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.     

A method for the computation of finite frequency body wave synthetic seismograms in laterally varying media

Summary. Body wave synthetic siesmograms for laterally varying media are computed by means of a slowness implementation of the extended WKBJ (EWKBJ) theory of Frazer & Phinney. An EWKBJ seismogram is computed by first tracing rays through a particular model to obtain conventional ray information (travel time, ray end point, ray slowness) and then using these data in the finite frequency integral expression for the EWKBJ seismogram. The EWKBJ seismograms compare favourably to geometrical ray theory (GRT) seismograms but are significantly better because of the finite frequency nature of the EWKBJ calculation. More realistic behaviour is obtained with EWKBJ seismograms at normal seismic frequencies near caustics, where the GRT amplitude is infinite, and within geometrical shadow zones where GRT predicts zero amplitudes. In addition the EWKBJ calculation is more sensitive than GRT to focuses and defocuses in the ray field. The major disadvantage of the EWKBJ calculation is the additional computer time over that of GRT, necessary to calculate one seismogram although an EWKBJ seismogram costs much less to compute than a reflectivity seismogram. Another disadvantage of EWKBJ theory is the generation of spurious, non-geometrical phases that are associated with rapidly varying lateral inhomogeneities. Fortunately the amplitudes of these spurious phases are usually much lower than that of neighbouring geometrical phases so that the spurious phases can usually be ignored. When this observation is combined with the moderately increased computational time of the EWKBJ calculation then the gain in finite frequency character significantly outweighs any disadvantages.     

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.     

On the focusing of seismic body waves at the epicentre's antipode

Summary. This note reports on the remarkable focusing of seismic body waves at or near the antipode (Δ= 180°) of an earthquake's epicentre. The particular seismic velocity structure and sphericity of the Earth cause body-wave phases such as P (diff), PKP, PP, PPP, PcPPKP, SKSSKS, SS , etc. to converge individually at antipodal distances after being diffracted, reflected or refracted at discontinuities. This focusing strongly amplifies each signal up to almost one order of magnitude with respect to the normal phase recorded two or more degrees away. Since the signal/noise ratio is enhanced in the same proportion, seismograms at antipodal distances provide clear and strong arrivals of otherwise weak phases. Antipodal monitoring of seismic waves is suggested as a powerful means of exploring the Earth's interior. The study of these 'seismic images' generated at focal points of seismic rays will yield information on the departures from lateral homogeneity and sphericity of the core, as well as stronger constraints on earth models. To interpret the observations correctly, the data must be compared with theoretically generated seismograms. Since the appropriate ray theory equations (see, e.g. Scholte; Gilbert & Helmberger; Richards) are singular at Δ=180°, a corrective measure is taken which provides a formal expression for the wave amplitude that remains finite at the antipode, and reproduces the usual expressions at other distances.     

Seismogram synthesis using normal mode superposition: the locked mode approximation

Summary. A normal mode superposition approach is used to synthesize complete seismic codas for flat layered earth models and the P-SV phases. Only modes which have real eigenwavenumbers are used so that the search for eigenvalues in the complex wavenumber plane is confined to the real axis. In order to synthesize early P -wave arrivals by summing a number of'trapped'modes, an anomalously high velocity cap layer is added to the bottom of the structure so that most of the seismic energy is contained in the upper layers as high-order surface waves. Causality arguments are used to define time windows for which the resulting synthetic seismograms are close approximations to the exact solutions without the cap layer. The traditional Thomson—Haskell matrix approach to computing the normal modes is reformulated so that numerical problems encountered at high frequencies are avoided and numerical results of the locked mode approximation are given.     

Seismic evidence for a sharp lithospheric base persisting to the lowermost mantle beneath the Caribbean

Broad-band data from South American earthquakes recorded by Californian seismic networks are analysed using a newly developed seismic wave migration method—the slowness backazimuth weighted migration (SBWM). Using the SBWM, out-of-plane seismic P -wave reflections have been observed. The reflection locations extend throughout the Earth's lower mantle, down to the core–mantle boundary (CMB) and coincide with the edges of tomographically mapped high seismic velocities. Modelling using synthetic seismograms suggests that a narrow (10–15 km) low- or high-velocity lamella with about 2 per cent velocity contrast can reproduce the observed reflected waveforms, but other explanations may exist. Considering the reflection locations and synthetic modelling, the observed out-of-plane energy is well explained by underside reflections off a sharp reflector at the base of the subducted lithosphere. We also detect weaker reflections corresponding to the tomographically mapped top of the slab, which may arise from the boundary between the Nazca plate and the overlying former basaltic oceanic crust. The joint interpretation of the waveform modelling and geodynamic considerations indicate mass flux of the former oceanic lithosphere and basaltic crust across the 660 km discontinuity, linking processes and structure at the top and bottom of the Earth's mantle, supporting the idea of whole mantle convection.     

A method for calculating synthetic seismograms in laterally varying media

Summary An effective algorithm for computing synthetic seismograms in laterally inhomogeneous media has been developed. The method, based on zero-order asymptotic ray theory, is primarily intended for use in refraction and reflection studies and provides an economical means of seismic modelling.
A given smoothed velocity-depth-distance model is divided into small squares with constant seismic parameters and first-order interfaces are represented by an arbitrary number of dipping linear segments. The computation of ray propagation and amplitudes through such a model does not involve complicated analytic expressions and therefore minimizes computer time.
Amplitudes are determined by geometrical spreading of spherical wave-fronts and energy partitioning at interfaces. Synthetic seismograms calculated for laterally homogeneous models are in good agreement with those obtained by the Reflectivity Method.     

Wave Propagation In A Vertical Transversely Isotropic Medium: Field Experiment and Model Study

Summary. The continent-ocean transition adjacent to Hatton Bank was studied using a dense grid of single-ship and two-ship multichannel seismic profiles. The interpretation of the explosive expanding spread profiles (ESPs) which were shot as part of this survey are discussed here in detail. Extensive seaward dipping reflectors are developed in the upper crust across the entire margin. These seaward dipping reflectors continue northwards on the Faeroes and Vøring margins, where they have been shown to be caused by basaltic lavas, as well as on the conjugate margin of East Greenland. The dipping reflectors are an important feature of the rifting history of the margin and show that extensive volcanism was associated with the extension. The ESPs show clear seismic arrivals out to ranges of 100 km. Wide-angle Moho reflections can be seen on all the lines as well as good mid and lower crustal arrivals. The determination of seismic velocity structure was constrained by ray tracing and by amplitude modelling using reflectivity synthetic seismograms. The results from the ESPs show that there is a thick region of lower crustal material beneath the margin with an unusually high crustal velocity of 7.3–7.4 km s⁻¹. This lower crustal material reaches a maximum thickness of 14 km beneath the central part of the margin and is terminated at depth by the Moho. The lower crustal lens of high-velocity material is interpreted as underplated or intruded igneous rocks associated with the large volumes of extrusive basaltic lavas, now seen as dipping reflectors on the margin.     

Scattering characteristics in heterogeneously fractured reservoirs from waveform estimation

Offset-dependent characteristics of seismic scattering are useful for characterizing fractured reservoirs. We use two models that have different background medium properties and different azimuthal AVO responses to study elastic wave propagation and scattering in gas-saturated, heterogeneously fractured reservoirs. Heterogeneous fracture density distributions are built through stochastic modelling. Synthetic seismograms are generated by 3-D finite difference modelling, and waveforms along crack-normal and strike directions are considered in this paper. The multiple signal classification (MUSIC) frequency estimator is used in waveform estimation to provide frequency-domain attributes related to seismic wave scattering by fracture heterogeneity. Our results indicate that the strength of the scattering field is a function of the background medium. The strength also increases with increasing fracture scatterer density and with decreasing correlation length of spatial variations of fracture density. The scattering field is weak at the top of the fractured reservoir. The first-order results are dominated by velocity anisotropy of the mean fracture density field. However, the base of the fractured reservoir corresponds to a strong scattering field on which fracture heterogeneity has a larger effect and is characterized by the loss of coherence.     

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.     

Comparison of global synthetic seismograms calculated using the spherical 2.5-D finite-difference method with observed long-period waveforms including data from the intra-Antarctic region

We have been developing an accurate and efficient numerical scheme, which uses the finite-difference method (FDM) in spherical coordinates, for the computation of global seismic wave propagation through laterally heterogeneous realistic Earth models. In the field of global seismology, traditional axisymmetric modeling has been used widely as an efficient approach since it can solve the 3-D elastodynamic equation in spherical coordinates on a 2-D cross-section of the Earth, assuming structures to be invariant with respect to the axis through the seismic source. However, it has the severe disadvantages that asymmetric structures about the axis cannot be incorporated and the source mechanisms with arbitrary shear dislocation have not been attempted for a long time. Our scheme is based on the framework of axisymmetric modeling but has been extended to treat asymmetric structures, arbitrary moment-tensor point sources, anelastic attenuation, and the Earth center which is a singularity of wave equations in spherical coordinates. All these types of schemes which solve 3-D wavefields on a 2-D model cross-section are classified as 2.5-D modeling, so we have named our scheme the spherical 2.5-D FDM. In this study, we compare synthetic seismograms calculated using our FDM scheme with three-component observed long-period seismograms including data from stations newly installed in Antarctica in conjunction with the International Polar Year (IPY) 2007–2008. Seismic data from inland Antarctica are expected to reveal images of the Earth's deep interior with enhanced resolution because of the high signal-to-noise ratio and wide extent of this region, in addition to the rarity of sampling paths along the rotation axis of the Earth. We calculate synthetic seismograms through the preliminary reference earth model (PREM) including attenuation using a moment-tensor point source for the November 9, 2009 Fiji earthquake. Our results show quite good agreement between synthetic and observed seismograms, which indicates the accuracy of observations in the Antarctica, as well as the feasibility of the spherical 2.5-D modeling scheme.     

Quantized Ray Theory for Non-Zero Focal Depths

The relation between p-Δcurves for surface and deep focus sources is investigated in order to construct synthetic body wave seismograms for non-zero focal depths by the quantized ray theory algorithm. The transformation of a surface focus p-Δ curve into a deep focus p-Δ curve is denned in terms of that curve which corresponds to surface focus rays reflected from the depth at which the deep focus is located. By analogy with the geometry of the surface focus formulation, paths of integration to obtain absolute travel-time and velocity-depth curves can be denned in the p-Δ plane. Explicit inversion from deep focus data is possible only when the velocity-depth structure above the depth of focus is known. Through a comparison of short period quantized ray theory synthetic seismograms with similar Cagniard-de Hoop computations, it is shown that quantized ray theory can be used for accurate predictions of body wave amplitude behaviour corresponding to a wide range of focal depths.     

The utility of regional Chinese seismograms for source and path studies in central Asia

Summary. Broadband seismograms from the National Seismic Network of the People's Republic of China (PRC) have recently become available through a data exchange programme between NOAA and the State Seismological Bureau of the PRC. In this study, regional surface waves recorded at the Urumchi station located about 700 km north of the Tibetan Plateau in the Sinkiang Province are used to study East Kazakh explosions and wave propagation in central Asia. The data consist of broadband (flat to displacement between 0.1 and 10 Hz), photographic records from an SK Kirnos galvanometric system. Simultaneous inversion of Rayleigh wave phase and group velocities for the path from East Kazakh through the Dzhungarian Basin yields a crustal model dominated by the presence of very low velocities and a strong positive velocity gradient above 15 km depth. Velocities below 15 km depth are not significantly different from other continental structures underlain by Palaeozoic or Precambrian basement. Seismic moments were estimated for seven East Kazakh explosions using models of explosion sources with associated tectonic strain release. The largest explosion studied occurred on 1980 September 14 and had an m_b of 6.2 and a seismic moment of 2.7 × 10²³ dyn cm. The observed amplitude spectra of Rayleigh waves are richer in high frequencies than spectra calculated from our models. This could be caused by a path effect involving seismic wave focusing by the Dzhungarian Basin, although source medium effects cannot be ruled out.     

Time-domain computation of scattering from a heterogeneous layer

Adopting Born and ray approximations, time-domain synthetic seismograms for P-P and P-S scattering from a plane wave incident on a thin, laterally heterogeneous layer are presented in this paper. The time-domain P coda is a convolution between a structure function and the second-order derivative of the time function of the incident P wave. Examples of synthetic seismograms are given using a time function from a computed short-period seismogram for a point explosive source in a half-space. These show that it is impossible, with realistic values of the parameters involved, to generate significant codas when only single scattering is involved.     

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.     

The effect of noise on seismograms

Summary. We describe a method which provides an estimate of the accuracy to which time-domain features of seismic signals can be measured in the presence of noise. Observed seismograms are simulated by adding random noise with the same frequency spectrum and signal-to-noise ratio to matching synthetic seismograms. The effect of noise on synthetic and observed P -wave first motions is used as an illustration. It is shown that the apparent reliability of such observations, as determined by visual estimation, is often illusory.     

Spectral aspects of the Gaussian beam method: reflection from a homogeneous half-space

Summary. Use of paraxially approximated Gaussian beams continues to be actively pursued for construction of synthetic seismograms in complicated environments. How to select the beams in the stack remains a source of difficulty which has primarily been addressed by semi-heuristic considerations. In this paper, the classical example of line-source field reflection from a homogeneous half-space that can sustain a head wave is examined from a plane-wave spectral point of view. The individual beam fields are modelled exactly by the complex source point technique, which emphasizes the complex spectral content of these wave objects. The quality of the paraxial approximation of a typical reflected (Gaussian) beam characterized by different parameters is examined from this perspective, and is compared with uniform and non-uniform asymptotics generated from the exact beam field spectral integral. With this information as background, the reflected field for a real line-source is synthesized by beam superposition. Except for the immediate vicinity of the critical reflection angle, the well-known failure of narrow paraxial beams, no matter how densely stacked, to reproduce the head wave effects is shown to be due to the inadequate spectral content of these beams and not to the failure of beam stacking per se. When the rigorous solutions are used for the narrow-waist beams, even relatively few suffice to yield agreement with the exact solution. This circumstance emphasizes the importance of fully understanding the spectral implications of various beam stacking schemes.     

Post‐seafloor spreading magmatism and associated magmatic hydrothermal systems in the Xisha uplift region,northwestern South China Sea

Submarine magmatism and associated hydrothermal fluid flows has significant feedback influence on the petroleum geology of sedimentary basins. This study uses new seismic profiles and multibeam bathymetric data to examine the morphology and internal architecture of post‐seafloor spreading magmatic structures, especially volcanoes of the Xisha uplift, in extensive detail. We discover for the first time hydrothermal systems derived from magmatism in the northwestern South China Sea. Numerous solitary volcanoes and volcanic groups occur in the Xisha uplift and produce distinct seismic reflections together with plutons. Sills and other localized amplitude anomalies were fed by extrusions/intrusions and associated fluid flow through fractures and sedimentary layers that may act as conduits for magma and fluid flows transport. Hydrothermal structures such as pipes and pockmarks mainly occur in the proximity of volcanoes or accompany volcanic groups. Pipes, pockmarks and localized amplitude anomalies mainly constitute the magmatic hydrothermal systems, which are probably driven by post‐seafloor spreading volcanoes/plutons. The hydrothermal fluid flows released by magma degassing or/and related boiling of pore fluids/metamorphic dehydration reactions in sediments produced local overpressures, which drove upward flow of fluid or horizontal flow into the sediments or even seafloor. Results show that post‐seafloor spreading magmatic activity is more intense during a 5.5 Ma event than one in 2.6 Ma, whereas the hydrothermal activities are more active during 2.6 Ma than in 5.5 Ma. Our analysis indicates that post‐seafloor spreading magmatism may have a significant effect on hydrocarbon maturation and gas hydrate formation in the Xisha uplift and adjacent petroliferous basins. Consequently the study presented here improves our understanding of hydrocarbon exploration in the northwestern South China Sea.     

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.