A numerical method to determine physical source parameters from free oscillation data

A method to determine physical source parameter using free oscillation data is presented. It is assumed that the geometry of the source is known, e.g. from P -wave data. The source is assumed to propagate in the horizontal direction, while unknown parameters to be determined are the azimuth and velocity of propagation, the distance over which the seismic source propagated and the source intensity as a function of propagation distance.
The method consists in the systematic search for the set of source parameters rendering phase corrections which maximize the spectral peak amplitudes within the excitation criterion scheme.
If there is no precursive motion, the average dislocation time function can be determined from the spectrum of the seismic moment and the space source intensity. The source intensity as a function of instantaneous source location is found independently of the P -wave origin time and source dislocation time function. The method does not require to correct the data for attenuation.     

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.     

Seismic anisotropy within the uppermost mantle of southern Germany

This paper presents an updated interpretation of seismic anisotropy within the uppermost mantle of southern Germany. The dense network of reversed and crossing refraction profiles in this area made it possible to observe almost 900 traveltimes of the P_n phase that could be effectively used in a time-term analysis to determine horizontal velocity distribution immediately below the Moho. For 12 crossing profiles, amplitude ratios of the P_n phase compared to the dominant crustal phase were utilized to resolve azimuthally dependent velocity gradients with depth. A P -wave anisotropy of 3–4 per cent in a horizontal plane immediately below the Moho at a depth of 30 km, increasing to 11 per cent at a depth of 40 km, was determined. For the axis of the highest velocity of about 8.03 km s⁻¹ at a depth of 30 km a direction of N31°F was obtained. The azimuthal dependence of the observed P_n amplitude is explained by an azimuth-dependent sub-Moho velocity gradient decreasing from 0.06 s⁻¹ in the fast direction to 0 s⁻¹ in the slow direction of horizontal P -wave velocity. From the seismic results in this study a petrological model suggesting a change of modal composition and percentage of oriented olivine with depth was derived.     

Detailed S-wave structure in the Dublin Basin and its northern margin

Summary. The seismic structure has been measured to a depth of about 3 km along a 30 km seismic profile in east central Ireland. This profile is unusual in that it is the S -wave velocity—depth structure that has been measured to a degree of precision more normally associated with P -wave results. One reason for this is that the sources used were quarry blasts which generated strong S -waves and short-period surface waves but rather weak P -waves.
The results show a layer of Carboniferous limestone with shear velocity 2.65 km⁻¹ s overlying a layer with a velocity of 3.06 km s⁻¹. This second layer was interpreted as Lower Palaeozoic strata (Silurian/Ordovician) since this velocity was evident in an inlier seen at the surface at the northern end of the line. A third refraction horizon, shear velocity 3.45 km s⁻¹ and displaying a basinal structure, was also recognized. This may be Cambrian or Precambrian basement.     

Constraining velocity and density contrasts across the crust–mantle boundary with receiver function amplitudes

This paper investigates the ability of P -wave receiver functions to constrain both the velocity and density contrasts across the Moho. Expressions for receiver function amplitudes corresponding to a layer over a half-space are extended to media with depth-dependent properties by explicitly accounting for free-surface reflection coefficients. Forward numerical computations show that receiver function amplitudes become frequency-dependent for depth-dependent structures and that, for a given frequency, wavelengths associated to Ps converted phases are larger than wavelengths associated to multiply reverberated phases. When consistent measurements of the amplitudes of Ps phase and multiples can be obtained, the extended expressions suffice to account for the observed amplitudes. Receiver function amplitudes are sensitive to both velocity and density contrasts across the Moho, and a two-step grid-search procedure is proposed to recover the contrasts from their measurement. The near-surface velocity is recovered in the first step from the amplitude of the direct P wave and then used in the second step to work out the relative density and S -wave velocity contrast from the amplitude of the secondary phases. Examples from central Spain (PAB) and the Indian Shield (HYB) are discussed and demonstrate that receiver function amplitudes can constrain contrasts across the Moho accurately enough to be utilized in geological interpretation.     

Seismic body waves in anisotropic media: reflection and refraction at a plane interface

Summary. A formulation is derived for calculating the energy division among waves generated by plane waves incident on a boundary between generally anisotropic media. A comprehensive account is presented for P, SV and SH waves incident from an isotropic half-space on an orthorhombic olivine half-space, where the interface is parallel to a plane of elastic symmetry. For comparison, a less anisotropic medium having transverse isotropy with a horizontal axis of symmetry is also considered. The particle motion polarizations of waves in anisotropic medium differ greatly from the polarizations in isotropic media, and are an important diagnostic of the presence of anisotropy. Incident P and SV waves generate quasi- SH waves, and incident SH waves generate quasi- P and quasi- SV waves, often of considerable relative magnitude. The direction of energy transport diverges from the propagation direction.     

Traveltimes for infrasonic waves propagating in a stratified atmosphere

The tau– p method of Buland & Chapman (1983) is reformulated for sound waves propagating in a stratified atmosphere under the influence of a height-dependent wind velocity profile. For a given launch angle along a specified azimuth, the ray parameter is redefined to include the influence of the horizontal wind component along the direction of wave propagation. Under the assumption of negligible horizontal wind shear, the horizontal wind component transverse to the ray propagation does not affect the direction of the wave normal, but displaces the reference frame of the moving wavefront, thus altering the observed incidence azimuth. Expressions are derived for the time, horizontal range, and transverse range of the arriving waves as a function of ray parameter. Algorithms for the location of infrasonic wave sources using the modified tau– p formulation in conjunction with regional atmospheric wind and temperature data are discussed.     

The polarization of P-waves in anisotropic media

Summary. The paper examines P -wave propagation in anisotropic solids, and demonstrates the effect of anisotropy on the polarizations of quasi P -waves. The deviation of the polarization of the quasi P -wave from the propagation vector may be significant, but is in almost the same direction as the deviation of the group-velocity vector. Since the group-velocity, or energy propagation, vector follows seismic ray paths, the apparent deviation is the difference of the polarization and group-velocity deviations and is small. Consequently, it may be easily overlooked, hidden by noise, or attributed to the effects of inhomogeneity.     

Recurrence relations for computing complete P and SV seismograms

Summary. A set of recurrence relations which are computationally more efficient than those of the reflection matrix method of Kennett & Kerry is presented for P - and SV -wave generation in a ( n + 1) layered medium. The recurrence relations contain no growing terms and thus provide a stable algorithm for computing complete P and SV synthetic seismograms. Our algorithm requires a fewer algebraic operations for computing the reflectivity and transmissivity coefficients, ranging from 15 per cent less for a source in the half-space to 30 per cent less for a source in the top layer, than the reflection matrix method.     

Surface-wave propagation in an ocean basin with an anisotropic upper mantle: numerical modelling

Summary. The characteristics of surface-wave propagation in ocean basins are examined numerically for models with two types of anisotropic alignment in the upper mantle: one resulting from glide-plane slip in olivine with horizontal or vertical slip-planes, and the other from syntectonic recrystallization of olivine in a zone of horizontal shear. Glide-plane slip can cause highly anomalous inclined-Rayleigh particle-motion in the third-generalized mode (corresponding to the isotropic second-Rayleigh mode). The amplitude of this anomaly is rather insensitive to details of the structure. Syntectonic recrystallization can cause an anomalous combination of inclined-and tilted-Rayleigh motion in all modes. The variation with period of the amplitude of the anomaly in the fundamental mode can indicate the approximate depth to the anisotropic layer. In both types of alignment, the sense of tilt and the inclination varies with direction of propagation in a manner characteristic of the structural symmetry.     

Velocity profile of a sand cloud blowing over a gravel surface

Particle dynamic analyzer (PDA) measurement technology was used to study the turbulent characteristics and the variation with height of the mean horizontal (in the downwind direction) and vertical (in the upward direction) particle velocity of a sand cloud blowing over a gravel surface. The results show that the mean horizontal particle velocity of the cloud increases with height, while the mean vertical velocity decreases with height. The variation of the mean horizontal velocity with height is, to some extent, similar to the wind profile that increases logarithmically with height in the turbulent boundary layer. The variation of the mean vertical velocity with height is much more complex than that of the mean horizontal velocity. The increase of the resultant mean velocity with height can be expressed by a modified power function. Particle turbulence in the downwind direction decreases with height, while that in the vertical direction is complex. For fine sands (0.2–0.3 mm and 0.3–0.4 mm), there is a tendency for the particle turbulence to increase with height. In the very near-surface layer (<4 mm), the movement of blown sand particles is very complex due to the rebound of particles on the bed and the interparticle collisions in the air. Wind starts to accelerate particle movement about 4 mm from the surface. The initial rebound on the bed and the interparticle collisions in the air have a profound effect on particle movement below that height, where particle concentration is very high and wind velocity is very low.     

Finite-frequency sensitivity kernels for head waves

Head waves are extremely important in determining the structure of the predominantly layered Earth. While several recent studies have shown the diffractive nature and the 3-D Fréchet kernels of finite-frequency turning waves, analogues of head waves in a continuous velocity structure, the finite-frequency effects and sensitivity kernels of head waves are yet to be carefully examined. We present the results of a numerical study focusing on the finite-frequency effects of head waves. Our model has a low-velocity layer over a high-velocity half-space and a cylindrical-shaped velocity perturbation placed beneath the interface at different locations. A 3-D finite-difference method is used to calculate synthetic waveforms. Traveltime and amplitude anomalies are measured by the cross-correlation of synthetic seismograms from models with and without the velocity perturbation and are compared to the 3-D sensitivity kernels constructed from full waveform simulations. The results show that the head wave arrival-time and amplitude are influenced by the velocity structure surrounding the ray path in a pattern that is consistent with the Fresnel zones. Unlike the 'banana–doughnut' traveltime sensitivity kernels of turning waves, the traveltime sensitivity of the head wave along the ray path below the interface is weak, but non-zero. Below the ray path, the traveltime sensitivity reaches the maximum (absolute value) at a depth that depends on the wavelength and propagation distance. The sensitivity kernels vary with the vertical velocity gradient in the lower layer, but the variation is relatively small at short propagation distances when the vertical velocity gradient is within the range of the commonly accepted values. Finally, the depression or shoaling of the interface results in increased or decreased sensitivities, respectively, beneath the interface topography.     

Significance of the sign changing of the imaginary arrows in geomagnetic induction investigation

Summary. In this investigation, we carry out a two-dimensional study of the dependence of the imaginary Parkinson arrows on the frequency of the inducing geomagnetic field. Our results demonstrate that the imaginary arrows reverse direction as the inducing period varies. Therefore, we consider that there is no way to fix a consistent sign convention for the imaginary arrows even when the time factor is taken into account. We find that in the twodimensional case there exists a characteristic period T _c at which the phase difference between the vertical and horizontal magnetic components is zero. It is anticipated that T _c is related to the parameters of the conductivity anomaly and the status of the half-space host.     

A Hybrid Collocation Method For Calculating Complete Theoretical Seismograms In Vertically Varying Media

A numerical method is presented for calculating complete theoretical seismograms, under the assumption that the earth models have velocity, density and attenuation profiles which are arbitrary piece-wise continuous functions of depth only. Solutions for the stress-displacement vectors in the medium are expanded in terms of orthogonal cylindrical functions. Our method for solving the resulting two-point boundary value problems differs from that of other investigators in three ways. First, collocation is used in traditionally troublesome situations, e.g. for highly evanescent waves, at turning points, and in regions having large gradient in material properties. Second, in some situations (high frequencies and small gradients) P and S -waves decouple and we use a different solution method for each wave type, instead of trying to force a single method to find all solutions. For example, above the P - and S -waves turning points an approximate fundamental matrix may be used for each wave type. At the P -wave turning point, the fundamental matrix may be used for the S -wave components but collocation is used for the P -wave. Between the P - and S -wave turning points collocation is used for the evanescent P -wave and the fundamental matrix is used for the S -wave. At the S -wave turning point and below, collocation is used for both. Third, the computational algorithm chooses the appropriate solution method and depth domain upon which it is employed based upon a specified error tolerance and the known inaccuracies of the various approximations employed. Once solutions of the boundary value problems are obtained, a Fourier—Bessel transform is then applied to get back into the space-time domain.     

Surface coseismic gravity changes caused by dislocations in a 3-D heterogeneous earth

This study describes an examination of surface gravity changes caused by dislocations within a 3-D heterogeneous earth. This new theory is described using six independent dislocations: a vertical strike-slip, two vertical dip-slips perpendicular to each other, and three tensile openings on three perpendicular planes. A combination of the six independent dislocations is useful to compute coseismic gravity changes resulting from an arbitrary seismic source at an arbitrary position. Based on the 3-D lateral inhomogeneous P -wave velocity model, we deduce the 3-D density and S -wave velocity models using the relation of Karato. Finally, numerical computations are performed for a location south of Japan (30°N, 135°E). We calculate the coseismic gravity changes resulting from the six independent dislocations for source depths of 100, 300 and 637 km, respectively. Numerical results show that the maximum 3-D effect varies concomitantly with the dislocation type and the source depth. For seismic problems, the effect of elastic parameter  μ  is dominant.     

Core-log integration studies in hole-A of Taiwan Chelungpu-fault Drilling Project

Taiwan Chelungpu-fault Drilling Project (TCDP) was initiated to understand the physical mechanisms involved in the large displacements of the 1999 Taiwan Chi-Chi earthquake. Continuous measurements of cores (including laboratory work) and a suite of geophysical downhole logs, including P - and S -wave sonic velocity, gamma ray, electrical resistivity, density, temperature, electrical borehole images and dipole-shear sonic imager, were acquired in Hole-A over the depth of 500–2003 m. Integrated studies of cores and logs facilitate qualitative and quantitative comparison of subsurface structures and physical properties of rocks. A total of 10 subunits were divided on the basis of geophysical characteristics. Generally, formation velocity and temperature increase with depth as a result of the overburden and thermal gradient, respectively. Gamma ray, resistivity, formation density, shear velocity anisotropy and density-derived porosity are primarily dependent on the lithology. Zones with changes of percentage of shear wave anisotropy and the fast shear polarization azimuth deduced from Dipole Shear-Imager (DSI) are associated with the appearance of fractures, steep bedding and shear zones. The fast shear wave azimuth is in good agreement with overall dip of the bedding (approximately 30° towards SE) and maximum horizontal compressional direction, particularly in the Kueichulin Formation showing strong shear wave velocity anisotropy. Bedding-parallel fractures are prevalent within cores, whereas minor sets of high-angle, NNW–SSE trending with N- and S-dipping fractures are sporadically distributed. The fault zone at depth 1111 m (FZA1111) is the Chi-Chi earthquake slip zone and could be a fluid conduit after the earthquake. The drastic change in fast shear wave polarization direction across the underlying, non-active Sanyi thrust at depth 1710 m reflects changes in stratigraphy, physical properties and structural geometry.     

Inversion of P-wave velocity anisotropy

Summary. We examine the way in which measurements of velocity anisotropy can add to our understanding of upper mantle structure. Measurements of P -wave velocity anisotropy in a single plane contain very little direct information about the anisotropic structure. A promising technique is to fit the observed velocity variation with a mixture of an assumed anisotropic constituent and a proportion of isotropic material. Using this technique, mixtures of orthorhombic and transversely isotropic olivine are obtained, which are in excellent agreement with observed velocity variations in the Pacific.     

Two-dimensional PP/PS-stereotomography: P- and S-waves velocities estimation from OBC data

We present the extension of stereotomography to P - and S -wave velocity estimation from PP - and PS -reflected/diffracted waves. In this new context, we greatly benefit from the use of locally coherent events by stereotomography. In particular, when applied to S -wave velocity estimation from PS -data, no pairing of PP - and PS -events is a priori required. In our procedure the P -wave velocity model is obtained first using stereotomography on PP -arrivals. Then the S -wave velocity model is obtained using PS -stereotomography on PS -arrivals fixing the P -wave velocity model. We present an application to an 'ideal' synthetic data set demonstrating the relevance of the approach, which allows us to recover depth consistent P - and S -waves velocity models even if no pairing of PP - and PS -events is introduced. Finally, results to a real data set from the Gulf of Mexico are presented demonstrating the potential of the method in a noisy data context.     

Reply to comment by J. L. Mateos, O. Novaro, T. H. Seligman and J. Flores on 'Can horizontal P waves be trapped and resonate in a shallow sedimentary basin?'

Using a complete mathematical formulation, we show that the trapping of horizontal P waves in a very soft shallow alluvial layer is a minor effect. These waves do not have a stable way of propagation since in order to exist they require an incident wave and are therefore incapable of resonating in the lateral direction when confined in a basin of limited extent.     

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.