Seismotectonics and analysis of earthquakes from the Hindukush region

Summary. Over 80 earthquakes, exclusively from the Hindukush focal region, which were recorded at the Gauribidanur seismic array (GBA) have been used in this study. These events have similar epicentral distances and a narrow azimuthal range from GBA but varying focal depths from 10 to 240 km. A fault plane dipping steeply (75°) in the north-west direction and striking N 66° E has been investigated on the basis of the spatial distribution of earthquakes in two vertical planes through 68° E and 32° N. Short period P -wave recordings up to 30 s were processed using the adaptive cross-correlation filtering technique. Slowness and azimuthal anomalies were obtained for first arrivals. These anomalies show positive as well as negative bias and are attributed to a steep velocity gradient in the upper mantle between the 400–700 km depth range where the seismic rays have their maximum penetration. Relative time residuals between the stations of GBA owe their origin very near to the surface beneath the array. A search of the signals across the array revealed that most of the events occurring at shallower depths had complex signatures as compared to the deeper events. The structure near the source region, complicated source functions and the scattering confined to the crust—upper mantle near source are mainly responsible for the complexity of the Hindukush earthquakes as the transmission zone of the ray tubes from turning point to the recording station is practically the same.     

Seismic vertical array analysis for phase decomposition

We propose a vertical array analysis method that decomposes complex seismograms into body and surface wave time histories by using a velocity structure at the vertical array site. We assume that the vertical array records are the sum of vertically incident plane P and S waves, and laterally incident Love and Rayleigh waves. Each phase at the surface is related to that at a certain depth by the transfer function in the frequency domain; the transfer function is obtained by Haskell's matrix method, assuming a 1-D velocity structure. Decomposed P , S and surface waves at the surface are estimated from the vertical array records and the transfer functions by using a least-squares method in the frequency domain; their time histories are obtained by the inverse Fourier transform. We carried out numerical tests of this method based on synthetic vertical array records consisting of vertically incident plane P and S waves and laterally incident plane Love and Rayleigh waves. Perfect results of the decomposed P , S , Love and Rayleigh waves were obtained for synthetic records without noise. A test of the synthetic records in which a small amount of white noise was added yielded a reasonable result for the decomposed P , S and surface waves. We applied this method to real vertical array records from the Ashigara valley, a moderate-sized sedimentary valley. The array records from two earthquakes occurring at depths of 123 and 148 km near the array (epicentral distance of about 31 km) exhibited long-duration later phases. The analysis showed that duration of the decomposed S waves was a few seconds and that the decomposed surface waves appeared a few seconds after the direct S -wave arrival and had very long duration. This result indicated that the long-duration later phases were generated not by multireflected S waves, but by basin-induced surface waves.     

Forward modelling of direct current and low-frequency electromagnetic fields using integral equations

We present a semi-analytical, unifying approach for modelling the electromagnetic response of 3-D bodies excited by low-frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell's equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green's function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipoledipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR-TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR-TE, where the mode of conduction is predominantly perpendicular to the profile.     

Wavepath traveltime tomography

The elastic-wave equation is used to construct sensitivity kernels relating perturbations in elastic parameters to traveltime deviations. Computation of the functions requires a correlation of the forward-propagating seismic wavefield with a backward propagation of the residual wavefield. The computation of the wavefields is accomplished using a finite difference algorithm and is efficiently executed on a CM-2 parallel processor. The source and receiver locations have maximum sensitivity to velocity structure. The sensitivity kernels or wavepaths are well suited for transmission traveltime inversion such as cross-borehole tomography and vertical seismic profiling. Conventional ray tomography and wavepath tomography are applied to a set of P -wave arrival times, from a cross-borehole experiment at Kesterson, California. Because the wavepaths have increased sensitivity near the source and receiver there are differences in resolution of the velocity structure. Both techniques recover the same relative variations in velocity where the coverage is adequate. The wavepath solution is more laterally continuous and the dominant variation is vertical, as is expected for the layered sediments in this region.     

Kirchhoff–Helmholtz reflection seismograms in a laterally inhomogeneous multi-layered elastic medium – II. Computations

Summary. High-frequency reflection and refraction seismograms for laterally variable multi-layered elastic media are computed by using the frequency domain elastic Kirchhoff–Helmholtz (KH) theory of Frazer and Sen. Both source and receiver wavefields are expanded in series of generalized rays and then elastic (KH) theory is applied to determine the coupling between each source ray and each receiver ray at each interface. The motion at the receiver is given as a series of integrals, one for each generalized ray. We use geometrical optics and plane wave reflection and transmission coefficients for rapid evaluation of the integrand. When the source or the receiver ray field has caustics on the surface of integration geometrical ray theory breaks down and this gives rise to singularities in the KH integrand. We repair this using methods suggested by Frazer and Sen.
Examples of reflection seismograms for 2-D structures computed by elastic KH theory are shown. Those for a vertical fault scarp structure are compared with the seismograms obtained by physical modelling. Then OBS data obtained from the mid-America trench offshore Guatemala area are analysed by computing KH synthetics for a velocity model that has been proposed for that area. Our analysis indicates the existence of a small low-velocity zone off the trench axis.
No head wave arrivals are obtained in our KH synthetics since we do not consider multiple interactions of a ray with an interface. The nearly discontinuous behaviour of elastic R/T coefficients near the critical angle causes small spurious phases which arrive later than the correct arrivals.     

Long-period corrections to body waves: theory

Summary. The usual asymptotic methods used to correct the high-frequency solutions of the wave equation are unsatisfactory as they do not give the low-frequency, partial reflections expected from a region of high velocity gradient. A new iterative solution is obtained which uses the first term of the Langer asymptotic expansion as the zeroth iterate. This satisfactorily gives the partial reflections from a region of high velocity gradient, even when they are generated near the turning point of the ray. Although the results are somewhat complicated in the frequency domain, in the time domain all types of wave interaction are described by six universal time functions. For any problem, these functions are scaled in time according to the depth of the interaction, and in strength according to the magnitude of the coupling parameter. Numerical results and approximations are given for these functions. Coupling parameters are investigated for acoustic and elastic waves in a plane model, and acoustic and elastic-gravitational waves in a spherical model. The same universal time functions allow the excitation of elastic waves to be studied when the source is in a region of high velocity gradient or is near the wave's turning point. Results are given for a moment tensor, point source in plane and spherical models.     

Generation of the teleseismic P-wave coda from Aleutian earthquakes

We investigate large-amplitude phases arriving in the P -wave coda of broad-band seismograms from teleseisms recorded by the Gräfenberg array, the German Regional Seismic Network and the Global Seismic Network. The data set consists of all events m _b≤ 5.6 from the Aleutian arc between 1977 and 1992. Earthquakes with large-amplitude coda waves correlate with the presence of oceanic crust in the source region. The amplitudes sometimes approach those of the P wave, much larger than predicted by theory. Modelling indicates that phases in the P -wave coda cannot be P -wave multiples beneath the source and receiver, or underside reflections, which precede PP , from upper-mantle discontinuities. Among the events, seismograms are very similar, where the arrival times of the unusual phases agree approximately with the predicted times of S -to- P conversions from the upper-mantle discontinuities under the source. Because the large-amplitude phases in the P -wave coda have little, if any, dependence on event depth and have predominantly an SV -wave radiation pattern towards the receiver, we suggest that they originate as SV and/or Rayleigh waves and are enhanced by lateral heterogeneity and multipathing from the subducting Aleutian slab.     

Improved resolution of reflections from the crystalline upper crust

Summary. Use of higher frequencies and a careful selection of the other data acquisition parameters can significantly enhance the resolution obtained in reflection seismic CDP profiling in hard rock terranes. Experiments with a 20–80 Hz non-linear vibroseis sweep near the projected ADCOH site reveal that the wave-field reflected from the upper crust contains frequencies spanning the entire source spectrum even in the presence of a weathered layer of saprolite. Attenuation of higher frequencies and the severe distortion produced by the 'notch' filter for line-frequency necessitate some pre-processing spectral shaping. The operations are linear and yield, as a by-product, an estimate of the average 'Q' for the section - about 250 in the present case.     

Exact synthetic seismograms for an inhomogeneity in a layered elastic half-space

Summary. The propagation of a pulsed elastic wave in the following geometry is considered. An elastic half-space has a surface layer of a different material and the layer furthermore contains a bounded 3-D inhomogeneity. The exciting source is an explosion, modelled as an isotropic pressure point source with Gaussian behaviour in time.
The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered.
The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P -waves, and head waves.     

A WKBJ spectral method for computation of SV synthetic seismograms in a cylindrically symmetric medium

Summary. A method of synthetic seismogram computation for teleseismic SV -waves is developed in order to treat quantitatively SV -waves in problems of body wave source inversion and source—receiver structure studies. The method employs WKBJ theory for a generalized ray in a vertically inhomogeneous half-space and the propagator matrix technique for waves in near-surface homogeneous layers. Wavenumber integration is done along the real axis of the wavenumber plane and anelasticity is included by using complex velocity in all regions of the earth model. The near-surface source structure is taken into account in the computation for the case of the shallow source by allowing a point source to be located in the homogeneous layers. Source and receiver area structures are also allowed to differ. A general moment tensor point source is considered.     

Matrix Green's functions for array-type sources and receivers in multiwave layered media

Summary. A previous formulation (Lu, Felsen & Kamel) of source-excited wave propagation in a multiwave layer is here extended to multiple layers, each of which may propagate different multiple wave species, and to simultaneous excitation and detection at arbitrarily specified multiple levels. Field variables are arranged so as to reveal 'interesting'layers requiring access (for example, those containing a source and/or receiver) but to hide in collective form all other 'uninteresting'layers. An ordering of wave constituents into array vectors provides not only a physically appealing view of the wave phenomena pertaining to array-type source and receiver arrangements but may also furnish numerical advantages. The variety of alternative representations in Lu et al. can be brought to bear directly on the present formulation which is thereby endowed with substantial versatility, especially that embodied within the hybrid ray-mode format.     

Multipathing and spectral modulation of the downgoing wavefield in a complex crust: an example from the KTB (Germany) borehole

VSP data collected in the KTB (Germany) borehole to a depth of 8.5 km in 1999 show a surprising spectral modulation of the downgoing wavefield. After filtering the data with the singular value decomposition technique it was found that below about 6.2 km there are two depth intervals where the modulation can be explained in terms of a basic wavelet plus two weighted and delayed copies of that wavelet, with the delay for each wavelet remaining almost constant in each interval. The boundary between the two intervals is at about 7.25 km depth and above and below this depth the delay for the second wavelet is almost the same, while the delay for the third wavelet is significantly different. Neither the modulation nor its depth variation are source related and cannot be explained in terms of multiple reflections in a subhorizontal low-velocity layer. On the other hand, finite difference synthetic data show that subvertical layering (which is prevalent in the borehole area) provides a mechanism that can explain the observations. This mechanism has analogies with the generation of the standard refracted (i.e. head) waves. When a plane wave front propagates perpendicular to the boundaries of a vertical low-velocity layer surrounded by two vertical high-velocity layers, refracted wave fronts are generated in the low-velocity layer, which in turn generate secondary wave fronts in the high-velocity layers. These wave fronts trail the primary wave fronts by a constant delay whose magnitude has a simple dependence on the thickness of the low-velocity layer and the velocities involved. This process creates multipath arrivals that in geological settings with steeply inclined and faulted layers may appear and disappear rather abruptly, which may contribute to a scattered appearance of the wavefield.     

Influence of the Interface Fresnel zone on the reflected P-wave amplitude modelling

The aim of the paper is to emphasize the importance of accounting for the Fresnel volume and for the Interface Fresnel zone (IFZ) for calculating the amplitude of the P wave emanating from a point source and recorded at a receiver after its specular reflection on a smooth homogeneous interface between elastic media. For this purpose, by considering the problem of interest as a problem of diffraction by the IFZ, that is, the physically relevant part of the interface which actually affects the reflected wavefield, we have developed a method which combines the Angular Spectrum Approach (ASA) with the IFZ concept to get the 3-D analytical solution. The variation in the reflected P -wave amplitude evaluated with the ASA, as a function of the incidence angle, is compared with the plane wave (PW) reflection coefficient and with the exact solution provided by the 3-D code OASES, for one solid/solid configuration and two dominant frequencies of the source. For subcritical incidence angles the geometrical spreading compensation is mostly quite sufficient to reduce the point-source amplitudes to the PW amplitudes. On the contrary, for specific regions of incidence angles for which the geometrical spreading compensation is not sufficient anymore, that is, near the critical region and in the post-critical domain, the ASA combined with the IFZ concept yields better results than the PW theory whatever the dominant frequency of the source, which suggests that the additional application of the IFZ concept is necessary to obtain the reflected P -wave amplitude. Nevertheless, as the ASA combined with the IFZ has been used only for evaluating the contribution of the reflected wavefield at the receiver, its predictions fail when the interference between the reflected wave and the head wave becomes predominant.     

Sampling efficiency of vertical array aeolian sand traps

Previous investigations have indicated that the sampling efficiency of aeolian sand traps is low and varies greatly in the near-bed region. Outside this region, the efficiency tends to be consistently higher for all types of trap. An evaluation was carried out to compare the sampling efficiency of different types of aeolian sand trap based on the comparison of the “actual” and the measured sand mass flux profiles, with emphasis on the single-tube vertical array trap, conventional array trap, and step-like array trap. A simple formula is proposed to express the actual vertical profile of sand mass flux, which has been validated with the unique data obtained with an isokinetic trap by [Sedimentology 45 (1998) 789]. Using the experimental data collected by the present authors and those by other investigators, sampling efficiencies of three types of trap are examined in terms of the frequency distribution of all the samples. For the single-tube traps, the sampling efficiency varies from 65% to 95%, with a mode at 75%. For both the conventional array and step-like array traps, sampling efficiencies range from 15% to 85%, with the modal frequencies at 35% and 75%, respectively. This review seems to suggest that the peak frequency with higher sampling efficiency coincides with the maximum sand-grain Reynolds number.     

Seismic attenuation values obtained from instantaneous-frequency matching and spectral ratios

In this paper, attenuation values are obtained from seismic data using instantaneous-frequency matching and spectral ratios. to obtain differential t * values using instantaneous-frequency matching, a near offset reference pulse is attenuated until the resulting instantaneous frequency matches the observed value at the receiver. Prior to matching, filtering can be applied to each trace in order to reduce the effects of noise on the calculated instantaneous frequencies. In the second method, the spectral ratio between a receiver pulse and a reference pulse is used to obtain differential t * values. to obtain an unbiased estimate, a variable spectral bandwidth is used depending on the noise level of the data. the two methods are tested using synthetic traces and then applied to crustal refraction data from the 1986 PASSCAL Ouachita experiment. Results show that the differential t * values obtained using filtered, instantaneous-frequency matching are consistent with and have less scatter than those obtained from spectral ratios with a variable bandwidth.     

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.     

New possibilities in controlled-source seismology with a magnetic levitation vibrator

Summary. A new-technology, broad-band seismic land source based on the principle of magnetic levitation is under development. The new source is designed to overcome limitations experienced with controlled-signal seismic sources at the present time, and to create new possibilities. In particular, She new source extends the constant peak force frequency band down to 2 Hz, and is capable of at least several weeks continuous, coherent transmission. It will enable three-dimensional long-range (>200 km) controlled-signal seismology with the potential for active earth tomography down into the mantle and systematic earthquake precursor measurement, and should improve shallow and deep seismic profiling technology. The optimum transmission frequencies depend on Q, transmission range, and noise spectrum.     

Three-dimensional location and waveform analysis of microseismicity in multi-anvil experiments

We present an acoustic emission (AE) monitoring technique to study high-pressure ( P > 1 GPa) microseismicity in multi-anvil rock deformation experiments. The application of this technique is aimed at studying fault mechanisms of deep-focus earthquakes that occur during subduction at depths up to 650 km. AE monitoring in multi-anvil experiments is challenging because source locations need to be resolved to a submillimetre scale due to the small size of the experimental assembly. AEs were collected using an 8-receiver array, located on the back truncations of the tungsten carbide anvils. Each receiver consists of a 150–1000 kHz bandwidth PZT transducer assembly. Data were recorded and processed using a high-speed AMSY-5 acquisition system from Vallen-Systems, allowing waveform collection at a 10 MHz sampling rate for each event signal. 3-D hypocentre locations in the assembly are calculated using standard seismological algorithms. The technique was used to monitor fault development in 3 mm long × 1.5 mm diameter olivine cores during axisymmetric compression and extension. The faults were generated during cold compression to ∼2 GPa confining pressure. Subsequent AEs at 2–6 GPa and 900 °C were found to locate near these pre-existing faults and exhibit high pressure stick-slip behaviour.     

The influence of fluid-sensitive dispersion and attenuation on AVO analysis

Analysis of seismic data suggests that hydrocarbon deposits are often associated with higher than usual values of attenuation, but this is generally ignored during amplitude-versus-offset (AVO) analysis. The effect can be modelled with equivalent medium theory based on the squirt flow concept, but the excess attenuation is associated with strong velocity dispersion. Consequently, when we study reflections from the interface between such an equivalent medium and an elastic overburden we find that the reflection coefficient varies with frequency. The impact of this variation depends on the AVO behaviour at the interface; class I reflections tend to be shifted to higher frequency while class III reflections have their lower frequencies amplified. We calculate synthetic seismograms for typical models using the reflectivity method for materials with frequency dependent velocities and attenuations, and find that these effects are predicted to be detectable on stacked data. Two field data sets show frequency anomalies similar to those predicted by the analysis, and we suggest that our modelling provides a plausible explanation of the observations.     

Gaussian beams for surface waves in laterally slowly-varying media

Summary. Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. Using ray-centred coordinates, parabolic equations are obtained for lateral variations while vertical structural variations at a given point are specified by eigenfunctions of normal mode theory as for the laterally homogeneous case. Final results on wavefields close to a ray can be expressed by formulations similar to those for elastic body waves in 2-D laterally heterogeneous media, except that the vertical dependence is described by eigenfunctions of 'local' Love or Rayleigh waves. The transport equation is written in terms of geometrical-ray spreading, group velocity and an energy integral. For the horizontal components there are both principal and additional components to describe the curvature of rays along the surface, as in the case of elastic body waves. The vertical component is decoupled from the horizontal components. With complex parameters the solutions for the dynamic ray tracing system correspond to Gaussian beams: the amplitude distribution is bell-shaped along the direction perpendicular to the ray and the solution is regular everywhere, even at caustics. Most of the characteristics of Gaussian beams for 2-D elastic body waves are also applicable to the surface wave case. At each frequency the solution may be regarded as a set of eigenfunctions propagating over a 2-D surface according to the phase velocity mapping.