a network of seismological stations along a 300 km profile across the Adamawa Plateau and the Central African Shear Zone of central Cameroon, to determine the variation in crust and upper mantle velocity associated with these structures. A plot of the mean relative residuals for the stations shows a long wavelength (> 300 km) variation of amplitude 0.45 s. the slowest arrivals are located over and just to the north, of the faulted northern margin of the Adamawa Plateau. the residuals do not correlate with topography, surface geology or the previously determined crustal structure, in any simple way.
The Aki inversion technique has been used to invert the relative residuals into a 3-D model of velocity perturbations from a mean earth model. the results show the region is divided roughly into three blocks by two subvertical boundaries, striking ENE and traversing both the crust and upper mantle down to depths greater than 190km. the central block, which is 2 per cent slower than the adjacent blocks, roughly corresponds to the Central African Shear Zone. the Adamawa Plateau, as an individual uplifted area, is explained by the interaction of a regional anomalous upper mantle associated with the West African Rift System, and the Central African Shear Zone, which provided a conduit for heat flow to the surface.     

Fault plane solutions using relative amplitudes of P and surface reflections: further studies

Summary. The method of computing fault plane solutions for small shallow earthquakes using relative amplitudes of P and pP , as described in an earlier paper, is extended to include sP. It is shown theoretically that even a single relative amplitude observation can impose a severe constraint on the orientation of an assumed double couple source, and earthquakes studied in the earlier paper are reprocessed with the inclusion of sP information. The method is also extended to deep earthquakes using long period seismograms, and to undersea earthquakes by allowing for the effect of a sea layer on the surface-reflected phases. Also described are options to search only a restricted range of source orientations, and to identify those orientations which are incompatible with one or more relative amplitudes. These options are applied to several earthquakes, to demonstrate the scope of the relative amplitude method. Results are illustrated using the seismic modelling method of Hudson (1969a, b) and Douglas, Hudson & Blamey (1972).     

Massif Central (France): new constraints on the geodynamical evolution from teleseismic tomography

The Massif Central, the most significant geomorphological unit of the Hercynian belt in France, is characterized by graben structures which are part of the European Cenozoic Rift System (ECRIS) and also by distinct volcanic episodes, the most recent dated at 20 Ma to 4000 years BP. In order to study the lithosphere-asthenosphere system beneath this volcanic area, we performed a teleseismic field experiment.
During a six-month period, a joint French-German team operated a network of 79 mobile short-period seismic stations in addition to the 14 permanent stations. Inversion of P -wave traveltime residuals of teleseismic events recorded by this dense array yielded a detailed image of the 3-D velocity structure beneath the Massif Central down to 180 km depth. The upper 60 km of the lithosphere displays strong lateral heterogeneities and shows a remarkable correlation between the volcanic provinces and the negative velocity perturbations. The 3-D model reveals two channels of low velocities, interpreted as the remaining thermal signature of magma ascent following large lithospheric fractures inherited from Hercynian time and reactivated during Oligocene times. The teleseismic inversion model yields no indication of a low-velocity zone in the mantle associated with the graben structures proper. The observation of smaller velocity perturbations and a change in the shape of the velocity pattern in the 60–100 km depth range indicates a smooth transition from the lithosphere to the asthenosphere, thus giving an idea of the lithosphere thickness. A broad volume of low velocities having a diameter of about 200 km from 100 km depth to the bottom of the model is present beneath the Massif Central. This body is likely to be the source responsible for the volcanism. It could be interpreted as the top of a plume-type structure which is now in its cooling phase.     

Improved ocean-geoid resolution from retracked ERS-1 satellite altimeter waveforms

The ocean geoid can be inferred from the topography of the mean sea surface. Satellite altimeters transmit radar pulses and determine the return traveltime to measure sea-surface height. The ERS-1 altimeter stacks 51 consecutive radar reflections on board the satellite to a single waveform. Tracking the time shift of the waveform gives an estimate of the distance to the sea surface. We retrack the ERS-1 radar traveltimes using a model that is focused on the leading edge of the waveforms. While earlier methods regarded adjacent waveforms as independent statistical events, we invert a whole sequence of waveforms simultaneously for a spline geoid solution. Smoothness is controlled by spectral constraints on the spline coefficients. Our geoid solutions have an average spectral density equal to the expected power spectrum of the true geoid. The coherence of repeat track solutions indicates a spatial resolution of 31  km, as compared to 41  km resolution for the ERS-1 Ocean Product. While the resolution of the latter deteriorates to 47  km for wave heights above 2  m, our geoid solution maintains its resolution of 31  km for rough sea. Retracking altimeter waveform data and constraining the solution by a spectral model leads to a realistic geoid solution with significantly improved along-track resolution.     

The elastodynamic near field

Summary. The elastodynamic fields of point forces and shear dislocations of finite source duration are analysed with the aim of establishing the frequency and time-domain characteristics of the field in the near-source region. Criteria are obtained for amplitude dominance in regions where the source–sensor distance is much smaller than the wavelength.
It is shown that in the frequency domain , the Green's tensor (and hence the displacement field of a single point force) attenuates like R ⁻¹ in the near-source region and there exists no region in which the 'near-field' term becomes dominant such that the 'far-field' term can be neglected. Hence, there is no real 'near-field' term for the elastodynamic Green's tensor. The near-field terms of the displacements, velocities and accelerations excited by a shear dislocation attenuate like R ⁻², since the R ⁻³ and R ⁻⁴ terms tend to be eliminated due to mutual cancellation of P and S motions in the near-source region.
In the time domain , the corresponding near field of the displacement field is defined for the steady amplitude interval (away from transients) R /β < t < R /α+ T by the condition R ≤βT where β is the shear velocity and T is the source's duration. The relative strengths of all other arrivals will depend on the particular time window under consideration.
The particle motion patterns due to a single force in the near-source region are shown to be similar to rotating hyperbolas with an axis along the force direction, which are quite different from the 'smoke ring' motion patterns of the so-called 'near-field' term itself.