Ray Parameter Research Articles

On the data integration of seismological observation and deep seismic exploration. The crustal modeling for the Messina Straits Area as an example

Given an earth crust model having homogeneous layers and sphericalsymmetry, the travel-times equations of the direct and refracted longitudinalwaves are first deduced. These linear equations are determinedfrom the seismic ray parameter p, and from the known term a,. Theparameter p, is connected with the velocity of the elastic waves that arerefracted on the i-th layer; «, depends on the velocity of the layers crossedby the seismic ray and on their thickness.Subsequently, the equations of the first arrivals, observed in quite anumber of stations surrounding the Straits of Messina during the seismiccrisis of the Gulf of Patti (1978), are utilized for working out a crustal modelfor the Messina Straits area. Given the inadequatly of the passive seismologydata both in number and in characteristics the most superficial layersof the model are defined using the results of deep seismic explorationcarried out in areas contiguous to the Straits. The thickness and velocityof the longitudinal waves in the underlying layers are, instead, determined

A global optimizing approach for waveform inversion of receiver functions

A global optimizing approach is developed and implemented to retrieve one-dimensional crustal structure by waveform inversion of teleseismic receiver functions. The global optimization for the inversion is performed using a Differential Evolution (DE) algorithm. This modeling approach allows the user to perturb, within a preset range of reasonable bounds, multiple parameters such as V p, V p/ V s, thickness and anisotropy of each layer to fit the receiver function waveforms. Compared with linear modeling methods, the global optimal solution can be achieved with fewer model parameters (e.g., a small number of layers) and hence eliminate potential artifacts in the final model. Receiver function bins with small ray parameter intervals are used in the inversion, which can reduce distortion caused by modeling a single receiver function stacked from many recordings spread over a wide range of epicenter distance. The efficacy of this global optimizing approach is demonstrated with synthetic datasets and real receiver functions from the permanent seismic station BJT.

Conditions for forming weakly diverging acoustic bundles in ocean waveguides

Necessary and sufficient conditions for the dependence of the cycle length of the Brilloin waves or rays of geometrical acoustics on the ray parameter that is inversely proportional to their phase velocity are formulated. The formulated conditions determine the existence of weakly diverging acoustic bundles in vertically stratified oceanic waveguides, even with a point sound source.

Velocity calibration for microseismic monitoring: A very fast simulated annealing (VFSA) approach for joint-objective optimization

To accurately locate microearthquakes that are genetically related to hydraulic fracture stimulation, a thorough knowledge of the velocity structure between monitoring and fracturing treatment wells is essential. Very fast simulated annealing (VFSA) is implemented to invert for a flat-layered velocity model between wells using perforation or string-shot data. A two-point ray-tracing method is used to find the ray parameter [Formula: see text] for a ray traveling from a source to a receiver. The original traveltime-calculation formula is modified to account for the borehole source-receiver geometry. VFSA is used as a tool to optimize P- and S-wave velocities simultaneously. Unlike previous applications of VFSA, two improvements result from a new study: (1) both P- and S-wave arrival-time misfits are considered in a joint-objective function, and (2) P- and S-wave velocities are perturbed simultaneously during annealing. The inverted velocities follow the true values closely with a very small root-mean-square error, indicating the inverted model is close to the global minimum solution whose rms error should be zero for synthetic examples. Data noise contaminates inverted models, but not substantially in synthetic test results. A comparison of models inverted using VFSA and Occam’s inversion technique indicates that inverted models using VFSA are superior to those using Occam’s method in terms of velocity accuracy.

Calculation of Body Waves, for Caustics and Tunnelling in Core Phases†

The known failure of classical ray theory at caustics has led to a reconsideration of displacement (in the frequency domain), expressed as an integral over ray parameter p. The integrand contains saddle-points on the real p-axis which correspond to rays for the associated physical problem, and it is shown here that direct computation of the complex integral is still straightforward, even when two saddle-points (rays) have coalesced to form a caustic. WKBJ theory is still usable for the vertical wave-functions, but one may avoid both the Taylor series expansion for the phase, and the steepest-descents approximation. Attention is first directed towards the PKKP caustic near 119°, to calculations of both amplitude and the phase slowness (dT/dΔ) as a function of frequency, and to a criticism of some uses of plane wave reflection coefficients across the core-mantle boundary. It is then shown that short-period P-wave energy is efficiently tunnelled into and out of the Earth's core, from body waves having their turning point just above the core-mantle boundary. This provides an explanation for observations of multiply reflected core phases, PmKP with m > 2, which are found usually at distances beyond the cutoff one would expect from requiring real angles of incidence (≤ 90°) from mantle to core. To obtain body wave pulse shapes in the time domain, a method is described which appears to offer some strong advantages over Cagniard-de Hoop inversion.

Array Analysis of Regional-Distance P-Coda in South Asia

Abstract We present a comprehensive study of regional distance P -coda recorded by a medium-aperture array station located in Chiang Mai, Thailand (CMAR). Using array processing techniques, we analyzed data from 955 events that occurred at distances of 13°–30° with primarily continental paths. Nearly all significant, coherent arrivals in the P -coda traveled along the great circle path with ray parameters within of the direct arrival. Most of this energy was created near the source, probably via ( L g , R g )→ P scattering. This was especially true at the larger distances of 28°–30° in which coda decay rates decreased and large-amplitude significant arrivals occurred throughout the first 30 sec of the coda. The codas from approximately 40 intermediate-depth events in our data set were generally less energetic than shallow-event coda at comparable distances. In some cases, the coherent later arrivals we observed were related to upper mantle triplications. At distances of 14°–17° we observed clear secondary arrivals related to the 410 km discontinuity. They appeared on average 2 sec later than expected relative to the first arrivals, which may be partially explained by a depressed 410 beneath Burma. We isolated the diffuse component of the P -coda by subtracting array beams from individual elements to create residual seismograms. The diffuse, residual energy was highly variable from trace to trace and became equal in amplitude to the coherent component after only 20–30 sec of lapse time. We used a high-resolution maximum-likelihood technique to compute frequency–wavenumber spectra of the residual seismograms but did not conclusively observe any deterministic P → R g scatterer locations. The majority of the diffuse energy is created quite close to CMAR and does not travel as a plane wave across the array.

Target-oriented curved-wave prestack depth migration by controlled illumination

Conventional prestack depth migration (PSDM) based on full prestack data involves many computations for wavefield extrapolation. Areal shot-record technology offers an attractive alternative for efficient PSDM because its synthesis process greatly decreases the amount of prestack data required for migration. Constructing its synthesis operator is key to the image quality of the migrated areal shot record. Curved-wave PSDM technology expands areal shot-record migration. It constructs synthesis operators by defining a complex function as a base kernel of curved wavefields multiplied by a factor of its illumination perturbation related to ray parameter and then synthesizes curved wavefields for migrations. Based on curved-wave-migration theory, we propose an efficient and accurate curved-wave, controlled-illumination method to migrate in a target-oriented way. We construct tar-get-oriented synthesis operators by wave theory, combined with rotation or perturbation of the illuminating direction of a base-kernel synthesis operator. The base-kernel operator is obtained by inverse extrapolation of a predefined source wavefield at the given target level. Different model-constrained synthesis operators are constructed by rotating or perturbing illumination of the kernel operator. Then they are applied to shot records to synthesize curved-wave records. The resulting curved wavefields are entered for depth extrapolation and imaging, combining image results from different curved wavefields to produce the total image. The method controls the illumination of synthesized source wavefields in a target-oriented way directly at the surface and can achieve high-quality images of the target zone with great efficiency. Numerical demonstrations on the standard Marmousi model provide good imaging results of the complicated structure.

Mantle reflectivity structure beneath oceanic hotspots

This study applies high-resolution Radon transform to a large set of SS precursors and explores the mantle reflectivity structure beneath 17 potentially ‘deep-rooted’ hotspots. The combined reduced time (τ) and ray parameter (p) information effectively constrains the depth, spatial distribution and sharpness of upper-/mid-mantle reflectors. The olivine to wadsleyite phase boundary is deeper than the ocean and global averages and produces a dominant τ–p domain signal. Laterally coherent observations of the deep 410-km seismic discontinuity, thin upper mantle transition zone and weak/absent 520-km reflector beneath hotspots make compelling arguments for large-scale, hot thermal anomalies in the top 400–600 km of the mantle. On the other hand, a relatively ‘flat’ and weak reflector at ∼653 km is inconsistent with ringwoodite to silicate perovskite + magnesiowüstite transformation at temperatures greater than 2000 K. The lack of a negative correlation between topography and temperature implies (1) average or below-average temperatures at 600–700 km depths or (2) high temperatures and a dominating majorite garnet to Ca perovskite phase transformation. The proper choice between these two scenarios will directly impact the origin and depth of mantle plumes beneath hotspots. We further identify lower-mantle reflectors at 800–950 and 1100–1350 km depths beneath a number of the hotspots. Their presence implies that the chemistry and thermodynamics of the mid-mantle may be more complex than suggested by seismic tomography.

A reflectivity method for laterally varying media: homogeneous layers with curved interfaces

SUMMARY 1-D reflectivity method in the frequency ray-parameter domain is the most popular method for computing synthetic seismograms. We explore an extension of this method to media consisting of homogeneous layers with curved interfaces. The 2-D extension of the method involves explicit evaluation of boundary conditions that results in a matrix formulation involving several matrix inversions in a coupled ray-parameter domain. First, we revisit this method by examining the intermediate results in the coupled shot-receiver ray-parameter domain for realistic models; numerous numerical artefacts are caused by matrix operations. Next we investigate an alternate asymptotic approach by examining a tangent plane or Kirchhoff formulation in the plane wave domain to replace the exact boundary condition evaluation. All other reflectivity operations such as the invariant imbedding or iterative computation of reflection, transmission, multiple and mode conversions can be readily applied even under this approximation. Our resulting algorithm computes noise free seismograms even with coarse sampling of the interfaces and ray parameters. Approximate calculation of reflection/transmission coefficients, however, does not include multiple interaction of a plane wave with an interface. We show examples of synthetic seismograms for a suite of realistic models. Our computations are performed in the coupled slowness domain and thus, multiple shot-receiver data can be synthesized rapidly. Intermediate results in the coupled slowness space provide important insight into understanding wave propagation in heterogeneous media.

Path-average kernels for long wavelength traveltime tomography

SUMMARY Although much effort goes into improving the resolution of tomographic models, investigating their quality has only just started. Probabilistic tomography provides a framework for the quantitative assessment of uncertainties of long-wavelength tomographic models. So far, this technique has been used to invert maps of surface wave phase velocities and normal-mode splitting functions. Including body waves would substantially increase the depth resolution in the lowermost mantle. In surface wave tomography, the construction of phase velocity maps and splitting functions is a well-defined inverse problem, and the depth inversion is less well constrained but characterized by a small number of dimensions suitable for a Monte Carlo search. Traveltime tomography is mostly based on ray theory that covers the 3-D Earth, thus the dimension of the inverse problem is too large for a Monte Carlo search. The ray-mode duality suggests to apply the path-average approximation to body wave traveltimes. In this way the measured traveltime residual as a function of ray parameter can be inverted using path-average kernels, which depend on depth only, similar to surface wave tomography. We investigate the validity of the path-average approximation for delay times in both the forward and the inverse problem using the velocity model S20RTS as well as random models. We numerically illustrate the precision of such kernels compared with ray-theoretic and finitefrequency ones. We further invert traveltime residuals, calculated from Fermat rays, using the path-average kernels. We find that the agreement between classical ray theory and path-average theory is good for long wavelength structures. We suggest that for mapping long wavelength structures, body waves can be inverted in two steps, similar to surface waves, where the ray parameter and the vertical traveltime play the role of frequency and phase velocity, respectively.

First arrival stochastic tomography: Automatic background velocity estimation using beam semblances and VFSA

We present a new tomography method based on the local beam semblance and the very fast simulated annealing (VFSA) global optimization method. The data space is the local beam semblance calculated using local slant stacks for overlapping offset windows, i.e. beam windows, of the original common‐shot or common‐receiver gathers. On each beam semblance panel, the first coherency peak can be identified with a particular ray parameter, first‐arrival traveltime and beam center position. The forward problem can be solved with any ray tracer to find arrivals matching the identified peaks. Our inversion scheme uses VFSA to find the maximum‐a‐posteriori (MAP) solution and estimates the uncertainty by applying Bayesian analysis of all the sampled models for a specified model parameterization. This integration of automatic local semblance evaluation instead of first‐arrival picking and a fast forward modeling method combined with VFSA to determine the optimal model makes our method robust, efficient and accurate.

Inner‐core fine‐scale structure from scattered waves recorded by LASA

Recent observations of inner‐core scattering (ICS) waves provide evidence that the outermost 300 km of the inner‐core has strong heterogeneities with a length scale of a few kilometers. These waves follow a path similar to that of the inner‐core–reflected waves PKiKP and were originally observed in data from 16 events in the distance range 58° to 73° recorded by the Large Aperture Seismic Array (LASA). Here we present additional observations of the ICS waves from a total of 78 events recorded by LASA at distances from 18° to 98°. We use a modified version of the Generic Array Processing software package to identify ICS waves on the basis of travel time, back azimuth, ray parameter, amplitude, and coherence. There are 44 events that produce clear ICS waves. We then perform forward modeling of the observed ICS waves using a Monte Carlo seismic phonon method that allows for multiple scattering along the raypath. Most of the ICS waves appear without a visible PKiKP phase, initially grow in time, and have a spindle‐shaped envelope. The duration, risetime, and decay rates of the observed ICS waves can be best explained by small‐scale volumetric heterogeneities in the outermost few hundred kilometers of the inner core. The average Qc value for the 44 events is ∼600. Most clear ICS waves are found for raypaths sampling the Pacific Ocean and Asia, and relatively few observations are from the Atlantic Ocean, roughly consistent with the recently observed hemispheric difference in the inner‐core structure.

RAY CHAOS IN UNDERWATER ACOUSTIC WAVEGUIDES

The chaotic motion of a ray path in a deep water acoustic waveguide with internal-wave-induced fluctuations of the sound speed is investigated. A statistical approach for the description of chaotic rays is discussed. The behavior of ray trajectories is studied using Hamiltonian formalism expressed in terms of action-angle variables. It is shown that the range dependence of the action variable of chaotic ray can be approximated by a random Wiener process. On the basis of this result, analytical expressions for probability density functions of ray parameters are derived. Distributions of coordinates, momenta (grazing angles), and actions of sound rays are evaluated. Numerical simulation shows that statistical characteristics of ray parameters weakly depend on a particular realization of random perturbation giving rise to ray chaos.

Stereotomography assisted by migration of attributes

ABSTRACTDepth velocity model building remains a difficult step within the seismic depth imaging sequence. Stereotomography provides an efficient solution to this problem but was limited until now to a picking of seismic data in the prestack time un‐migrated domain. We propose here a method for stereotomographic data picking in the depth migrated domain. Picking in the depth migrated domain exhibits the advantage of a better signal‐to‐noise ratio and of a more regular distribution of picked events in the model, leading to a better constrained tomographic inverse problem. Moreover, any improvement on the velocity model will improve the migrated results, again leading to improved picking. Our strategy for obtaining a stereotomographic dataset from a prestack depth migration is based on migration of attributes (and not on a kinematic demigration approach!). For any locally coherent event in the migrated image, migration of attributes allows one to compute ray parameter attributes corresponding to the specular reflection angle and dip. For application to stereotomography, the necessary attributes are the source/receiver locations, the traveltime and the data slopes. For the data slope, when the migration velocity model is erroneous, some additional corrections have to be applied to the result of migration of the attributes. Applying these corrections, our picking method is theoretically valid whatever the quality of the migration velocity model. We first present the theoretical aspects of the method and then validate it on 2D synthetic and real seismic reflection data sets.

Receiver function method in reflection seismology

ABSTRACTThe receiver function method was originally developed to analyse earthquake data recorded by multicomponent (3C) sensors and consists in deconvolving the horizontal component by the vertical component. The deconvolution process removes travel path effects from the source to the base of the target as well as the earthquake source signature. In addition, it provides the possibility of separating the emergent P and PS waves based on adaptive subtraction between recorded components if plane waves of constant ray parameters are considered. The resulting receiver function signal is the local PS wave's impulse response generated at impedance contrasts below the 3C receiver.We propose to adapt this technique to the wide‐angle multi‐component reflection acquisition geometry. We focus on the simplest case of land data reflection acquisition. Our adapted version of the receiver function approach consists in a multi‐step procedure that first removes the P wavefield recorded on the horizontal component and next removes the source signature. The separation step is performed in the τ−p domain while the source designature can be achieved in either the τ−p or the t−x domain. Our technique does not require any a priori knowledge of the subsurface. The resulting receiver function is a pure PS‐wave reflectivity response, which can be used for amplitude versus slowness or offset analysis. Stack of the receiver function leads to a high‐quality S wave image.

Upper mantle discontinuity structure beneath East Anatolian Plateau (Turkey) from receiver functions

Imaging of seismic velocity discontinuities with receiver functions suggests a complex mantle structure beneath the East Anatolian Plateau. By stacking all the receiver functions as a function of ray parameter, we examined the moveout characteristics of the data set and tested different velocity models to fit the arrival times of converted phases from the Moho and the lithosphere–asthenosphere boundary and their multiples. The best fitting model shows anomalously thin crust (40 km) and lithosphere (65 km), and low uppermost mantle velocities causing systematic delays on later discontinuity arrivals. These findings are consistent with the high plateau supported by partially molten and buoyant asthenosphere. The upper mantle discontinuities are all visible in different frequencies (0.15 and 0.4 Hz). Especially, the 410 km discontinuity does not show frequency dependence in amplitude and suggests a sharpness of 10 km or less. Spatial variations of the 410 and 660 km discontinuities reveal anticorrelated topography and distinct zones of diminished amplitude associated with a detached slab and delaminated fragments of lithospheric mantle. In the south, the slab becomes deeper and horizontally deflected towards the east suggesting westward migration of slab detachment and resistance to slab penetration at the 660 km discontinuity. In the north, the mantle transition zone is characterized by two spatially limited lithospheric fragments with complex geometry. At the center of the study area, the transition zone is thin (230 km) suggesting excess temperature of 120 °C. This warm mantle anomaly most likely is due to hot material trapped within the upper mantle between slab in the south and delaminated fragments in the north.

Cosmic Rays at Extreme Energies: Status and Recent results of the Pierre Auger Observatory

The Pierre Auger Observatory is designed to study the origin and the nature of the highest energy cosmic rays. The southern observatory, currently under construction in Province of Mendoza, Argentina, is nearing completion. The observatory is taking data in a hybrid mode, in the final phase incorporating both, a ground array of 1600 Cherenkov water tanks spread over 3000 km 2 , and 24 wide-angle Schmidt fluorescence telescopes placed at four sites on the boundary of the surface array. Hybrid detection of extended air showers improves considerably the precision on reconstructed primary cosmic ray parameters and serves as a cross-calibration between the two techniques. Despite the fact that the observatory is still under construction, data is routinely recorded since 2004. The current status of the observatory, its characteristics and recent results on primary cosmic ray spectrum, arrival directions and the photon fraction limit are presented.

Identification of yellow stringybark (Eucalyptus muelleriana) and silvertop ash (E. sieberi) wood is improved by canonical variate analysis of ray anatomy

Summary The woods of yellow stringybark (Eucalyptus muelleriana) and silvertop ash (E. sieberi) are both used for the manufacture of flooring, but yellow stringybark is the preferred species because it contains fewer natural defects and dries faster and with less degrade than silvertop ash. Sometimes companies manufacturing flooring from yellow stringybark find that the wood they process contains higher levels of natural defects than expected, possibly due to the presence of silvertop ash in the wood that they receive from sawmills. It is difficult to prove this, however, because timber from both species looks similar in the rough-sawn condition and is similar anatomically. Hence, a reliable method of identifying the two species is needed. This study used canonical variate analysis to analyse linear combinations of quantitative indicators of ray anatomy in an attempt to clearly separate the wood of the two species. Canonical variate analysis scores derived from the analysis of ray height and cell number, frequency of biseriate rays and frequency of rays per square millimetre were able to completely separate 13 authentic samples of each species. This approach to separating the two species was validated using a further 16 reference specimens provided by industry (eight of each species) and 16 unknown specimens. Analysis of the reference specimens identified one specimen labelled silvertop ash that was clearly yellow stringybark, and one sample of yellow stringybark was identified as silvertop ash. Overall, however, canonical variate analysis of linear combinations of ray features produced fewer misclassifications of the two species than the use of ray parameters on their own. Canonical variate analysis shows promise as a means of more clearly separating yellow stringybark from silvertop ash and may also prove useful in separating those eucalypt wood species whose final identification in taxonomic keys depends on their ray anatomy.

Direct illumination LED calibration for telescope photometry

A calibration method for telescope photometry, based on the direct illumination of a telescope with a calibrated light source regrouping multiple LEDs, is proposed. Its purpose is to calibrate the instrument response. The main emphasis of the proposed method is the traceability of the calibration process and a continuous monitoring of the instrument in order to maintain a 0.2% accuracy over a period of years. Its specificity is to map finely the response of the telescope and its camera as a function of all light ray parameters. This feature is essential to implement a computer model of the instrument representing the variation of the overall light collection efficiency of each pixel for various filter configurations. We report on hardware developments done for SNDICE, the first application of this direct illumination calibration system which will be installed in Canada France Hawaii telescope (CFHT) for its leading supernova experiment (SNLS).

Imaging mantle discontinuities using least squares Radon transform

Differential traveltimes of SS precursors have been widely used to map large‐scale mantle structure and depths of discontinuities. Measurements are commonly made by stacking individual records to increase the signal‐to‐noise ratio pertaining to these mild reflections. However, ray parameters of the SS precursors are typically less well constrained and undesired seismic arrivals with vastly different slownesses (for example, scattered waves) could potentially contaminate the time domain stacks. To overcome these pitfalls, we introduce a processing scheme based on the Radon transform and well‐constrained inversions. Our method is particularly effective in suppressing background noise, constraining differential ray parameter and traveltime, and detecting weak reflected or converted phases. We apply the Radon‐based method to delineate the discontinuity structure beneath the northeastern Pacific Ocean and the northwestern Canada. An elevated 410‐km discontinuity and a thickened transition zone (252 km) are observed beneath the northern British Columbia, which may be caused by remnant oceanic lithosphere from the subduction of Kula‐Farallon plate under North America. A thin transition zone is identified beneath the northern Pacific Ocean and its presence is supported by a low shear‐velocity anomaly from recent tomographic models. The improved accuracy and resolution using the least squares Radon transform also offer clear evidence for a regional 520‐km discontinuity and several mild reflectors in the depth ranges of 250–330 km and 900–1200 km. We do not observe a 220‐km discontinuity beneath the study region.