P-wave Pulse Research Articles

An EGF technique to infer the source parameters of a circular crack growing at a variable rupture velocity

Circular crack models with a constant rupture velocity struggle to effectively model both the amplitude and duration of first P-wave pulses generated by small magnitude seismic events. Assuming a constant rupture velocity is unphysical, necessitating a deceleration phase in the rupture velocity to uphold the causality of the healing process. Moreover, a comprehensive failure model might encompass an initial nucleation phase, typically characterized by an increase of the initial rupture velocity. Studies have demonstrated that quasi-dynamic circular crack models featuring variable rupture velocities can accurately model the shape of the observed first P-wave pulse. Based on these principles, an Empirical Green’s function (EGF) approach was previously formulated to estimate the source parameters of small magnitude earthquakes, called MAIN. In addition to determine the source radius and stress drop, this method also enables the inference of the temporal evolution of rupture velocity. However, this method encounters difficulties when the noise-to-signal ratio in the recordings of smaller earthquakes used as EGF exceeds 5%, a common situation when employing regional-scale recordings of small-magnitude earthquakes as EGF. Through synthetic tests, we demonstrated that, in such instances, the problem of this technique is that the alignment between the onset of P waves of EGF and MAIN is not rightly recovered after the initial inversion step. Consequently, a novel inversion method has been developed to address this issue, enabling the identification of the optimal alignment of P-wave arrivals in EGF and MAIN across all stations. A Bayesian statistical approach is proposed to meticulously investigate the solutions of model parameters and their correlations. Using the new technique on a small magnitude earthquake (ML = 3.3) occurred in Central Italy enabled us to identify the most likely rupture models and examine the issue of correlation among model parameters. Application of Occam’s Razor Principle suggests that, for the investigated event, a circular crack model should be favored over a heterogeneous rupture model.

The 2022 MW 6.0 Gölyaka–Düzce earthquake: an example of a medium-sized earthquake in a fault zone early in its seismic cycle

Abstract. On 23 November 2022, a MW 6.0 earthquake occurred in the direct vicinity of the MW 7.1 Düzce earthquake that ruptured a portion of the North Anatolian Fault in 1999. The Mw 6.0 event was attributed to a small portion of the Karadere fault off the main North Anatolian Fault that did not rupture during the 1999 sequence. We analyze the spatiotemporal evolution of the MW 6.0 Gölyaka–Düzce seismic sequence at various scales and resolve the source properties of the mainshock. Modeling the decade-long evolution of the background seismicity of the Karadere fault employing an Epistemic Type Aftershock Sequence model shows that this fault was almost seismically inactive before 1999, while a progressive increase in seismic activity is observed from 2000 onwards. A newly generated high-resolution seismicity catalog from 1 month before the mainshock until 6 d after was created using artificial-intelligence-aided techniques and shows only a few events occurring within the rupture area within the previous month, no spatiotemporal localization process and a lack of immediate foreshocks preceding the rupture. The aftershock hypocenter distribution suggests the activation of both the Karadere fault, which ruptured in this earthquake, and the Düzce fault that ruptured in 1999. First results on the source parameters and the duration of the first P-wave pulse from the mainshock suggest that the mainshock propagated eastwards, which is in agreement with predictions from a bimaterial interface model. The MW 6.0 Gölyaka–Düzce event represents a good example of an earthquake rupture with damaging potential within a fault zone that is in a relatively early stage of the seismic cycle.

Wettability-dependent wave velocities and attenuation in granular porous media

Understanding seismic wave propagation in granular porous media is important for subsurface characterization. The presence of fluids, their distribution, and the prevailing wettability condition result in additional complexities. Although it is known that wave propagation in dry granular porous media is dominated by the presence of force chains, their influence in (partially) saturated granular porous media with different wettability conditions remains largely unexplored. To make progress in this direction, we have designed laboratory experiments by combining core flooding and ultrasonic measurements in glass bead packings that are chemically treated to alternate the wettability. The P- and S-wave velocity-saturation relation and attenuation-saturation relation are retrieved from the waveforms for water- and gas-wetting samples. The results demonstrate that there is a transition from an attenuating but stable P-wave pulse at low and moderate saturation to a set of incoherently scattered waves at high saturation. The incoherent scattering in the gas-wetting case is negligibly small, whereas it is more pronounced in the water-wetting case. We interpret these observations in terms of the wettability-dependent ability for water to penetrate into grain contacts. In the water-wetting case, liquid bridges are thought to locally reinforce the force chains and to increase their characteristic length scale. This leads to an increase in P-wave velocity and promotes incoherent scattering because the ratio of dominant wavelength to characteristic length scale decreases. In the gas-wetting case, however, the presence of gas prevents the water from direct contact with the glass beads and therefore stops the formation and growth of the liquid bridges within the force-chain network.

Reduction of peak ground velocity by nonlinear soil response — II: excitation by a P-wave pulse

Reduction of peak ground velocity by nonlinear soil response — II: excitation by a P-wave pulse

Reduction of peak ground velocity by nonlinear soil response – III: Excitation by an SV-wave pulse

We study how the peak velocity of an SV-wave pulse on the ground surface of a two-dimensional soil valley is reduced by loss of wave energy during large nonlinear response inside the valley. This is a follow-up on our previous studies in which we considered excitation by an SH-pulse and a P-wave pulse. We consider in-plane response for incident angle below critical and assume that the soil material does not support tension, but the normal stress at a point in the soil can be compression. A point in the soil with zero stress behaves as stress-free, does not transmit normal stress and appears as a crack. We study the interplay of two opposing effects. The first effect is a jump in impedance from a higher value (in the half-space) to a lower value (in the valley), which amplifies the linear motions at the free surface of the valley. The second effect is the occurrence of nonlinear zones in the valley, which reduce the motion at the valley surface. We show how, for small excitations, when the response is linear or almost linear, the valley amplifies the motion. As the excitation amplitudes increase, at low frequencies, at which the nonlinearities are weak, the effect of decrease in impedance is stronger than the effect of nonlinear zones and the valley amplifies the motion. At higher frequencies, the effect of nonlinearity becomes stronger and the amplitudes of motion are reduced. As the excitation further increases, the effect of nonlinear soil response prevails at all frequencies and the motion is reduced significantly.

Characterizing CO2 plumes in deep saline formations: Comparison and joint evaluation of time-lapse pressure and seismic tomography

Monitoring the migration of sequestered [Formula: see text] in deep heterogeneous reservoirs is inherently difficult. Geophysical methods have been successfully used, but flow conditions are only indirectly linked to the measured properties. Besides geophysical methods, pressure tomography (PT) is proposed as an alternative method to depict the structure of deep saline formations for [Formula: see text] sequestration and to continuously delineate [Formula: see text] plumes. In contrast to more established geophysical measurements, pressure transients are directly related to flow properties, which allows for the estimation of permeability. We investigate the influence of aquifer heterogeneity on PT performance, and we compare the PT results to crosshole seismic tomography (ST). Multilevel fluid injections and high-frequency P-wave pulses are induced in a simulated deep borehole, and the recorded signals at another well are processed by a traveltime inversion scheme. The reservoir structure is inferred by clustering the inverted hydraulic diffusivity prior to [Formula: see text] injection, and the plume distribution is determined by clustering the tomograms of the inverted mixed-phase diffusivity difference and P-wave velocity difference. The clustered structures are then used for zonal calibration to acquire the saturation within the plumes. Modeling results indicate that PT provides clearer structural information on the [Formula: see text]-free aquifer due to its direct linkage to permeability. However, the plume depicted by PT can be ambiguous, whereas ST is less sensitive to the prevailing heterogeneity of permeability at postinjection and can thus image the plume more clearly. PT and ST can be complementary to each other through the joint clustering to improve plume shape identification and estimation of spatial [Formula: see text] saturation.

Two-dimensional translation, rocking, and waves in a building during soil-structure interaction excited by a plane earthquake P-wave pulse

A two-dimensional model of a building supported by a rectangular, flexible foundation embedded in the soil is analyzed for excitation by an incident plane P-wave. The building, the foundation, and the soil have different material properties. The building is assumed to be anisotropic and linear, while the soil and the foundation are assumed to be isotropic and can experience nonlinear deformations. In general, the work spent for the development of nonlinear strains in the soil can consume a significant part of the input wave energy and thus less energy is available for the excitation of the building. However, in the case of excitation by a plane P-wave pulse, we show that the nonlinear response in the soil and the foundation does not significantly change the nature of excitation in the base of the building. It is noted that the response of a building can be approximated by base translation and rocking for excitation by long, strong motion waves.

Freeze–thaw fracturing in building granites

Four types of granite widely exported and used in construction around the world were subjected to 280 accelerated freeze–thaw test cycles, conducted as stipulated in European standard UNE-EN, 12371, 2001 to ascertain their petrophysical response.The techniques used to characterise the granite before and after freeze–thaw-induced microcracking included vacuum water absorption, ultrasonic P-wave pulse velocity and ultrasonic S-wave pulse velocity, mercury intrusion porosimetry and polarised optical and fluorescence microscopy to quantify the type of microcracks developing (inter-, intra- or transcrystalline) and identify the associated mineral phases: quartz, feldspar and biotite. The linear crack density (number of cracks per millimetre) was calculated based on the microscopic data collected. Young's modulus was likewise found before and after the freeze–thaw cycles.The chief ice crystallisation mechanism was involved in microcracking and hence deterioration was ice segregation. In all four granites, ultrasonic propagation velocities and strength parameters declined with the development of freeze–thaw-induced microcracking. More intercrystalline microcracks were developed in the early cycles, while larger numbers of intracrystalline microcracks were found at the end of the test.The results of this study can be applied to other granites with similar characteristics and whose microcracks are generated with same mechanisms of frost damage.Upon conclusion of the cycles, Zarzalejo granite exhibited the largest number of microcracks, with a linear crack density of 3.9, as well as the highest rise in microcracking. Colmenar Viejo ended the freeze–thaw test with the fewest number of microcracks and a post-test linear crack density of 2.3, denoting greater freeze–thaw resistance. The smallest increase in the number of microcracks was found for Cadalso de los Vidrios granite.The microscopic and microporosity findings reported in this paper revealed the existence of freeze–thaw test-induced microcracking which, while barely affecting mechanical stability (Young's modulus), did cause damage.

Source parameters of the M 6.5 Skyros Island (North Aegean Sea) earthquake of July 26, 2001

Teleseismic body wave modelling, time domain moment tensor inversion of regional waveforms and spectral analysis of the far-field P-wave pulses are used to derive the source parameters of the July 26, 2001 Skyros earthquake (M 6.5). Its epicentre is located south of the Sporades Islands in the North Aegean Sea (Greece). Previous focal mechanism solutions indicate motion on strike-slip faults. The time domain moment tensor inversion is applied for the first time to the regional waveforms of the recently established broadband network in Greece. Its application gave results which are highly consistent with teleseismic waveform modelling. The results of this study, in combination with the distribution of aftershocks, indicate left-lateral strike slip motion on a NW-SE striking fault with parameters: fault plane (strike = 151°, dip = 83°, rake = 7°) and auxiliary plane (strike = 60°, dip = 84°, rake = 173°), depth 12 km and M 0 = 5.98e18 Num. Moreover, the time domain moment tensor inversion technique yielded a pure double couple source with negligible CLVD. The spectral analysis of the far-field P-wave pulses resulted in a fault length L ~ 32 km, stress drop 6m ~ 9 bars and average displacement u ~ 30 cm. These values are in very good agreement with those estimated from empirical scaling relations applicable to the Aegean area.

Effect of Sliding Rate on the Activity of Acoustic Emission During Stable Sliding

—The mechanical and statistical characteristics of acoustic emission (AE) events during stable sliding are investigated through a laboratory experiment using a granite specimen with a pre-cut fault. Numerous AE events are found to be generated on the pre-cut fault, indicating that microscopically unstable fracture occurs during macroscopically stable sliding. The composite focal mechanism solution of AE events is determined from the first motion directions of P-waves. The determined mechanism is consistent with the double-couple one expected for the slip on the pre-cut fault. The source radii of large AE events are estimated to be about 10 mm from the widths of the first P-wave pulses. These indicate that the AE events are generated by shear fracture whose faulting area is a part of the pre-cut fault plane. The occurrence of AE events as a stochastic process approximately obeys the Poisson process, if the effect of mutually dependent events consti tuting clusters is corrected. The observed amplitude-frequency relation of AE events approximately follows a power law for a limited amplitude range. As the macroscopic sliding rate increases, the number of AE events per unit sliding distance decreases. This rate dependence of the AE activity is qualitatively consistent with the observation that the real area of contact between sliding surfaces decreases with an increase in the sliding rate as reported in the literature.

Attenuation of body waves in Southeastern Sicily (Italy)

The attenuation of P- and S-waves in Southeastern Sicily was estimated by applying two different methods in time and frequency domains. We analyzed waveforms from about 290 local events (0.6≤ M L≤4.6) recorded at a three-component digital network. By applying the pulse broadening method to the first P-wave pulse, we found an average Q p value of ca. 140. The application of the frequency decay method provided a Q p value of ca. 120, in the low-frequency band (3–9 Hz). Conversely, in the high frequency range (16–27 Hz) the average Q p is significantly larger (ca. 640). The frequency decay method was also applied to S-waves spectra. In the low frequency range (2–5 Hz) the estimated average Q s is ca. 190. As for Q p, also Q s, in the high frequency range (16–27 Hz), is larger (ca. 700). These results evidenced a frequency dependence of both the quality factors Q p and Q s, as commonly observed in tectonically active zones characterized by high degree of heterogeneity.

Effects of Source RDP Models and Near-source Propagation: Implication for Seismic Yield Estimation

Ithas proven difficult to uniquely untangle the source and propagation effects on the observed seismic data from underground nuclear explosions, even when large quantities of near-source, broadband data are available for analysis. This leads to uncertainties in our ability to quantify the nuclear seismic source function and, consequently the accuracy of seismic yield estimates for underground explosions. Extensive deterministic modeling analyses of the seismic data recorded from underground explosions at a variety of test sites have been conducted over the years and the results of these studies suggest that variations in the seismic source characteristics between test sites may be contributing to the observed differences in the magnitude/yield relations applicable at those sites. This contributes to our uncertainty in the determination of seismic yield estimates for explosions at previously uncalibrated test sites. In this paper we review issues involving the relationship of Nevada Test Site (NTS) source scaling laws to those at other sites. The Joint Verification Experiment (JVE) indicates that a magnitude(m b )bias(6m b )exists between the Semipalatinsk test site (STS) in the former Soviet Union (FSU) and the Nevada test site (NTS) in the United States. Generally thisSmbis attributed to differential attenuation in the upper-mantle beneath the two test sites. This assumption results in rather large estimates of yield for largem b tunnel shots at Novaya Zemlya. A re-examination of the US testing experiments suggests that thisSm b bias can partly be explained by anomalous NTS (Pahute) source characteristics. This interpretation is based on the modeling of US events at a number of test sites. Using a modified Haskell source description, we investigated the influence of the source Reduced Displacement Potential (RDP) parameters LKand Bby fitting short-and long-period data simultaneously, including the near-field body and surface waves. In general, estimates of Band Kare based on the initial P-wave pulse, which various numerical analyses show to be least affected by variations in near-source path effects. The corner-frequency parameter Kis 20% lower at NTS (Pahute) than at other sites, implying larger effective source radii. The overshoot parameter Bappears to be low at NTS (although variable) relative to other sites and is probably due to variations in source conditions. For a low B,the near-field data require a higher value of to match the long-period M s and short-periodmbobservations. This flexibility in modeling proves useful in comparing released FSU yields against predictions based onm b andM s .

The 1996 June 17 Flores Sea and 1994 March 9 Fiji-Tonga earthquakes: source processes and deep earthquake mechanisms

Source parameters of the 1996 Flores Sea and 1994 Fiji–Tonga deep earthquakes are derived from teleseismic body waves recorded by the global seismic network of broad-band seismograph stations. Both events consisted of several subevents. Models to approximate the spatial and temporal extent of the source process include point sources, propagating point sources and a combination of these. For the Flores Sea event, rupture lasted about 23 s and terminated some 70 km east of the nucleation point as inferred from the duration of P-wave pulses, in agreement with the findings reported by other investigators. Our preferred model suggests bilateral rupture propagation. It consists of four point sources that have variable double-couple radiation patterns and source time histories, and explains well the large compensated linear vector dipole (CLVD) component inferred from the Harvard centroid moment tensor (CMT) solution. The main moment release in the Fiji–Tonga event lasted only about 15 s. Our best model consists of two point sources with a total moment release of 2.8 × 1020 N m. Rupture propagated subhorizontally from the nucleation point to the north. The termination of rupture was located about 40 km to the north of rupture initiation. The inferred velocity of moment release in the Flores Sea and Fiji–Tonga events was 3–5 km s-1, a value which is higher than that inferred for the great Bolivian earthquake of June 1994. Other derived source parameters (static stress drop, radiated seismic energy and maximum seismic efficiency) are also significantly different from those inferred for the 1994 Bolivian event, suggesting that deep earthquake processes do not follow an easily detectable common mechanism.

Attenuation of short-period seismic waves at Mt Vesuvius, Italy

We analysed short-period seismograms from about 250 very local events recorded by a network of high dynamic range short-period seismic stations deployed on Mt Vesuvius to estimate the site-corrected short-period seismic attenuation. We calculated QC− 1, the inverse of the quality factor for coda waves, for short lapse times (12 s), and QP− 1 and QS− 1, the inverse of the direct body wave quality factors for P and S waves follow- ing shallow ray paths. We used the single scattering assumption to fit the amplitude envelopes of the coda at different frequency bands, obtaining a QC− 1 slowly varying with frequency, similar to values measured for other volcanoes at the same lapse time. Site-corrected QP− 1 and QS− 1 were estimated using the frequency decay method for both P and S waves in two frequency bands, 1–6 Hz and 15–24 Hz. Results show that QP− 1 is 0.028 in both frequency bands, and QS− 1 is 0.015 and 0.017 at low and high frequencies respectively, almost independent of the frequency, and that the value of QP− 1 is about twice that of QS− 1, as measured worldwide. A check was made by measuring the broadening of the first P-wave pulse with station–source distance, finding QP− 1=0.024. Using the independent estimates of QC− 1 and QS− 1, we separated the intrinsic from the scattering quality factor at Mt Vesuvius, obtaining a high scattering and a low intrinsi c Q− 1, as already observed for other volcanoes. This result confirms the hypothesis of the predominant role of the scattering phenomena with respect to the intrinsic dissipation in the seismogram formation for volcanic earthquakes.

Fault Lengths During the Patras 1993 Earthquake Sequence as Estimated from the Pulse Width of Initial P Wave

Usually, earthquake source parameters are estimated using spectral techniques; the corner frequency is related to a source dimension through scaling laws that make assumptions about source geometry and rupture velocity, and the seismic moment is evaluated from the long-period spectral level (i.e., BRUNE, 1970). This conventional method however is not highly efficient when we deal with a large number of earthquakes, as in the present case. An alternative approach is based on the measured pulse width of the initial P wave at an observation station of far-field. Pulse width methods, like spectral methods, do not require precise measurement of pulse amplitudes or instrumental response. Unlike spectral methods, though, the pusle width methods only require a very short part of the first arriving signal, which is relatively free of other interfering waveforms such as reflection, scattering, or multiple travel paths (WU and LEES, 1996). In order to make accurate spectrum estimates, spectral methods typically use 0.5 to 2 sec of data, whereas the pulse width may be estimated over half a wavelength of the P-wave arrival. O’NEILL and HEALY (1973) proposed such an approach for a spherical source. FRANKEL (1981) applied this method for an expanding circular crack. FRANKEL and KANAMORI (1983) extended the initial P-wave pulse width method by

Measuring wave propagation characteristics in artificial sand-clay mixtures

Ultrasonic compressional (V p ) and shear (V s ) velocities have been measured on artificial sand-clay mixtures. The measurements were carried out in a drained triaxial load cell using a pulse transition method. The measuring device was equiped with a waveform storage facility. The investigated mixtures consisted mainly of kaolinite and quartz sand. Some mixtures also contained Na-montmorillonite, illites or quartz-flour. The acoustic behaviour was observed during a pressure increase up to 72 MPa vertical and 36 MPa horizontal pressure. At a given pressure,V p andV s in pure sand turned out to be similar to those in pure kaolinite. As predicted by the sand-clay model of Marion (1990), a velocity maximum corresponds to a minimum in total porosity. This porosity minimum marks the transition from a clayey sand to a sandy clay. It is not only reflected in bothV p andV s , but also in the quality of the received pulse. The effective tension of the received signal during 20µs after the first arrival, was used as an indication for P-wave pulse attenuation. This apparent attenuation decreases with increasing clay content and increases with increasing porosity. It is shown that clay mineralogy does not measurably affect wave velocities in clayey sands.

Aftershock stress release along active fault planes of the 1984 Round Valley, California, earthquake sequence applying a time-domain stress drop method

AbstractThe 23 November 1984 ML 5.8 Round Valley earthquake is one in a series of moderate (ML ≈ 6) earthquakes to have occurred in the Bishop-Mammoth Lakes, California, area since 1978. This earthquake and its aftershock sequence occurred within a dense seismic network, and hypocentral location quality is excellent. In a previous study, we determined that the Round Valley sequence involved faulting on a conjugate set of fault planes; one, a near-vertical plane striking N30°E, the mainshock fault plane showing principally left-lateral strike-slip motion, and another subperpendicular to the mainshock fault plane striking N40°W and dipping 55°NE, exhibiting dominantly right-lateral strike slip. This conjugate fault plane conforms to a postulated extension of the Hilton Creek fault and is the only significant activity on this structure in the 12-year Bishop-Mammoth Lakes earthquake sequence. Source dimensions and stress drops for 87 aftershocks (ML 2.8 to 4.2) of the Round Valley sequence have been determined using an adaptation of the initial P-wave pulse width time-domain deconvolution technique of Frankel and Kanamori (1983). The aftershock sequence is confined to a limited volume of crust. We have shown that site and instrument effects and not whole-path attenuation control the minimum pulse widths for this limited region. The determination of a site minimum pulse width, rather than a minimum pulse width for each source receiver pair as in the Frankel and Kanamori study, makes the deconvolution procedure practical for processing the large numbers of events in an aftershock sequence. With the large data set available for the Round Valley aftershock sequence, patterns of the stress drop along the active fault planes can be seen in detail. Source radii systematically increase with magnitude from about 100 m for events near magnitude 3.0 to 500 m for events near magnitude 4.0. Static stress drops range from 10 to 200 bars and are not strongly correlated with magnitude or depth. The stress release pattern reveals a broad stress drop low (Δσ ≈ 10 bars) for aftershocks within the mainshock fault plane that is consistent with other evidence of the rupture surface of the Round Valley mainshock. Higher stress release occurs above and below the mainshock rupture surface and on the shallower, conjugate fault plane. Further distant from the rupture surface of the mainshock, stress drops decrease to average values. On the conjugate fault surface, stress drops are seen to be high in areas that may be interpreted as “off-fault” clusters with respect to the mainshock rupture surface.

The effect of crustal scattering on observed high-frequency earthquake seismograms

A comparison of high-frequency (1–100 Hz) local (out to 40 km) earthquake seismograms at stations of the Southern Black Forest Digital Seismic Network is made in an attempt to isolate the effects of near-receiver structure and of crustal scattering on the waveforms of the direct body-waves and on the coda waves. Angle of incidence and azimuth of approach analyses from lower-crustal earthquakes show that near-surface weathering layers with low body-wave velocities and with laterally varying thicknesses exist under all of the stations, even those at hard rock sites of the Black Forest. The similarity of direct P-wave pulse shapes at each site for events of different sizes, the time-domain form of the so-called fmax phenomenon, is attributed to the response from this weathering zone. The amplitude of the P-wave coda of an event is found to be independent of the earthquake radiation pattern and to depend only on the absolute size of the event and on epicentral distance to the receiver. Furthermore, the high-frequency P-wave coda is found to be generated, at least in part, from random crustal scattering, including that within 100 m of the earthquake focus. Direct S waveforms are shown to be more complicated than their P-wave counterparts, probably due to the same near-receiver and crustal scattering phenomena. However, in the case of S waves scattered energy can arrive before as well as at and after the direct S arrival, making the identification of the direct S difficult, especially for nodal arrivals.

Earthquake seismograms that show Doppler effects due to crack propagation

Examples are presented of earthquake P-wave pulses seen on broadband seismograms, to show that on such recordings the pulse shapes are more clearly seen than on conventional short-period and long-period seismograms. Most of the broadband seismograms have been chosen because they show marked differences between the pulse lengths of P and those of the surface reflections. In addition some of the pulses appear to have smooth onsets and abrupt trailing edges so that the onset of the pulse is difficult to observe and the largest amplitude arrivals seen on the seismogram coincide not with the onset of motion but with the termination of motion: that is the large arrivals mark stopping phases of motion. We assume that the differences in pulse length are due to the effects of a moving source — that is a Doppler effect — and that the pulses with smooth onsets and abrupt trailing edges can be modelled simply by a source propagating on a line with low radiation amplitude at the start of motion. A trial and error method guided by a published fault plane solution is then used to obtain a fit between observed and computed seismograms for one of the earthquakes. This process leads to an estimate of the crack speed of about 1.4 times the S-wave speed. The errors that may arise in estimating source depths and orientation, if stopping phases are not recognized as such, is discussed.

Time functions appropriate for some aftershocks of the point Mugu, California earthquake of February 21, 1973

abstract Broad-band recordings of aftershocks of the Pt. Mugu earthquake at small epicentral distances provided an excellent opportunity to test source models for small earthquakes. Simple events recorded at nearly vertical incidence produced a single P-wave pulse of a duration of about 0.07 sec and a somewhat more complicated S wave with a slightly longer duration. Such events are consistent with a point dislocation source for which Qβ = 100 or for which there is directivity with the fault breaking downward. We attribute the more usual complexities of small earthquake records to multiple events, some of which we observed, layering effects combined with greater epicentral distances, and scattering.