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.     

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).     

Earthquake seismograms that show Doppler effects due to crack propagation

Summary. 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 5-wave speed.
The errors that may arise in estimating source depths and orientation, if stopping phases are not recognized as such, is discussed.     

The PWaves From the Amchitka Island Explosions

Summary. There is evidence that the equivalent seismic sources of the Amchitka Island explosions — Longshot, Milrow and Cannikin — depart significantly from the simple model of a point compressional-source in a layered elastic-medium. Consequently modelling the observed seismograms using standard source-models may not be the most efficient method of determining source properties. Here an alternative to modelling is used to obtain information on the seismic sources due to the explosions. Broad-band (BB) estimates of the P signals are obtained from the short-period (SP) seismograms, corrected for attenuation, and interpreted in terms of P, pP and radiation from secondary sources. the main conclusions are:
(i) BB estimates of the radiated displacement from the explosions can be obtained with only a small reduction in the signal-to-noise ratio seen on SP seismograms;
(ii) observations of differences in pulse amplitudes and spectra are not necessarily due to differences in anelastic attenuation;
(iii) P and pP at a given station may differ in shape so that notches in the signal spectrum may not be related to source depth;
(iv) there is evidence of arrivals that others have identified as due to slap-down but which could be interpreted as an overshoot to pP;
(v) direct interpretation of the estimated ground displacement is a better procedure for determining the seismic source properties of explosions than modelling SP seismograms using idealised models as a starting point.     

High-resolution structures of the Landers fault zone inferred from aftershock waveform data

High-frequency body waves recorded by a temporary seismic array across the surface rupture trace of the 1992 Landers, California, earthquake were used to determine fault-zone structures down to the seismogenic depth. We first developed a technique to use generalized ray theory to compute synthetic seismograms for arbitrarily oriented tabular low-velocity fault-zone models. We then generated synthetic waveform record sections of a linear array across a vertical fault zone. They show that both arrival times and waveforms of P and S waves vary systematically across the fault due to transmissions and reflections from boundaries of the low-velocity fault zone. The waveform characteristics and arrival-time patterns in the record sections allow us to locate the boundaries of the fault zone and to determine its P - and S -wave velocities independently as well as its depth extent. Therefore, the trade-off between the fault-zone width and velocities can be avoided. Applying the method to the Landers waveform data reveals a low-velocity zone with a width of 270–360 m and a 35–60 per cent reduction in P and S velocities relative to the host rock. The analysis suggests that the low-velocity zone extends to a depth of ∼7 km. The western boundary of the low-velocity zone coincides with the observed main surface rupture trace.     

A seismological study of normal faulting in the Demirci, Alaşehir and Gediz earthquakes of 1969–70 in western Turkey: implications for the nature and geometry of deformation in the continental crust

Summary. In this study, seismological techniques are combined with surface observations to investigate the faulting associated with three large earthquakes in western Turkey. All involved normal faulting that nucleated at 6–10 km depth with dips in the range 30–50°. The two largest earthquakes, at Alaşehir (1969.3.28) and Gediz (1970.3.28), were clearly multiple events and their seismograms indicate that at least two discrete subevents were involved in producing the observed surface faulting. In addition, their seismograms contain later, longer-period signals that are likely to represent source, not structure or propagation, complexities. These later signals can be modelled by subevents with long time functions on almost flat detachment-type faults.
As a result of these observations, we propose a model for the deformation of the lower crust, in which brittle failure of the top part occurs when high strain rates are imposed during an earthquake that ruptures right through the upper, brittle crust. Under these special circumstances, seismic motion occurs on discrete faults in the lower crust, which otherwise normally deforms by distributed creep. In the case of the normal faults studied here, motion in the uppermost lower crust takes place on shallow dipping faults that are downward continuations of the steeper faults that break to the surface. The faults thus have an overall listric geometry, flattening into a weak zone below the brittle layer at a depth that is probably dependent on the termperature gradient. This interpretation explains why detachment-type mechanisms are not seen in first motion fault plane solutions of normal faulting earthquakes, and suggests an origin for the Metamorphic Core Complexes seen in the Basin and Range Province, which probably represent flat lower crustal faults, analogous to those postulated at Alaşehir and Gediz, that have been uplifted to the surface.     

Piezomagnetic potentials due to an inclined rectangular fault in a semi-infinite medium

Analytical solutions for the piezomagnetic potentials are derived for strike-slip, dip-slip and tensile-opening fault motions with arbitrary dip and strike angles, so as to be applicable in various types of earthquakes. These solutions are expressed as the composition of elementary functions which are identical to the magnetic potentials produced by magnetic dipoles, quadrupoles and octupoles distributed on the fault plane and other planes. Therefore, the geomagnetic field changes due to the piezomagnetic effect are expressed by the superposition of the fields produced by these equivalent sources.
Examples of calculated results show characteristic features for various types of fault motions as follows: (1) the pattern of the geomagnetic field changes becomes significantly different depending on the strike direction, although the maximum amplitude is almost the same for all directions; (2) the geomagnetic field change reaches a maximum at a dip angle of 90° for strike-slip and tensile-opening fault motions and at 45° for dip-slip fault motion.     

Amplification of ground motion and waveform complexity in fault zones: examples from the San Andreas and Calaveras Faults

Summary. P -wave seismograms at ranges less than 10 km are synthesized by asymptotic ray theory and by summation of Gaussian beams for point sources located in a low-velocity wedge surrounding a fault. The computations are performed using models of the wedge inferred from the analysis of reflection and refraction experiments across the San Andreas and Hayward-Calaveras faults. Calculations in these models show that the 10–20Hz vertical displacements of earthquakes located at 3–10km depth are amplified by up to an order of magnitude in a 1–2km wide region centred on the fault trace compared to displacements predicted by laterally homogeneous models of the crust. This amplification is not cancelled by high attentuation in the fault zone and compensates for the reduction in amplitudes directly above the source predicted from the radiation pattern of a strike-slip earthquake. Depending on the source depth of the earthquake and the structure and velocity contrast of the wedge, multiple triplications in the travel-time curve of direct P - and S -waves will occur at stations in the fault zone. A wedge model successfully predicts the triplications observed in the P waveforms of aftershocks of the Coyote Lake earthquake recorded in the fault zone, showing that body waves from microearthquakes can be used to determine the three-dimensional velocity structure of the fault zone. The amplification, waveform complexity, and distortion of ray paths introduced by the low- velocity wedge suggest that its effects should be included in the interpretation of strong ground motions and travel times observed in the fault zone. For realistic models of the wedge, asymptotically approximate methods of calculating the body waveforms are strictly valid for frequencies greater than 20Hz. Numerical methods may be necessary to calculate accurately the wavefield at lower frequencies.     

Shear-wave polarizations on a curved wavefront at an isotropic free surface

Summary. We present polarization diagrams of the particle motions at the free surface of an isotropic half-space generated by incident shear waves from a local buried point source. The reflectivity technique is used to calculate synthetic seismograms from which the particle motions are plotted. The particle motions are examined over a range of epicentral distances in a uniform isotropic half-space for different source frequencies and polarization angles, and for different Poisson's ratios. The particle motions due to a curved wavefront possess different characteristics from those generated by plane wavefronts at corresponding incidence angles. A curved wavefront generates a local SP -phase: a P -headwave which propagates along the free surface, and arrives shortly before the direct S -wave. These two arrivals give rise to cruciform particle motions in the sagittal and horizontal planes, which could be misinterpreted as anisotropy-induced shear-wave splitting. An examination of the particle motion in the transverse plane, mutually orthogonal to the sagittal and horizontal planes, can be used to discriminate between isotropic and anisotropic interpretations. The amplitude of the SP -phase is enhanced when it propagates in a low-velocity surface layer overlying the source layer, and may then become the dominant phase on radial-component seismograms. The presence of even a single surface layer may introduce considerable complexity into the seismogram, and we examine the effects of layer thickness, velocity contrast, and source depth on the corresponding polarization diagrams. Reliable information on the source and propagation path characteristics of shear waves from a buried local point source can only be obtained from free-surface records if they are recorded within a very limited epicentral distance range.     

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.     

A method of extracting phase-velocity curves from seismograms

Summary. The Lanczos method of separating exponentials is applied to the Fourier transform of seismograms in order to separate the various modes that contribute to the given portion of the seismograms. Phase velocities and amplitudes are obtained as functions of the frequency. When applying the method to artificial seismograms, which are built as an exact superposition of a number of modes, the separation is very accurate. The method was also applied to the surface-wave portion of numerical seismograms for a vertical point force in a layered medium. The phase velocity and amplitude of the fundamental mode are obtained. These functions were taken as the first guess in the Backus—Gilbert generalized inverse procedure and the process converged very rapidly. When a perturbation of the phases and amplitudes is taken as the first guess the process converges to the true model when enough data are available.     

Determination of the fault plane using a single near-field seismic station with a finite-dimension source model

We explore the possibility of determining the actual fault plane of an earthquake from the inversion of near-source displacement seismograms of one station when a finite-dimension source is used instead of a point source model and when the complete displacement is taken into account, including near-field waves. Tests on synthetic seismograms and real data recorded at local distances show that this is possible even with a single, three-component station. A single accelerogram available for the Erzincan, Turkey, 1992 March 13, M _s = 6.8 earthquake is inverted and the solution found is compatible with other seismological studies and with the mechanism expected for the North Anatolian Fault.     

Focal mechanisms of recent earthquakes in the Southern Korean Peninsula

We evaluate the stress field in and around the southern Korean Peninsula with focal mechanism solutions, using the data collected from 71 earthquakes ( M_L = 1.9–5.2) between 1999 and 2004. For this, the hypocentres were relocated and well-constrained fault plane solutions were obtained from the data set of 1270 clear P -wave polarities and 46 SH / P amplitude ratios. The focal mechanism solutions indicate that the prevailing faulting types in South Korea are strike-slip-dominant-oblique-slip faultings with minor reverse-slip component. The maximum principal stresses (σ₁) estimated from fault-slip inversion analysis of the focal mechanism solutions show a similar orientation with E–W trend (269°–275°) and low-angle plunge (10°–25°) for all tectonic provinces in South Korea, consistent with the E–W trending maximum horizontal stress (σ_Hmax) of the Amurian microplate reported from in situ stress measurements and earthquake focal mechanisms. The directions of the intermediate (σ₂) and minimum (σ₃) principal stresses of the Gyeongsang Basin are, however, about 90 deg off from those of the other tectonic provinces on a common σ₂–σ₃ plane, suggesting a permutation of σ₂ and σ₃. Our results incorporated with those from the kinematic studies of the Quaternary faults imply that NNW- to NE-striking faults (dextral strike-slip or oblique-slip with a reverse-slip component) are highly likely to generate earthquakes in South Korea.     

Focal Mechanism of the Koyna, India Earthquake of 1967, December 10

One of the two alternate fault plane solutions determined in this study for the Koyna earthquake of 1967 December 10 shows a component of normal faulting. This possibility remained unnoticed in previous focal mechanism studies. Both solutions show left lateral motion along the nodal plane striking towards north-north-east. The origin of the tectonic stress causing the earthquake is believed to be related to the collision of Indian and Eurasian continents, following which the entire Indian Peninsula may be under a state of left lateral shear.     

Simulations of strong ground motion for earthquakes in the Mexicali–Imperial Valley region

Summary. In this paper computer modelling is used to test simple approximations for simulating strong ground motions for moderate and large earthquakes in the Mexicali–Imperial Valley region. Initially, we represent an earthquake rupture process as a series of many independent small earthquakes distributed in a somewhat random manner in both space and time along the rupture surface. By summing real seismograms for small earthquakes (used as empirical Green's functions), strong ground motions at specific sites near a fault are calculated. Alternatively, theoretical Green's functions that include frequencies up to 20 Hz are used in essentially similar simulations. The model uses random numbers to emulate some of the non-deterministic irregularities associated with real earthquakes, due either to complexities in the rupture process itself and/or strong variations in the material properties of the medium. Simulations of the 1980 June 9 Victoria, Baja California earthquake ( M _L= 6.1) approximately agree with the duration of shaking, the maximum ground acceleration, and the frequency content of strong ground motion records obtained at distances of up to 35 km for this moderate earthquake. In the initial stages of modelling we do not introduce any scaling of spectral shape with magnitude, in order to see at what stage the data require it. Surprisingly, such scaling is not critical in going from M = 4–5 events to the M = 6.1 Victoria earthquake. However, it is clearly required by the El Centro accelerogram for the Imperial Valley 1940 earthquake, which had a much higher moment ( Ms ∼ 7). We derive the spectral modification function for this event. The resulting model for this magnitude ∼ 7 earthquake is then used to predict the ground motions at short distances from the fault. Predicted peak horizontal accelerations for the M ∼ 7 event are about 25–50 per cent higher than those observed for the M = 6.1 Victoria event.     

Earthquake processes of the Himalayan collision zone in eastern Nepal and the southern Tibetan Plateau

Focal mechanisms determined from moment tensor inversion and first motion polarities of the Himalayan Nepal Tibet Seismic Experiment (HIMNT) coupled with previously published solutions show the Himalayan continental collision zone near eastern Nepal is deforming by a variety of styles of deformation. These styles include strike-slip, thrust and normal faulting in the upper and lower crust, but mostly strike-slip faulting near or below the crust–mantle boundary (Moho). One normal faulting earthquake from this experiment accommodates east–west extension beneath the Main Himalayan Thrust of the Lesser Himalaya while three upper crustal normal events on the southern Tibetan Plateau are consistent with east–west extension of the Tibetan crust. Strike-slip earthquakes near the Himalayan Moho at depths >60 km also absorb this continental collision. Shallow plunging P -axes and shallow plunging EW trending T -axes, proxies for the predominant strain orientations, show active shearing at focal depths ∼60–90 km beneath the High Himalaya and southern Tibetan Plateau. Beneath the southern Tibetan Plateau the plunge of the P -axes shift from vertical in the upper crust to mostly horizontal near the crust–mantle boundary, indicating that body forces may play larger role at shallower depths than at deeper depths where plate boundary forces may dominate.     

Seismic body waves in anisotropic media: synthetic seismograms

Summary. Synthetic seismograms and particle motion diagrams are computed for simple, layered Earth models containing an anisotropic layer. The presence of anisotropy couples the P, SV and SH wave motion so that P waves incident on the anisotropic layer from below produce P, SV and small-amplitude SH waves at the surface both the P velocity and the amplitudes of the converted phases vary with azimuth. Significant SH amplitudes may be generated even when the wavelength of the P wave is much greater than the thickness of the anisotropic layer. Incident SV or SH waves may each generate large amplitudes of both SV and SH motion. This strong coupling is largely independent of the degree of velocity anisotropy of the medium. The arrivals from short-period S waves exhibit S-wave splitting, but arrivals from longer period S waves superpose into a modified waveform. This strong coupling does not allow the arrival of separate phases with pure SV and SH polarization except along directions of symmetry where the motion decouples.     

Modelling of ground motion in the Higashinada (Kobe) area for an aftershock of the 1995 January 17 Hyogo-ken Nanbu, Japan, earthquake

We model the ground motion from an aftershock of the 1995 January 17 Hyogo-ken Nanbu (Kobe) earthquake to investigate basin edge effects on wave propagation in Higashinada ward, downtown Kobe. Point-source finite-difference seismograms calculated using a double-couple solution and a 2-D basin structure are compared with the ground-motion velocity seismograms recorded in a small station array deployed at sites within and outside the heavily damage zone in Higashinada ward. The comparison suggests that in the frequency range 0.1-2 Hz that was analysed, the observed spatial amplitude variation of the aftershock ground motion is attributable mainly to the basin edge effects. We found that the basin edge effect, caused by the superposition of the direct S wave and the basin-edge-diffracted waves, amplified the ground motion in a narrow zone that is offset by about 0.7 km from the basin edge.     

1986年冬季中国南极长城站的地震观测

1986年3月30日至12月25日为期271天的冬季地震观测中,中国南极长城站地震台共记录到各种震动3000余次,其中大部分为长城湾冰层破裂产生的微震,4次为南设得兰群岛邻近海域中的浅源地震以及5月7日阿留申群岛发生的8.1级地震和4月14日南桑韦奇群岛发生的6.4级地震。冰震与构造地震具有明显的差异。1986年11月16日的地震记录为分析冰震与构造地震的区别提供了很好的例证。冰震具有初动尖锐、频率高和衰减快的特征。根据初动和波型很容易将冰震与构造地震区分开。     

Source investigation of a small event using empirical Green's functions and simulated annealing

We propose a two-step inversion of three-component seismograms that (1) recovers the far-field source time function at each station and (2) estimates the distribution of co-seismic slip on the fault plane for small earthquakes (magnitude 3 to 4). The empirical Green's function (EGF) method consists of finding a small earthquake located near the one we wish to study and then performing a deconvolution to remove the path, site, and instrumental effects from the main-event signal.
The deconvolution between the two earthquakes is an unstable procedure: we have therefore developed a simulated annealing technique to recover a stable and positive source time function (STF) in the time domain at each station with an estimation of uncertainties. Given a good azimuthal coverage, we can obtain information on the directivity effect as well as on the rupture process. We propose an inversion method by simulated annealing using the STF to recover the distribution of slip on the fault plane with a constant rupture-velocity model. This method permits estimation of physical quantities on the fault plane, as well as possible identification of the real fault plane.
We apply this two-step procedure for an event of magnitude 3 recorded in the Gulf of Corinth in August 1991. A nearby event of magnitude 2 provides us with empirical Green's functions for each station. We estimate an active fault area of 0.02 to 0.15 km² and deduce a stress-drop value of 1 to 30 bar and an average slip of 0.1 to 1.6 cm. The selected fault of the main event is in good agreement with the existence of a detachment surface inferred from the tectonics of this half-graben.