Asymptotic Ray Theory Research Articles

Ray perturbation theory, dynamic ray tracing and the determination of Fresnel zones

Ray perturbation theory and dynamic ray tracing both describe the behaviour of seismic rays near a reference ray. The equations of dynamic ray tracing relate changes in position and direction of a ray in the vicinity of a reference ray (paraxial ray) to changes in the reference ray's initial conditions. Ray perturbation theory relates changes in paraxial rays to changes in the slowness field or the reference ray's endpoints. Dynamic ray tracing is performed in ray-centred coordinates, whereas ray perturbation theory may be performed in either ray-centred coordinates or in an external reference frame. Both methods derive from asymptotic ray theory, but their developments have proceeded along largely independent paths. In this paper we explore the relationship between dynamic ray tracing and ray perturbation theory and outline an efficient scheme, based on ray perturbation theory, to compute approximate Fresnel zones in inhomogeneous media.

Structure and ageing of oceanic crust at 14°S on the East Pacific Rise

A wide-angle reflection/refraction survey was conducted along a flow line on the eastern flank of the East Pacific Rise at 14°S. The data were acquired with a single 32-litre airgun and ocean-bottom hydrophones (OBH) and consist of six profiles on 0.5–8.3 Myr old seafloor. In total, 17 OBHs provided seismic records of excellent quality. To generate 2-D velocity models, traveltimes and amplitudes have been calculated using asymptotic ray theory. A comparison of the traveltimes and amplitudes of P-wave arrivals on all lines revealed important similarities that correlate well with the classical model of oceanic crust. The uppermost crust is composed of a 0.4–0.7 km thick low-velocity (2.9–4.6 km s−1) surficial layer (layer 2A) and is bounded at its base by a sharp velocity increase to ∼5.5 km s−1 at the top of layer 2B. Overall, layer 2 is 1.4–1.8 km thick. Small seamounts, frequently superposed on fast-spreading crust, are characterized by velocities lower than within the adjacent upper crust. Velocities <6.0 km s−1 exist throughout the edifices, suggesting that the seamounts are dominantly extrusive. Decreasing amplitudes beyond 8–10 km offset constrain a moderate-gradient lower crust (layer 3) with velocities of 6.8–7.2 km s−1. Crustal thickness is found to be remarkably uniform, at 6.11±0.14km. Nevertheless, the seismic data provide evidence for age-dependent variations in both the low-velocity surficial layer and the upper mantle. We find that velocities in layer 2A increase from 2.9 to 4.3 km s−1. Velocities in the middle and lower crust show uniform values, while velocities within the uppermost mantle increase gradually from <7.5 km s−1 to 8.0 km s−1. The most viable explanation for increasing velocities in the upper crust is that off-axis hydrothermal circulation was accompanied by the precipitation of secondary minerals in open void spaces, thereby decreasing the porosity and increasing the velocity. Low mantle velocities beneath young crust are suggested to be a temperature-controlled phenomenon and may indicate the presence of partial melt in the upper mantle.

Maslov Shear-Waveforms in Highly Anisotropic Shales and Implications for Shear-Wave Splitting Analyses

Shales are the most common sedimentary rocks in hydrocarbon environments often forming the source rock and trapping rock for a reservoir. Due to the platey nature of the constituent grains, shales are commonly anisotropic. In this paper we calculate seismic waveforms for highly anisotropic shales using Maslov asymptotic theory (MAT). This theory is an extension of classical ray theory which provides valid waveforms in regions of caustics (wavefront folding) where ray theory amplitudes are unstable. Asymptotic ray theory (ART) is based on the Fermat or geometrical ray which connects the source and receiver. In contrast, the Maslov solution integrates the contributions from neighbouring non-Fermat rays. Raypaths, travel-times, amplitudes and synthetic seismograms are presented for three highly anisotropic shales using a very simple 1D model comprised of an anisotropic shale overlying an isotropic shale. The ART waveforms fail to account for complex waveform effects due to triplications. In comparison, the MAT waveforms predict nonsingular amplitudes at wavefront cusps and it predicts the diffracted signals from these cusps. A Maslov solution which integrates ray contributions over a single slowness component will break down when rays focus in 3D (at a point rather than along a line). One of the tested shales shows such a point caustic and integration over 2 slowness components is required to remove the amplitude singularity. Finally, we examine the effects of wavefront triplications on Alford rotations which are used to estimate shear-wave splitting. In such cases, the rotation successfully finds the fast shear-wave polarization, but it can be unreliable in its estimate of the time separation.

Diffractions and boundary conditions in asymptotic ray theory

Summary Bakker (1990) and, earlier, Klem-Musatov & Aizenberg (1984) have provided formulations for diffracted waves that complete the zero-order approximation to the seismic wavefield of asymptotic ray theory (ART). This combined solution is correct to O(1/√ω). An advantage of ART is its ability to deal with complex geological situations, and hence one must establish that the diffracted waves of Klem-Musatov & Aizenberg (1984) and Bakker (1990) satisfy the relevant boundary conditions for a complex model. We show that the diffracted waves do indeed satisfy the elastic boundary conditions to O(1/√ω) when they reflect from or transmit through a smooth interface. If a diffracted wave is incident near a point on the interface that is not smooth, then the above-mentioned formulation only applies to the reflected and transmitted diffracted waves on one side of the irregularity, and here the boundary conditions are met. (This is the side upon which the geometrical rays are incident.) Also, we calculate the synthetic seismograms for the so-called Amoco model of Hron & Chan (1995) for an impulsive source for zero-order ART, both with and without diffractions. This illustrates the effectiveness of the diffracted waves in smoothing discontinuities in the seismic wavefield common in the zero-order ART approximation.

Three-dimensional geometrical ray theory and modelling of transmitted seismic energy of data from the Nevada Test Site

This paper presents a geometrically based algorithm for computing synthetic seismograms for energy transmitted through a 3-D velocity distribution. 3-D ray tracing is performed to compute the traveltimes and geometrical spreading (amplitude). The formulations of both kinematic and dynamic ray-tracing systems are presented. The two-point ray-tracing problem is solved by systematically updating the initial conditions and adjusting the ray direction until the ray intersects the specified endpoint. The amount of adjustment required depends on the derivatives of the position with respect to the given starting angles between consecutive rays. The algorithm uses derivatives to define the steepest-descent direction and to update the initial directions. The convergence rate depends on the complexity of the model. Test seismograms compare favourably with those from a 2-D asymptotic ray theory algorithm and a 3-D Gaussian-beam algorithm. The algorithm is flexible in modelling arbitrary source and recorder geometries for various smoothly varying 3-D velocity distributions. The algorithm is further tested by simulating surface-to-tunnel vibroseis field data. Shear waves as well as compressional waves may be approximately included. Application of the algorithm to a data set from the Rainier Mesa of the Nevada Test Site produced a good fit to the transmitted (first arrival) traveltimes and amplitudes, with approximately 15 per cent variation in the local 3-D velocity.

Precision analysis of first‐break times in grid models

Rectangular grid velocity models and their derivatives are widely used in geophysical inversion techniques. Specifically, seismic tomographic reconstruction techniques, whether they be based on raypath methods (Bregman et al., 1989; Moser, 1991; Schneider et al., 1992; Cao and Greenhalgh, 1993; Zhou, 1993) or full wave equation methods (Vidale, 1990; Qin and Schuster, 1993; Cao and Greenhalgh, 1994) for calculating synthetic arrival times, involve propagation through a grid model. Likewise, migration of seismic reflection data, using asymptotic ray theory or finite difference/pseudospectral methods (Stolt and Benson, 1986; Zhe and Greenhalgh, 1997) involve assigning traveltimes to upward and downward propagating waves at every grid point in the model. The traveltimes in both cases depend on the grid specification. However, the precision level of such numerical models and their dependence on the model parameters is often unknown. In this paper, we describe a two‐dimensional velocity model and derive an error bound for first‐break times calculated with such a model. The analysis provides clear guidelines for grid specifications.

Chaotic ray behaviour in regional seismology

SUMMARY Rays propagating through strongly laterally varying media exhibit chaotic behaviour. This means that initially close rays diverge exponentially, rather than according to a power law. This chaotic behaviour is especially pronounced if the medium contains laterally varying interfaces. By studying simple 2-D and 3-D versions of models with laterally varying interfaces, the importance of chaotic ray behaviour is determined. A model of the Moho below Germany produces sharp variations with epicentral distance of the number of arrivals. In addition, the number of caustics grows dramatically: up to 1200 caustics are present between a distance of 0 and 800 km. Using the theory of Hamiltonian systems, a more in-depth study of the chaotic character of the ray equations is obtained. It is found that for realistic heterogeneous models most of the relevant rays will exhibit chaotic behaviour. The degree of chaos is quantified in terms of predictability horizons. Beyond the predictability horizons ray tracing cannot be carried out accurately. For the models under consideration, the length from the source to the predictability horizon has an order of magnitude of 1000 km. The chaotic behaviour of the rays makes it necessary to use extensions of asymptotic ray theory, such as Maslov theory, to compute seismic waveforms. It is shown that pseudo-caustics, an important obstacle in computing Maslov synthetics, are a generic feature of the 2-D laterally varying models that are studied. Eventually, the use of asymptotic methods is restricted because of the inaccuracy in the computation of the ray paths.

Effects of anelasticity on reflection and transmission coefficients

It is known that the reflection and transmission coefficients used in the zeroth order approximation of asymptotic ray theory (ART) are identical to those obtained for the plane wave impinging on a plane interface separating two perfectly elastic half‐spaces. We have used ART to compute reflection and transmission coefficients for two viscoelastic media separated by a plane interface. Our method is different from the plane‐wave approach because the ART approach requires only a local application of the boundary conditions both for the eikonal and the ray amplitudes.Several types of viscoelastic media were studied. For a given model, the elastic case was emulated by setting all the quality factors Q equal to each other. Several anelastic cases were computed by keeping the same velocities and densities while changing the Qs. The quality factor is a relatively difficult parameter to measure exactly. Hence elastic coefficients are used in most synthetic seismogram computations, and the quality factors are chosen from experimental measurements or simply estimated.From these computations, amplitude and phase differences between elastic coefficients and coefficients for dissipative media are observed in some cases. These differences show the importance of knowing the exact values of Q. Incorrect Q values can lead to unrealistic moduli and to noticeable phase differences of these viscoelastic coefficients.

Uniformly valid body-wave ray theory

We present a uniformly valid ray theory for body-wave propagation in laterally heterogeneous earth models. This is accomplished by implementing Maslov theory, which is a 3-D analogue of the widely used WKBJ seismogram method for spherically symmetric earth models. Away from caustics, complete seismic waveforms can be calculated by solving a system of 14 coupled first-order ordinary differential equations: four equations determine the ray geometry, eight additional equations determine the amplitude, and two further equations determine traveltime and attenuation. In the vicinity of a caustic, neighbouring rays cross, and asymptotic ray theory breaks down. Rather than considering the contribution to the wavefield of one single ray, our strategy is to express the wavefield in the vicinity of a caustic as a summation over neighbouring, non-Fermat rays based upon Maslov theory. Away from caustics, Maslov theory reduces to asymptotic ray theory. We present examples of the ray geometry in the 3-D model SKS12WM13, and demonstrate that small-scale triplications in the traveltime curve associated with large-scale heterogeneities in the lowermost mantle are ubiquitous. The theory is applicable to direct, turning and reflected waves, may to a limited extent be advanced to include head waves, but does not describe waves that are diffracted into the deep shadow. The determination of the geometric ray that connects a given source and receiver is based upon a ‘shooting’ method. Initial guesses for the take-off angles are determined based upon perturbation theory, which substantially reduces the number of iterations required to hit a receiver. Perturbation theory also provides predictions for arrival angles and amplitude anomalies. These predictions incorporate the effects of long-wavelength topography on internal boundaries and the free surface, and may be used as a basis for tomographic inversions. Generally, predictions based upon perturbation theory agree very well with exact 3-D ray tracing. Just as traveltime measurements provide constraints on velocity, arrival angles constrain velocity gradients, and amplitude anomalies put constraints on second derivatives in velocity. In SKS12WM13, traveltime anomalies can be as much as ±10 s, arrival-angle anomalies can be larger than ±5°, and 3-D amplitudes can differ by more than 100 per cent from PREM amplitudes.

SH-wave Green tensor for homogeneous transversely isotropic media by higher-order approximations in asymptotic ray theory

Tensor equations of the ray theory for homogeneous anisotropic elastic media are presented. For a point source, an explicit solution of the transport equation is obtained, thus the additional as well as principal components of the ray amplitudes for higher-order ray approximations are expressed only by differential operators of lower-order terms. Possibility of analytical calculation of higher-order approximations is exemplified for SH waves in a transversely isotropic medium. The ray series of the SH-wave Green tensor for the transversely isotropic medium involves only two non-zero terms and the complete ray solution coincides with an exact solution obtained by other complicated procedures.

Asymptotic ray theory for transient diffusive electromagnetic fields

We develop an asymptotic ray theory for transient diffusive electromagnetic fields in isotropic media. The formulation is first derived in the time Laplace transform domain by introducing an ansatz procedure, whereby appropriate expansions for the electric and the magnetic field strengths are substituted in the original field equations. We arrive at consistent recurrence formulas for the sequences of field amplitude vectors that multiply appropriately chosen asymptotic sequences of algebraic powers of the Laplace transform parameter. These representations differ for the two types of fields (electric and magnetic fields) and for the two types of sources (electric current source and magnetic current source). The exponential part of the field expressions contains the diffusive equivalent of the eikonal function in the asymptotic ray theory of wave propagation. This function satisfies the diffusive equivalent of the eikonal equation. Next, we derive the transport equations for the vectorial electric and magnetic field amplitudes of the successive orders. Transient field representations within the asymptotic ray approximation are then obtained by carrying out the inverse Laplace transformation to the time domain by inspection. The ray approximation thus obtained is asymptotic for “early times”. We consider as an example the case of the electric and the magnetic dipole radiation in a homogeneous medium. Here an exact solution exists, which we show to exhibit the structure of the original ansatz but with a finite number of terms. The asymptotic ray theory for transient diffusive electromagnetic fields is expected to lend itself to important applications in surface, surface‐to‐borehole, and crosswell transient electromagnetic prospecting.

Tutorial on the numerical modeling of edge diffracted waves by the ray method

The concept of diffracted rays introduced by Keller (1962) opened the way for a ray approach in the numerical modeling of the diffraction phenomena frequently seen in the seismic field records. Unlike the computation of travel times, which has never caused any difficulties being governed by the same eikonal equation as are the rays of ordinary seismic body waves, the evaluation of the diffracted ray amplitude has been another story. In this paper we give a tutorial account of a highly promising technique for the computation of the ray amplitude of seismic waves diffracted by linear edges on seismic interfaces originally presented by Klem-Musatov (1980, 1995). We demonstrate the adequacy of this technique on a series of SH synthetic traces containing diffracted arrivals, some of them diffracted more than once. Our computer program is based on a successful combination of Klem-Musatov's approach with the zero order approximation of the Asymptotic Ray Theory (Cervený and Hron, 1980). We showed in the paper that both techniques are ideally suited for such a combination, since the ray amplitude evaluation in each of them is based on the same transport equation. In our tutorial review we present all formulae which are needed for a practical implementation of the method and provide their physical interpretation, wherver possible, by using the numerical examples presented in the paper.

Synthetic seismograms from generalized ray tracing1

AbstractA new method of numerical computation of elastic wavefields in regions containing caustics is tested. The method is an extension of the asymptotic ray theory (ART). The essential features of the method consist of the application of expressions which are well defined at caustics and expressed in terms of ray tracing combined with complex ray tracing in caustic shadows. The method and an outline of the underlying theory are briefly presented, followed by a comparison with finite differences on a test model involving a caustic cusp. The comparison reveals the unexpectedly high degree of accuracy of the new method.

Migration/inversion for transversely isotropic elastic media

SUMMARY Seismic migration and inversion are closely related processes for obtaining images of the subsurface. Both techniques attempt to infer petrophysical and structural parameters from seismic data, and both are driven by an underlying mathematical model for wave propagation in the earth. In this sense, migration can be regarded as the first step in’ a general linearized-inversion scheme; we adopt this viewpoint here in formulating a joint migration/inversion method for anisotropic elastic media. Our derivation is based on the distorted-wave Born approximation, where approximate Green’s functions for the background medium are determined using asymptotic ray theory. We also make use of a stationary-phase correction to account for out-of-plane scattering in a 2-D earth model. The inversion is cast as a discrete, generalized l2 optimization problem, which we regularize using a priori model variances. An approximate solution is obtained in one or more iterations using a quasi-Newton technique. Our implementation is tailored for weakly anisotropic elastic media possessing transversely isotropic (TI) symmetry, and so is well suited for investigations of earth models characterized by a singe set of parallel fractures or periodic thin layering. Several TI model parametrization schemes are evaluated for a vertical-incidence narrow-aperture recording configuration. By applying singular-value decomposition to the approximate Hessian operator used in the inversion, we find that when the symmetry axis of the medium is vertically oriented the condition number is minimized by choosing vertical impedance parameters, density and Thomsen’s (1986) anisotropy parameters. Elastic stiffnesses and density may be a better parametrization choice if the symmetry axis is either horizontal or unknown. The small effective rank (2-3) of the Hessian in our narrow-aperture tests implies that migration inversion (without a priori constraints) of surface-reflection data may be inadequate to fully characterize a TI medium, which would require six parameters. However, this result does not in itself justify the use of simpler isotropic inversion schemes, since the principal eigenvectors determined here represent a blend of ‘isotropic’ and ‘anisotropic’ information about the earth. A suite of point-diffractor tests shows that individual perturbation amplitudes recovered in the inversion are smaller, but cover a larger region of the image, than those used in the original model, consistent with the band-limited nature of the input signal. Parameter cross-coupling problems affect the inversion results for all parameters, but are more prominent in the inversion images for anisotropy parameters. In our tests, the linearized-inversion results converge to a local minimum after three iterations, and the scatterer distributions in the inversion images are essentially fixed after a single iteration.

Complex rays in elastic and anelastic media

SUMMARY The concept of complex rays plays an important role in wave-propagation modelling. In this study we describe an efficient method for complex ray tracing. Our objective is to facilitate generalization of this concept to wave-propagation studies in general inhomogeneous media. By solving rigorously the complex eikonal equation arising from medium anelasticity, we strive to provide an accurate description of the wave-attenuation process in a realistic earth structure. to enhance practical utility of our method, we have developed a ray-perturbation scheme which keeps the computation to a minimum. A further advantage of our approach is that it can be used to extend the technique of complex source point to general inhomogeneous media. the said extension overcomes the singularity problem encountered by asymptotic ray theory near a caustic and is capable of modelling evanescent waves.

Understanding finite-frequency wave phenomena: phase-ray formulation and inhomogeneity scattering

SUMMARY A straight line connecting two points in a homogeneous elastic medium defines a body-wave ray path. A single wavefront can be said to be uniquely associated with a body-wave signal propagating along this path. Ray path and wavefront are concepts at once straightforward and useful in such media, where exact solutions may be attainable. In inhomogeneous media, signal distortions accompany the physical processes of focusingfdefocusing and scattering. The ray path depends on the signal frequency; the very concept of a single wavefront for each propagating body wave is blurred. To assume otherwise is tantamount to neglecting a host of wave phenomena intrinsically connected with the scattering effects due to medium inhomogeneities. An example of such a scattering-related wave phenomenon is frequency-dependent partial reflection of a body wave propagating in a zone of high-velocity gradient. These phenomena are not modelled by the published ray methods for seismic wavefield computation, limiting their applicability to homogeneous and weakly inhomogeneous media. The scattering-induced wave phenomena become increasingly more difficult to ignore as the wave-medium heterogeneity strengthens. To achieve a higher order of accuracy than the published ray methods, it is necessary to incorporate the scattering effects. The principal objective of this study is to extend our wavefield modelling capability to rapidly varying media by proper accounting for the scattering effects embodying, among others, frequency-dependent ray paths and scatteringinduced wave attenuation and dispersion. We demonstrate that the new formulation based on a phase eikonal equation can now model frequency-dependent partial reflections from a gradient zone. It is shown that the scattering process introduces signal smoothing and its incorporation in the wavefield calculation results in natural removal of the singularity of asymptotic ray theory near a caustic.

Generalized Born scattering in anisotropic media

The Born scattering approximation has been widely used in seismology to study scattered waves, and to linearize the propagation problem for inversion. The standard Born theory requires the model be separated into a smooth, reference model and a perturbation. Scattering occurs from the pertubation. In the distorted Born approximation, when the reference model is inhomogeneous, the reference Green's functions are normally not known exactly, but the error in these Green's functions is rarely quantified. In this paper, we generalize Born scattering theory to include the errors in the Green's functions explicitly, and obtain scattering integrals from these errors. For forward modelling, there is no need to separate the model into a reference and perturbation part - approximate Green's functions in the true model can be used to calculate the scattered signals. The theory is developed for inhomogeneous, anisotropic media. Asymptotic ray theory results are suitable approximate Green's functions for the generalized Born scattering theory. The error terms are simple, easily calculated and included in the scattering integrals. Various applications of generalized Born scattering theory have already appeared in the literature, e.g. quasi-shear ray coupling, and this paper is restricted to an improved and more complete theoretical development. Further applications will appear elsewhere.

The complete ordered ray expansion-I. Calculation of synthetic seismograms

SUMMARY As high-quality broad-band data become more widely available, efficient methods for modelling and inverting such data are increasingly required. In this paper we describe a novel method for calculating seismograms, referred to as the Complete Ordered Ray Expansion or CORE. This technique is based on a ray-generation algorithm involving the symbolic manipulation of complete wavefield expressions from reflectivity theory, truncated to produce a finite ray series. CORE represents an extremely flexible tool for the generation of body wave synthetics, and for the interpretation of observed seismograms. It also provides a framework for waveform inversion that exploits the natural division between smooth structure and discontinuities. We describe the ray-generation algorithm, and show examples of the effect of varying degrees of truncation on the ray series. Although CORE uses asymptotic ray theory to generate the seismograms from the ray series, the resulting traces show surprisingly good agreement with full reflectivity synthetics. We show comparisons of broad-band CORE and reflectivity synthetics, as well as a comparison with observed data. Our method is particularly useful in modelling the complete broad-band wave train at teleseismic distances, where the computing time for reflectivity becomes excessively large. The computational procedure is readily extended to a laterally heterogeneous model, where it forms the basis for a fully automated procedure for phase association and waveform inversion.

Anisotropic reflection and transmission calculations with application to a crustal seismic survey from the East Greenland Shelf

A three‐component refraction data set recorded over the East Greenland Shelf contained two anomalous shear wave arrivals. The direct‐S phase emerged at the receiver as an apparent SH wave even though the airgun source was purely compressional. We have concluded that this arrival is the result of anisotropy in the upper crust. By employing a number of fairly simple techniques we were able to highlight a second, delayed quasi‐shear arrival and interpret shear wave splitting. Modeling of the polarization, amplitude, and delay time of direct‐S suggested that the anisotropy is due to aligned subvertical fractures perpendicular to the local seafloor spreading direction. The second shear arrival of interest is a P to S conversion from the Moho (PmS). The relative strength of this arrival suggests that the Moho is a sharp transition in this region. PmS also contained a significant transverse component but attempts to identify shear wave splitting were inconclusive. However, modeling revealed that the transverse PmS displacement may be due to anisotropy in the upper mantle (alignment of olivine crystals with the spreading direction), which causes the converted S reflection to have a significant SH (transverse) component. An understanding of, and ability to model, anisotropic reflection and transmission effects are essential to these interpretations. Therefore we also outline an efficient method to obtain all of the reflection and transmission coefficients at boundaries between anisotropic media. This has been incorporated into a new ray tracing package, A‐TRAK, based on asymptotic ray theory, capable of modeling three‐dimensional inhomogeneous media separated by curved interfaces.

Crustal structure of Endeavour Ridge Segment, Juan de Fuca Ridge, from a detailed seismic refraction survey

A detailed seismic refraction survey was carried out over the Endeavour Segment of the Juan de Fuca Ridge, a medium‐rate spreading center which lies off western North America, to investigate the creation and evolution of oceanic crust. A bathymetric high and the presence of hydrothermal vents suggested that the study area was the most recent locus of spreading. Travel time and amplitude data from 15 in‐line air gun/ocean bottom seismometer profiles were forward modeled using asymptotic ray theory to obtain two‐dimensional velocity models consisting of four primary layers which correlate well with classic models of oceanic crust. Significant lateral variations in thicknesses and velocities on the scale of a few to 10 km are superimposed on this basic velocity structure, but they appear to be random rather than distributed symmetrically about the ridge. We attribute them to fracturing which causes porosity changes, hydrothermal circulation which fills voids and fractures with alteration products, and variations in magmatic and/or deformational processes at the spreading center. Layer 2A is found to have low (2.6–2.8 km/s) velocities, to average 0.4 km in thickness with variations up to 0.2 km, and to be bounded at its base by a sharp velocity increase to 4.8 km/s. Along the axial ridge, velocities 0.4–0.6 km/s higher than average are interpreted for layers 2B and 2C, but these values are confined to a 2‐km‐wide zone centered below the ridge. Velocities along ridge‐parallel lines offset 10 km are normal, indicating that maturation to off‐ridge structure has occurred within at most 0.3 Ma. Layer 3 velocities decrease by 0.1–0.2 km/s for arrivals traveling along and under the axial ridge, perhaps caused by higher temperatures. However, we find no anomalously low velocities beneath the ridge, indicating that no large crustal magma chamber exists. On the basis of this study, we conclude that magmatic accretion is a fully three‐dimensional process within ridge segments such as Endeavour Ridge.