Ray Travel Times Research Articles

Viscoacoustic wave form inversion of transmission data for velocity and attenuation

This study investigates the performance of a frequency domain viscoacoustic full wave form nonlinear inversion to obtain high resolution images of velocity and attenuation. An efficient frequency domain implementation is applied that consists of performing a series of single frequency inversions sweeping from low to high frequency. A cascaded inversion was adopted in which the real part of the velocity is first imaged using the phase information, then the quality factor (Q) is imaged using the amplitude information. Tests with synthetic data indicate that our approach yielded better images than the simultaneous determination of the real and imaginary parts of the complex velocity. The method is applied to laboratory data obtained in a water tank with suspended acrylic bars. Broadband 200 kHz data are obtained for a crosshole configuration with a computer-controlled scanning system and piezofilm source and detector. The velocity image produced by the full wave form inversion is compared to a curved ray travel time tomography velocity image, and was observed to possess higher resolution and more precise locations of the acrylic bars. The Q image shows a lower resolution than the velocity image, but recovers the correct Q for acrylic. This method can be applied for geophysical applications targeted to soil, unconsolidated rocks, and marine sediments and also nondestructive evaluation and medical applications.

Ray and travel time stability in weakly range-dependent sound channels

Ray path and travel time stability are investigated in environments consisting of a range-independent background on which a weak range-dependent perturbation is superimposed. Theoretical arguments suggest and numerical results confirm that both ray path and travel time stability are strongly influenced by the background sound speed profile. Both ray path and travel time stability are shown to increase with increasing magnitude of α(I)=(I/ω)dω/dI, where 2π/ω(I) is the range of a ray cycle (double loop in a deep ocean sound channel) and I is the ray action variable. This behavior is illustrated using internal-wave-induced scattering in deep ocean environments and rough surface scattering in upward refracting environments. [Work supported by ONR.]

Wavefield stability in weakly range-dependent sound channels

It is shown that the mode-based ‘‘waveguide invariant’’ β is asymptotically equivalent to the ray-based ‘‘stability parameter’’ α. These parameters are known to control the dispersive properties of the sound channel and various measures of both ray path and travel time stability. This leads to the expectation that finite-frequency wavefield stability is also largely controlled by β (or α). PE simulations are shown to confirm this expectation. [Work supported by ONR.]

Global tomographic images of mantle plumes and subducting slabs: insight into deep Earth dynamics

A new model of whole mantle P-wave tomography is determined with a novel approach. A grid parameterization instead of blocks and spherical harmonics is adopted to express the Earth structure. Depth variations of the Moho, 410 and 660 km discontinuities are taken into account in the inversion. Ray paths and travel times are computed with an efficient 3-D ray tracing scheme. This new approach was applied to a large data set of ISC (International Seismological Center) travel times (P, PP, PcP, pP, Pdiff) to determine a whole mantle P-wave tomography. For the shallow mantle, the new model contains the general features observed in the previous models: a low-velocity ring around the Pacific Ocean basins and high-velocity anomalies under the old and stable continents in the depth range of 0–300 km. One significant difference from the previous models is that stronger and wider high-velocity anomalies are visible in the transition zone depths under the subduction regions, which suggests that most of the slab materials are stagnant in the transition zone before finally collapsing down to the lower mantle as a result of very large gravitational instability from phase transitions. Very slow anomalies exist in the upper mantle right beneath the Wudalianchi and Changbai active volcanoes in Eastern China, right above the stagnant Pacific slab in the transition zone, suggesting that the origin of the intraplate volcanism in East Asia is closely related to the Pacific plate subduction process, such as deep slab dehydration and convective circulation in the mantle wedge. Plume-like slow anomalies are clearly visible under the major hotspot regions in most parts of the mantle, in particular, under Hawaii, Iceland, South Pacific and Africa. The slow anomalies under South Pacific and Africa have lateral extensions of over one thousand kilometers and exist in the entire mantle, representing two superplumes. The Pacific superplume has a larger spatial extent and stronger slow anomalies than that of the Africa superplume. The Hawaiian plume is not part of the Pacific superplume. The slow anomalies under hotspots usually do not show a straight pillar shape, but exhibit winding images, suggesting that plumes are not fixed in the mantle but can be deflected by the mantle flow. As a consequence, hotspots are not really fixed but can wander on the Earth’s surface, as evidenced by the recent paleomagnetic and numeric modeling studies. Wider and more prominent slow anomalies are visible at the core–mantle boundary (CMB) than most of the lower mantle, and there is a good correlation between the distribution of slow anomalies at the CMB and that of hotspots on the surface, suggesting that most of the strong mantle plumes under the hotspots originate from the CMB. However, there are some small-scaled, weak plumes originating from the transition zone or mid mantle depths.

Practical VTI approximations: a systematic anatomy

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a13 with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109).

Travel time estimation for ocean acoustic thermometry

The basic datum of ocean acoustic thermometry experiments is the ray travel time, thus an accurate and precise estimator is of paramount importance. It is well known that a matched filter gives the best estimate if the transmitted signal is known exactly. At basin-scale ranges, the signal becomes a random process due to the limited coherence time and coherent bandwidth of the channel. A matched filter is no longer optimum in this case, but since the reception is still partially coherent, an energy detector is not optimum either. A better estimator is the RAKE correlator, which can account for the signal variability at the cost of increased receiver complexity and a reduction of resolution. In this talk, the performance of the RAKE correlator, the matched filter, and the energy detector versus coherence time, coherent bandwidth, and SNR is explored by simulation of realistic cases. The RAKE is then applied to a 4000-km range, 75-Hz sonar transmission and the performance improvement is remarkable. An added benefit of the RAKE is that there is less clutter, or fewer false alarms in the detection theory jargon, and thus tracking an arrival over multiple transmissions is much easier.

Ray Chaos in the Long-Range Propagation of Sound in the Ocean

We develop an approximate analytical approach for a description of the stochastic behavior of sound rays in deep-sea acoustic waveguides with paths up to 3 to 5 thousands of kilometers. The ray dynamics is studied using the Hamiltonian formalism in terms of the action–angle canonical variables. A realistic model of underwater waveguide with internal-wave-induced perturbations of the sound speed field is applied. We point out a small parameter of the problem, which allows one to linearize the Hamilton (ray) equations and approximate the action variable by a Wiener process representing the simplest model of diffusion. The stochastic ray theory based on this approximation is applied to an analysis of ray travel times, i.e., the travel times of sound pulses coming to a receiver via different ray paths. The formation of compact clusters of the chaotic-ray travel times is explained quantitatively.

Sensitivity of ray paths to initial conditions

Using a parabolic equation, we consider ray propagation in a waveguide with the sound speed profile that corresponds to the dynamics of a nonlinear oscillator. An analytical consideration of the dependence of the travel time on the initial conditions is presented. Using an exactly solvable model and the path integral representation of the travel time, we explain the step-like behavior of the travel time T as a function of the starting momentum p0 (related to the starting ray grazing angle v0 by p0 ¼ tan v0). A periodic perturbation of the waveguide along the range leads to wave and ray chaos. We explain an inhomogeneity of distribution of the chaotic ray travel times, which has obvious maxima. These maxima lead to the clustering of rays and each maximum relates to a ray identifier, i.e. to the number of ray semi-cycles along the ray path. 2003 Elsevier B.V. All rights reserved.

Ray travel times at long ranges in acoustic waveguides.

The Hamiltonian formalism in terms of the action-angle variables is applied to study ray travel times in a waveguide with a smooth sound speed profile perturbed by a weak range-dependent inhomogeneity. A simple approximate formula relating the differences in ray travel times to range variations of action variables is derived. This relation is applied to study range variations of the timefront (representing ray arrivals in the time-depth plane). Widening and bias of timefront segments in the presence of perturbations are considered. Qualitative and quantitative explanations are given to surprising stability of early portions of timefronts observed in both numerical simulations and field experiments. This phenomenon is interpreted from the viewpoint of Fermat's principle. By ray tracing in a realistic deep water environment with an internal-wave-induced perturbation it has been demonstrated that our approach can be used at ranges up to, at least, 3000 km.

Numerical simulation of wave propagation in media with discrete distributions of fractures: effects of fracture sizes and spatial distributions

SUMMARY We model seismic wave propagation in media with discrete distributions of fractures using the pseudospectral method. The implementation of fractures with a vanishing width in the 2-D finite-difference grids is done using an effective medium theory (that is, the Coates and Schoenberg method). Fractures are treated as highly compliant interfaces inside a solid rock mass. For the physical representation of the fractures the concept of linear slip deformation or the displacement discontinuity method is used. According to this model, the effective compliance of a rock mass with one or several fracture sets can be found as the sum of the compliances of the host (background) rock and those of all the fractures. To first order, the background rock and fracture parameters can be related to the effective anisotropic coefficients, which govern the influence of anisotropy on various seismic signatures. We test the validity of the method and examine the accuracy of the synthetic seismograms by a comparison with theoretical ray traveltimes. We present three numerical examples to show the effects of different fracture distributions. The first example shows that different spatial distributions of the same fractures produce different wavefield characteristics. The second example examines the effects of variation of fracture scale length (size) compared with the wavelength. The final example examines the case of fractures with a power-law (fractal) distribution of sizes and shows how that affects the wavefield propagation in fractured rock. We conclude that characterization of fractured rock based on the concept of seismic anisotropy using effective medium theories must be used with caution. Scale length and the spatial distributions of fractures, which are not properly treated in such theories, have a strong influence on the characteristics of wave propagation.

Long range sediment tomography

The development of long range sediment tomography using shot data and its application in various field experiments is presented. Whereas traditional ocean acoustic tomography has mainly relied on linear inverse theory using the travel time of rays in deep water, our technique relies on nonlinear optimization techniques using the frequency-dependent travel time of normal modes in shallow water. Our experience with broadband sediment tomography using explosive sources started with the Barents Sea Polar Front Experiment where sediment properties were extracted using ground wave analysis. The techniques were further refined during the Shelf Break Primer Experiment in the New England Bight where a nonlinear inversion scheme using the Genetic Algorithm was successfully applied. The inversion scheme was based on modal travel time dispersion characteristics, which in shallow water conditions, is highly sensitive to the bottom properties. Advanced signal processing tools for the space–time–frequency processing and hybrid optimizaton techniques for global search were developed and implemented in parallel. In addition to the individual modal arrival times, emphasis has now been placed on the arrival corresponding to the Airy phase. These inversion techniques are currently being applied to the data from ASIAEX-East China Sea Experiment. Characteristics of this tomography approach such as spatial coverage, resolution, error bars, robustness, and simple instrumentation requirements will be presented. The usefulness of this inversion approach as a rapid environmental assessment tool will be highlighted. [Work supported by ONR.]

Internal gravity waves and horizontal refraction of sound in the ocean

Horizontal refraction, i.e., the deviation of acoustic propagation paths from the source–receiver vertical plane, is usually weak in the ocean. In this paper, a perturbation approach [O. A. Godin, J. Comput. Acoust. 10, 123–151 (2002)] to describe horizontal refraction within the ray and the ‘‘vertical modes—horizontal rays’’ theories is extended to media with a combination of stochastic and deterministic inhomogeneities and subsequently utilized to quantify 3-D acoustic effects due to internal gravity waves. Within the perturbation approach, statistical moments of adiabatic mode amplitude and phase and ray travel time are given explicitly by integrals of respective moments of cross-range derivatives of environmental parameters along the trajectory of the sound wave in an unperturbed (range-dependent) medium. Specific scenarios considered simulate conditions of recent propagation experiments. In shallow water, internal wave soliton-induced horizontal refraction can result in travel time biases O(10 ms) at propagation ranges as small as 10 km. In deep water, at ranges about 1000 km horizontal refraction due to internal waves with the Garrett–Munk spectrum leads to acoustic travel times being O(10 ms) less than in 2-D simulations. Without the internal waves, the travel time bias is found to be smaller by an order of magnitude. [Work supported by ONR.]

Propagation variability and localization accuracy of infrasonic networks

Prediction of propagation variability induced by the environment is used to evaluate the localization performance of infrasonic networks. The dominant source of variability affecting infrasonic propagation is believed to result from gravity waves. A gravity wave spectral model based on scale-independent diffusive filtering is used to generate multiple wind perturbation realizations. A Monte Carlo simulation is executed where rays are traced through the perturbed environmental fields, and uncertainty in ray travel time and azimuthal deviation is calculated. The propagation uncertainties, along with uncertainty in infrasonic measurements, are then used to compute 90 percent confidence bounds of multi-station event localizations. Infrasonic data from the April 2001 Pacific bolide event are used to compute the performance of a five station network, and the network localization is compared to that found from satellites. [Work sponsored by Defense Threat Reduction Agency, Contract No. DTRA01-00-C-0063.]

Travel time bias at sound reflection from an uneven surface: Implications for ocean remote sensing

Travel time is the acoustic quantity which is most frequently used to infer physical properties of the ocean or its bottom from acoustic measurements. Ocean boundaries typically have a complicated shape with smaller-scale features normally described as random roughness. The roughness translates into fluctuations of reflected acoustic arrivals. In this paper, statistical properties of acoustic travel time are considered in homogeneous and a vertically-stratified 3-D ocean with rough boundaries and interfaces. On average, the rough surfaces can be either horizontal planes, corresponding to the ocean surface, or deterministic curved surfaces, corresponding to the sea floor or interfaces within the ocean bottom. It is shown that mean acoustic travel time differs from the travel time in an average medium. In particular, in agreement with Fermat’s principle, small cross-range slopes of the reflecting surface always decrease ray travel time. The travel time bias is studied using the ray and the adiabatic normal mode theories. Implications are analyzed of the travel time bias on interpretation of measurements made with echo sounders, inverted echo sounders, and tomography systems employing surface- and/or bottom-reflected arrivals. [Work supported by ONR.]

Seismic structure of western end of the Nankai trough seismogenic zone

In 1998 a seismic experiment along a 320‐km‐long profile using an air gun array and ocean bottom seismographs (OBSs) was collected in the on shore‐offshore, forearc region of the western Nankai trough seismogenic zone, southwestern Japan. This area is outside the coseismic rupture area of the 1946 Nankaido earthquake (Ms = 8.2). The main objectives of this paper are to clarify the P wave and the Poisson's ratio profile around the forearc region of southwestern Japan, and estimate differences between this area and the Nankaido coseismic rupture area. The P wave velocity model estimated by two‐dimensional (2‐D) ray tracing and travel time inversion indicates three units with distinctive velocity patterns. The lens‐shaped unit has a maximum thickness of 5 km and velocity of 3.4–4.0 km/s. The underlying unit has velocity of 5.4–5.6 km/s, and its P wave velocity increases on land (Vp = 6.2–6.4 km/s). The relative homogeneous unit with P wave velocity of 6.6–6.9 km/s exists just beneath secondary unit with P velocity of 5.4–5.6 km/s. The angle of subduction is ∼7°. We also obtained a Poisson's ratio of the crustal structure of the forearc region. The Poisson's ratio of the southern part of secondary unit is larger than that of the northern part. We conclude that these data indicate clay‐rich metamorphic rocks plus oceanic basaltic rocks, rather than high‐porosity materials, comprise the majority of the layer. We suggest that the region of high Poisson's ratio probably corresponds to underplating and the metamorphism of the clay‐rich sediments and possibly the oceanic basalt just below the decollement.

Sensitivity of ray travel times.

Ray in a waveguide can be considered as a trajectory of the corresponding Hamiltonian system, which appears to be chaotic in a nonuniform environment. From the experimental and practical viewpoints, the ray travel time is an important characteristic that, in some way, involves an information about the waveguide condition. It is shown that the ray travel time as a function of the initial momentum and propagation range in the unperturbed waveguide displays a scaling law. Some properties of the ray travel time predicted by this law still persist in periodically nonuniform waveguides with chaotic ray trajectories. As examples we consider few models with special attention to the underwater acoustic waveguide. It is demonstrated for a deep ocean propagation model that even under conditions of ray chaos the ray travel time is determined, to a considerable extent, by the coordinates of the ray endpoints and the number of turning points, i.e., by a topology of the ray path. We show how the closeness of travel times for rays with equal numbers of turning points reveals itself in ray travel time dependencies on the starting momentum and on the depth of the observation point. It has been shown that the same effect is associated with the appearance of the gap between travel times of chaotic and regular rays. The manifestation of the stickiness (the presence of such parts in a chaotic trajectory where the latter exhibits an almost regular behavior) in ray travel times is discussed. (c) 2002 American Institute of Physics.

Wavefronts and waveforms in deep-water sound propagation.

A new method of calculating waveforms in underwater sound propagation is presented. The method is based on a Hankel transform-generalized Wentzel-Kramers-Brillouin (WKB) solution of the wave equation. The resulting integral leads to a new form of ray theory which is valid at relatively low frequencies and allows evaluation of the acoustic field on both the illuminated and shadow sides of caustics and at cusps where two caustics meet to form a focus. The integral is evaluated by stationary phase methods for the appropriate number of stationary points. Rays of nearby launch angle which have a travel time difference less than a quarter period must be considered together. The description of all other ray arrivals corresponds to simple ray theory. The phase, amplitude, and travel time of broadband acoustic pulses are obtainable directly from a simple graph of ray travel time as a function of depth at a given range. The method can handle range dependence but is illustrated here in long-distance propagation in deep water where the ray paths do not pass close to surface or bottom. The method is fast and gives close agreement with normal-mode calculations. The field on the shadow side of a caustic is properly given in terms of rays with complex launch angles, but good approximations can be obtained without the need to find complex rays.

Study and review on crust-mantle velocity structure in Bohai Bay and its vicinity

Observational data from some of the 10-odd deep seismic sounding profiles in Bohai Bay and its adjacent areas were processed with the methods of two-dimensional ray tracing, travel-time fitting and synthetic seismogram. The crust and upper-mantle velocity structure model in this area was built. The results show that the crust and upper mantle structures present obvious lateral and vertical inhomogeneity. The upper mantle uplifts near Yongqing of northeast Jizhong depression, in Bohai Bay of Huanghua depression and near Kenli of Jiyang depression, where crustal depths are about 31 km, 28 km and 29 km, respectively. According to the dynamic and kinetic characteristics of seismic waves as well as the seismic interfaces and velocity contour undulation in the 2-D velocity structure model, three deep crustal fault zones are inferred in the area. Low velocity (5.90–6.10 km/s) layers (bodies) exist on one or two sides of these deep crustal fault zones.

Ocean tomography, inverse methods, and broadband ocean acoustics

Ocean acoustic tomography, as proposed by Munk and Wunsch in 1979, and as implemented by the Ocean Tomography Group, uses ray travel times to estimate ocean sound speed and currents. Earlier work by Medwin (1970) and Hamilton (1977) used pulse travel times as measures of integrated sound speed along paths at short and long range, respectively. Munk and Wunsch (1979) recognized that broadband transmissions between many instruments could be used with inverse methods [Backus and Gilbert (1967); Liebelt (1967)] to reconstruct 3D ocean sound speed fields from the travel times along multiple paths. Inverse methods are widely used in ocean acoustics and in physical oceanography, and the modern challenge is to incorporate time dependence into the inverse methods to take advantage of the improving ocean dynamical models. In addition, the understanding of broadband acoustic propagation has improved to the point of refining the sensitivity kernel for travel time measurements beyond the simple geometrical optics of ray paths. This paper will review the evolving use of forward and inverse methods in acoustical oceanography, primarily with application to acoustic tomography.

Investigation of blast-induced fracture in rock mass using reversed vertical seismic profiling

The rock mass on quarry and pit wall surfaces is usually fractured during production blasting. Quantitative investigations of the fractured zones are needed for stabilization of the rock walls. In this study, the principle of reversed vertical seismic profiling (RVSP) was applied. A set of seismic geophones were arranged on the horizontal bench surface and seismic signals were generated along the vertical rock wall using a free-swinging hammer. The travel times of seismic rays were recorded and the P-wave velocities of the rock mass were analyzed using the Simultaneous Iterative Reconstruction Technique (SIRT). A series of site tests have been carried out on the rock walls at a granite quarry that are characterized by fractures. The fracture depth at various locations on the wall surface is thereby determined. The results indicate that RVSP provides an easy and reliable method to quantitatively evaluate the blasting-induced fractures in the rock mass.