Isotropic Phase Velocity Research Articles

Integrating controlled-source and ambient noise seismic measures for archaeological prospection: the Scrovegni Chapel case

SUMMARY In this paper, we present the results of an analysis of passive seismic noise recorded around the Scrovegni Chapel in Padua (Italy), using a dense 2-D network with nearly 1500 autonomous seismic nodes. Surface wave tomography using the active records allowed the imaging of several structures located at a depth of few metres, while this study focuses on the processing of about 22 hr of continuous passive records. First, the ambient noise is characterized in terms of amplitude, frequency content and azimuthal distribution, in order to ensure the applicability of the interferometric method. Second, a cross-correlation analysis is performed to retrieve virtual source gathers. Third, traveltimes are extracted from virtual source gathers using the same processing sequence applied to active gathers. Fourth, Eikonal tomography is run to retrieve isotropic phase velocity maps and azimuthal anisotropy. We compare and discuss the results obtained from the active and the passive methods, and finally propose a strategy for the integration of passive and active information. The new quasi-3-D shear wave velocity model obtained from the joint active and passive analysis is more accurate at depth, due to the addition of the passive low-frequency information.

Velocity and azimuthal anisotropy structure underneath the Reelfoot Rift region from Rayleigh wave phase velocity dispersion curves

SUMMARYPhase velocity and azimuthal anisotropy maps for fundamental mode Rayleigh waves are determined for a portion of the central United States including the seismically active Reelfoot Rift (RFR) and the enigmatic Illinois Basin. Dense seismic array installations of the Northern Embayment Lithosphere Experiment, the EarthScope transportable array and the Ozarks Illinois Indiana Kentucky array allow a detailed investigation of phase velocity and anisotropy in a broad period range (20–100s).We obtain more than 12 000 well-constrained, unique two-station paths from teleseismic events. The two-station method is used to determine dispersion curves and these are inverted for isotropic phase velocity maps and azimuthal anisotropy maps for each period. The presence of fast phase velocities at lower crustal and uppermost mantle depths is found below the RFR, and Ste. Genevieve and Wabash Valley fault zones. At periods of 30s and higher, the RFR is underlain by slow phase velocities and is flanked to the NW and SE by regions of fast velocity. Fast phase velocities are present below the centre of the Illinois Basin in the period range 75–100s. Anisotropy fast axis orientations display complex patterns for each period and do not trend parallel to the direction of absolute plate motion. Anisotropy fast directions are consistently parallel to the trend of the RFR from 50s to higher periods, suggesting the presence of either frozen-in anisotropic fabric or fabric related to material transport from a recently discovered, pronounced low velocity zone below the Mississippi Embayment.

Surface-wave phase-velocity maps of the Anatolia region (Turkey) from ambient noise tomography

The Anatolian region is an area with very heterogeneous crustal structure accompanied by large velocity contrasts. Despite the complexity of the region, the detailed crustal structure remains to be unraveled. In this study, we first measure the dispersion curves of Rayleigh waves between 1,721 pairs of station and then invert these dispersion curves to obtain high-resolution isotropic and azimuthally anisotropic phase-velocity maps in the period range of 5–25 s. The resulting isotropic phase-velocity patterns display strong correlation with the geological features, while the anisotropic patterns are highly consistent with the GPS-measured surface velocity field in the region. Variations of the isotropic as well as anisotropic patterns indicate the presence of active faulting, especially beneath the East and North Anatolian Faults. Beneath the locations of Holocene volcanoes and crystalline massifs in Cappadocia, high velocities (up to 2.5%) are present, whereas negative velocity anomalies (up to −2%) are found beneath the Menderes Massif in southwestern Anatolia (at periods of 5–20 s), suggesting different origins and tectonic regimes of those massifs. On either side of an active fault, two terranes with different stress patterns are generally found. Active fault can thus be identified by different anisotropy patterns on either sides of the fault. The Central Anatolian Fault do not display strong isotropic velocity contrasts, as well as no noticeable variation in the anisotropic pattern across the fault, suggesting that this fault may not be active in recent times.

Modeling of pure qP- and qSV-waves in tilted transversely isotropic media with the optimal quadratic approximation

Seismic forward modeling in tilted transverse isotropic (TTI) media is crucial for the application of reverse time migration and full-waveform inversion. Modeling based on conventional coupled pseudoacoustic wave equations not only generates SV-wave artifacts, but it also suffers from instabilities in which the anisotropy parameter [Formula: see text]. To address these issues, we have started with the exact vertical transversely isotropic phase velocity formula and developed novel pure qP- and qSV-wave governing equations in TTI media by using the optimal quadratic approximation. For the convenience of using finite-difference (FD) method to solve the new pure qP- and qSV-wave wave equations, we decompose the equations into a combination of a time-space-domain wave equation that can be solved by the FD method and a Poisson equation that can be solved by the pseudospectral method. We find that the high-frequency errors caused by the pseudospectral method and the usual truncation errors in FD schemes may be responsible for the instability of the numerical simulations. To stabilize the computation, we design a 2D low-pass filtering operator to eliminate severe high-frequency numerical noise. Several numerical examples demonstrate that modeling using the new pure qP-wave equations does not have qSV-wave artifacts interference and is stable for [Formula: see text]. Our results indicate that our method can achieve highly accurate and stable modeling results even in extremely complex TTI media.

Eikonal Tomography of the Southern California Plate Boundary Region

AbstractWe use Eikonal tomography to derive phase and group velocities of surface waves for the plate boundary region in Southern California. Seismic noise data in the period range 2 and 20 s recorded in year 2014 by 346 stations with ~1‐ to 30‐km station spacing are analyzed. Rayleigh and Love wave phase travel times are measured using vertical‐vertical and transverse‐transverse noise cross correlations, and group travel times are derived from the phase measurements. Using the Eikonal equation for each location and period, isotropic phase and group velocities and 2‐psi azimuthal anisotropy are determined statistically with measurements from different virtual sources. Starting with the SCEC Community Velocity Model, the observed 2.5‐ to 16‐s isotropic phase and group dispersion curves are jointly inverted on a 0.05° × 0.05° grid to obtain local 1‐D piecewise shear wave velocity (Vs) models. Compared to the starting model, the final results have generally lower Vs in the shallow crust (top 3–10 km), particularly in areas such as basins and fault zones. The results also show clear velocity contrasts across the San Andreas, San Jacinto, Elsinore, and Garlock Faults and suggest that the San Andreas Fault southeast of San Gorgonio Pass is dipping to the northeast. Investigation of the nonuniqueness of the 1‐D Vs inversion suggests that imaging the top 3‐km Vs structure requires either shorter period (≤2 s) surface wave dispersion measurements or other types of data set such as Rayleigh wave ellipticity.

Anisotropic Rayleigh wave tomography of Northeast China using ambient seismic noise

The ambient noise data recorded by 249 seismic stations in the permanent and temporary networks in Northeast China are used to invert for the isotropic phase velocity and azimuthal anisotropy of Rayleigh waves in the period band 5–50s. The inversion results reflect the structure from the shallow crust to upper mantle up to approximately 120km depth. Beneath the Songliao basin, both the fast direction in shallow crust and strike of a low-velocity anomaly in the middle crust are NNE–SSW, which is coincident with the main tectonic trend of the (Paleo) Pacific tectonic domain. This indicates that the rifting of the Songliao basin is influenced by the subduction of (Paleo) Pacific plate. The upper mantle of Songliao block (except the central area of Songliao basin) to the west of Mudanjiang fault, and the east of the North–South Gravity Lineament, is characterized by high-velocity and weak anisotropy up to approximately ​120km depth. We infer that there is delamination of lithospheric mantle beneath the Songliao block. Obvious N–S, NE–SW, and E–W trending fast directions are found in the lithospheric mantles of the east, west, and south sides of Songliao block, respectively, which coincide with the strikes of the Paleozoic tectonic in these areas. This suggests that the frozen-in anisotropic fabric in the lithospheric mantle can be used to indicate the historical deformation of the lithosphere. In the northern margin of the North China Craton, the spatial variations of phase velocity and azimuthal anisotropy are more dramatic than those in Northeast China blocks, which indicates that the lithosphere of the North China Craton has experienced more complicated tectonic evolution than that of the Northeast China blocks.

Time‐lapse analysis of ambient surface wave anisotropy: A three‐component array study above an underground gas storage

We perform a time‐lapse analysis of Rayleigh and Love wave anisotropy above an underground gas storage facility in the Paris Basin. The data were acquired with a three‐component seismic array deployed during several days in April and November 2010. Phase velocity and back azimuth of Rayleigh and Love waves are measured in the frequency range 0.2–1.1 Hz using a three‐component beamforming algorithm. In both snapshots, higher‐surface wave modes start dominating the signal above 0.4 Hz with a concurrent increase in back azimuth ranges. We fit anisotropy parameters to the array detections above 0.4 Hz using a bootstrap approach which also provides estimation uncertainty and enables significance testing. The isotropic phase velocity dispersion for Love and Rayleigh waves match for both snapshots. We also observe a stable fast direction of NNW‐SSE for Love and Rayleigh waves which is aligned with the preferred orientation of known shallow (<300 m) and deeper (∼1000 m) fault systems in the area, as well as the maximum horizontal stress orientation. At lower frequencies corresponding to deeper parts of the basin, the anisotropic parameters exhibit higher magnitude in the November data. This may perhaps be caused by the higher pore pressure changes in the gas reservoir in that depth range.

Surface wave phase velocity maps from multiscale wave field interpolation

Availability of spatially dense broadband observations of seismic surface wave fields allows to derive phase velocity maps on regional scale by non-tomographic means. I present a multiscale interpolation scheme for surface wave fields where for each observed wave field, a multiscale phase velocity map and its standard deviation are calculated from subsets of the available data. Isotropic phase velocity (with an estimate on its standard deviation) is then found as the weighted mean of multiscale maps from different observations. Comparison of different interpolation schemes on synthetic wave fields shows that bivariate linear interpolation of phases in a triangulated region, in conjunction with multiscale stacking, is not inferior than methods involving higher-order polynomials. The recovered phase velocity maps are, in the presence of random uncertainties with realistic magnitude, largely free of artifacts and restore a synthetic input model reasonably well. The method is applied to a subset of Rayleigh wave observations at USArray which yields phase velocity maps well within the range of published results. Multiscale interpolation seems to be a practical alternative to tomographic inversion for regional broadband seismic networks (≥30 stations). It requires no choice of arbitrary parameters and is insensitive to number of earthquakes and their azimuthal distribution.

A global model of Love and Rayleigh surface wave dispersion and anisotropy, 25-250 s

SUMMARY A large number of fundamental-mode Love and Rayleigh wave dispersion curves were determined from seismograms for 3330 earthquakes recorded on 258 globally distributed seismographic stations. The dispersion curves were sampled at periods between 25 and 250 s to determine propagation-phase anomalies with respect to a reference earth model. The data set of phase anomalies was first used to construct global isotropic phase-velocity maps at specific frequencies using spherical-spline basis functions with a nominal uniform resolution of 650 km. Azimuthal anisotropy was then included in the parametrization, and its importance for explaining the data explored. Only the addition of 2ζ azimuthal variations for Rayleigh waves was found to be resolved by the data. In the final stage of the analysis, the entire phase-anomaly data set was inverted to determine a global dispersion model for Love and Rayleigh waves parametrized horizontally using a spherical-spline basis, and with a set of B-splines to describe the slowness variations with respect to frequency. The new dispersion model, GDM52, can be used to calculate internally consistent global maps of phase and group velocity, as well as local and path-specific dispersion curves, between 25 and 250 s.

Helmholtz surface wave tomography for isotropic and azimuthally anisotropic structure

SUMMARY The growth of the Earthscope/USArray Transportable Array (TA) has prompted the development of new methods in surface wave tomography that track phase fronts across the array and map the traveltime field for each earthquake or for each station from ambient noise. Directionally dependent phase velocities are determined locally by measuring the gradient of the observed traveltime field without the performance of a formal inversion. This method is based on the eikonal equation and is, therefore, referred to as ‘eikonal tomography’. Eikonal tomography is a bent-ray theoretic method, but does not account for finite frequency effects such as wave interference, wave front healing, or backward scattering. This shortcoming potentially may lead to both systematic bias and random error in the phase velocity measurements, which would be particularly important at the longer periods studied with earthquakes. It is shown here that eikonal tomography can be improved by using amplitude measurements to construct a geographically localized correction via the Helmholtz equation. This procedure should be thought of as a finite-frequency correction that does not require the construction of finite-frequency kernels and is referred to as ‘Helmholtz tomography’. We demonstrate the method with Rayleigh wave measurements following earthquakes between periods of 30 and 100 s in the western US using data from the TA. With Helmholtz tomography at long periods (>50 s): (1) resolution of small-scale isotropic structures, which correspond to known geological features, is improved, (2) uncertainties in the isotropic phase velocity maps are reduced, (3) the directionally dependent phase velocity measurements are less scattered, (4) spurious 1-psi azimuthal anisotropy near significant isotropic structural contrasts is reduced, and (5) estimates of 2-psi anisotropy are better correlated across periods.

Ambient noise tomography with a large seismic array

The emergence of large-scale arrays of seismometers across several continents presents the opportunity to image the Earth's structure at unprecedented resolution, but methods must be developed to exploit the capabilities of these deployments. The capabilities and limitations of a method called “eikonal tomography” applied to ambient noise data are discussed here. In this method, surface wave wavefronts are tracked across an array and the gradient of the travel time field produces estimates of phase slowness and propagation direction. Application data from more than 1000 stations from EarthScope USArray in the central and western US and new Rayleigh wave isotropic and anisotropic phase velocity maps are presented together with an isotropic and azimuthally anisotropic 3D Vs model of the crust and uppermost mantle. As a ray theoretic method, eikonal tomography models bent rays but not other wavefield complexities. We present evidence, based on the systematics of an observed 1 ψ component of anisotropy that we interpret as anisotropic bias caused by backscattering near an observing station, that finite frequency phenomena can be ignored in ambient noise tomography at periods shorter than ∼ 40 to 50 s. At longer periods a higher order term based on wavefront amplitudes or finite frequency sensitivity kernels must be introduced if the amplitude of isotropic anomalies and the amplitude and fast-axis direction of azimuthal anisotropy are to be determined accurately.

Depth constraints on azimuthal anisotropy in the Great Basin from Rayleigh-wave phase velocity maps

We present fundamental-mode Rayleigh-wave azimuthally anisotropic phase velocity maps obtained for the Great Basin region at periods between 16 s and 102 s. These maps offer the first depth constraints on the origin of the semi-circular shear-wave splitting pattern observed in central Nevada, around a weak azimuthal anisotropy zone. A variety of explanations have been proposed to explain this signal, including an upwelling, toroidal mantle flow around a slab, lithospheric drip, and a megadetachment, but no consensus has been reached. Our phase velocity study helps constrain the three-dimensional anisotropic structure of the upper mantle in this region and contributes to a better understanding of the deformation mechanisms taking place beneath the western United States. The dispersion measurements were made using data from the USArray Transportable Array. At periods of 16 s and 18 s, which mostly sample the crust, we find a region of low anisotropy in central Nevada coinciding with locally reduced phase velocities, and surrounded by a semi-circular pattern of fast seismic directions. Away from central Nevada the fast directions are ∼ N–S in the eastern Great Basin, NW–SE in the Walker Lane region, and they transition from E–W to N–S in the northwestern Great Basin. Our short-period phase velocity maps, combined with recent crustal receiver function results, are consistent with the presence of a semi-circular anisotropy signal in the lithosphere in the vicinity of a locally thick crust. At longer periods (28–102 s), which sample the uppermost mantle, isotropic phase velocities are significantly reduced across the study region, and fast directions are more uniform with an ∼ E–W fast axis. The transition in phase velocities and anisotropy can be attributed to the lithosphere–asthenosphere boundary at depths of ∼ 60 km. We interpret the fast seismic directions observed at longer periods in terms of present-day asthenospheric flow-driven deformation, possibly related to a combination of Juan de Fuca slab rollback and eastward-driven mantle flow from the Pacific asthenosphere. Our results also provide context to regional SKS splitting observations. We find that our short-period phase velocity anisotropy can only explain ∼ 30% of the SKS splitting times, despite similar patterns in fast directions. This implies that the origin of the regional shear-wave splitting signal is complex and must also have a significant sublithospheric component.

Analysis of ambient noise energy distribution and phase velocity bias in ambient noise tomography, with application to SE Tibet

SUMMARY Green’s functions (GFs) of surface wave propagation between two receivers can be estimated from the cross-correlation of ambient noise under the assumption of diffuse wavefields or energy equipartitioning. Interferometric GF reconstruction is generally incomplete, however, because the distribution of noise sources is neither isotropic nor stationary and the wavefields considered in the cross-correlation are generally non-diffuse. Furthermore, medium complexity can affect the empirical Green’s function (EGF) from the cross-correlation if noise sources are all far away (i.e. approximately plane-wave sources), which makes the problem non-linear. We analyse the effect of uneven ambient noise distribution and medium heterogeneity and azimuthal anisotropy on phase velocities measured from EGFs with an asymptotic plane wave (far-field) approximation (which underlies most constructions of phase velocity maps). Phase velocity bias due to uneven noise distribution can be determined (and corrected) if the noise energy distribution and the velocity model are known. We estimate the (normalized) azimuthal distribution of ambient noise energy directly from the cross-correlation functions obtained through ambient noise interferometry. The (smaller, second order) bias due to non-linearity can be reduced iteratively, for instance by using the tomographic model that results from the inversion of uncorrected data. We illustrate our method for noise energy estimation, phase velocity bias suppression, and ambient noise tomography (including azimuthal anisotropy) with data from a seismic array (26 stations) in SE Tibet. We show that the phase velocity bias due to uneven noise energy distribution (and medium complexity) in SE Tibet has a small effect (<1 per cent) on the isotropic part phase velocities (for T = 10–30 s) and the azimuthal anisotropy obtained before and after bias correction shows very similar pattern and magnitude.

Rayleigh wave phase-velocity heterogeneity and multilayered azimuthal anisotropy of the Superior Craton, Ontario

SUMMARY We study the azimuthally anisotropic upper-mantle structure of the Superior Craton and Grenville Province in Ontario, Canada, using Rayleigh wave phase-velocity data in the period range 40–160 s. 152 two-station dispersion measurements are combined in a tomographic inversion that solves simultaneously for isotropic and anisotropic terms using a least-squares technique. We perform a series of tests to derive optimal regularization (smoothing and damping) and to assess the resolution of, and trade-offs between, isotropic and anisotropic anomalies. The tomographic inversion is able to resolve isotropic phase-velocity anomalies on a scale of 200-300 km and to distinguish between different anisotropic regimes on a 500-km scale across the study region. Isotropic phase-velocity anomalies in the tomographic model span a range of up to ±2 per cent around a regional average which is similar to the Canadian Shield dispersion curve of Brune & Dorman (1963), with phase velocities up to 3 per cent above global reference models. The amplitude of azimuthal phase-velocity anisotropy reaches a maximum of ∼1.2 per cent. A clear east–west division of the study area, based on both isotropic phasevelocity anomalies and azimuthal anisotropy, is apparent. In the western Superior, isotropic phase velocities are generally higher than the regional average. Anisotropy is observed at all periods, with ENE–WSW to NE–SW fast-propagation directions. At periods ≤120 s, the anisotropy likely results from frozen lithospheric fabric aligned with tectonic boundaries, whereas the anisotropy at longer periods is interpreted to arise from present-day sublithospheric flow. The fast directions from published SKS measurements are close to the fast Rayleigh wave propagation directions throughout the period range sampled, and the large SKS splitting times may be accounted for by this near-coincidence of fast-propagation directions. Across most of eastern Ontario, phase velocities are lower than the regional average. Fast-propagation directions rotate from ∼NW–SE at 40–130 s period to WNW–ESE at periods 140–160 s. The results suggest a difference in fast-propagation directions between the anisotropic fabric frozen into the lithosphere and the fabric due to current and recent sublithospheric flow. The Superior Craton and Grenville Province are characterized by large-scale structural variations that reflect the complex tectonic history of the region. This study highlights differences between the characteristics of eastern and western Ontario and indicates the occurrence of multiple layers of anisotropy in the subcratonic upper mantle.

P-wave propagation in transversely isotropic media: I. Finite-frequency theory

We generalize the theory of 3D Fréchet kernels for P-wave traveltimes in isotropic media to the case of transversely isotropic media. Using the first-order Born approximation and the far-field approximation of the Green’s tensor, we show that three anisotropic perturbations of the stiffness tensor, in addition to the perturbation of the isotropic phase velocity, are required to describe the effects of hexagonal perturbations of the stiffness tensor. We derive the expressions of the scattering tensors and of the sensitivity kernels corresponding to the three anisotropic parameters.

Azimuthal anisotropy and phase velocity beneath Iceland: implication for plume–ridge interaction

We have determined the pattern of azimuthal anisotropy beneath Iceland from shear-wave splitting and Rayleigh wave tomography using seismic data recorded during the ICEMELT and HOTSPOT experiments. The fast directions of shear-wave splitting are roughly N–S in western Iceland and NNW–SSE in eastern Iceland. In western Iceland azimuthal variations in Rayleigh wave phase velocity show that fast directions are close to the plate spreading direction at short periods of 25–40 s and roughly parallel to the Mid-Atlantic Ridge at longer periods of 50–67 s. Beneath the rift zones in central Iceland, we find a ridge-parallel fast direction at periods of 25–40 s and significantly weaker azimuthal anisotropy at periods of 50–67 s. The 2-D variation of isotropic phase velocity at periods of 33–67 s indicates that the lowest velocities are beneath the rift zones in central Iceland rather than above the plume conduit in southeast Iceland. While ridge-parallel alignment of melt films might contribute to anisotropy above 50 km depth beneath the rift zones, the overall observations are consistent with a model in which plume-influenced, hot, buoyant mantle rises beneath the Mid-Atlantic Ridge at depths greater than 50 km and is preferentially channeled along the ridge axis at the base of the lithosphere beneath Iceland. The shear-wave splitting results are attributed primarily to a N–S mantle flow at depths greater than 100 km.

Explicit Anisotropic P-wave Ray Velocity Functions

Sedimentary rocks encountered in seismic exploration frequently exhibit directional seismic wave velocity dependence. These anisotropic rocks often can be regarded as transversely isotropic (TI) media in which the ray velocity surface of SH-waves is elliptical, while those of P- and SV-waves are non-elliptical. Transversely isotropic phase velocity expressions exist for P-, SH- and SV-waves. Unfortunately, until now no explicit exact analytical ray velocity functions exist for P- or SV-waves propagating in TI media. In exploration seismology, explicit ray velocity functions are needed for efficient migration, velocity analysis and other seismic processing procedures.Approximate explicit analytical P-wave ray velocity functions in transversely isotropic media have now been developed. These ray velocity functions include a new dimensionless constant, A, which depends on elastic parameters C11, C33, C44, and C13 or Thomsen's parameters ε, δ, α0 and (β0. The accuracy of the functions has been tested for all the materials published by Thomsen (1986). From these ray velocity functions, the travel time between any two points in homogeneous transversely isotropic media may be calculated. Reflection travel times from a single horizontal reflector overlain by transversely isotropic media with vertical symmetrical axis (VTI) are also calculated and compared with those obtained by Tsvankin (1996). The results show that the proposed explicit ray velocity functions have high accuracy.

Surface wave dispersion and upper mantle structure beneath southern Germany from joint inversion of network recorded teleseismic events

We have determined the dispersion of fundamental mode Rayleigh waves in Southern Germany in the frequency range 4–50 mHz by simultaneously inverting data from 66 teleseismic events recorded at a network of up to 9 broadband stations. Three different inversion experiments were performed: determination of (1) isotropic phase velocity, of (2) azimuthally anisotropic phase velocity assuming a plane wave traveling across the network, and (3) isotropic phase velocity but now allowing for non‐plane properties of the wavefield. In experiments (1) and (2), for each event amplitude, phase and deviation from the great circle azimuth were estimated as well. We have obtained remarkably stable results for phase velocity over the whole frequency range. Between 7 and 25 mHz azimuthal anisotropy is definitely below 0.5 percent. Below 7 and above 25 mHz we found up to 3 percent anisotropy but with negligible variance reduction compared to the isotropic inversion experiment (1). Admitting non‐plane wavefields in the inversion still yields nearly identical phase velocities. On inversion of the phase velocity curve in terms of shear‐wave velocity we obtained a rather shallow asthenosphere with minimum υS of 4.28 km/s at about 130 km depth covered by a thin lid with υS of 4.63 km/s.

Transversely isotropic phase velocity analysis from slowness estimates

Near‐offset vertical seismic profiling (VSP) is an established technique to obtain interval velocities for lithology characterization, time‐to‐depth calibrations, and seismic data processing. Unfortunately, these velocities are often insufficient to distinguish lithology types and can disagree with surface seismic stacking velocities. Multiple‐source offset VSPs provide additional travel time information for calculating interval anisotropic velocities that can help discriminate lithology. In this paper, a technique is developed for computing transversely isotropic phase velocities over intervals less than the dominant seismic wavelength. Independent estimates of vertical and horizontal slowness are made for each receiver depth and source offset pair. These provide the magnitude and direction of phase velocity for calculating the in situ elastic properties of a transversely isotropic medium. This technique requires the assumption of lateral homogeneity because horizontal slowness components are related to surface properties between sources and not to rock properties between receivers at depth. Factors that violate this assumption such as source elevation differences and dipping layers are evaluated with synthetic data. Six impulsive source P wave offset VSPs in a 663‐m well in east Texas are analyzed and a near offset SH wave vibrator VSP provides vertical shear wave phase velocities. Strong transversely isotropic velocity variations observed in the Tertiary and Cretaceous sediments penetrated by this well correlate with lithology types, suggesting that this technique is sensitive to local properties at the receiver. These results may not indicate exact intrinsic elastic properties and could be due in part to dipping layers, vertical heterogeneities, and unknown local surface variations. Percent “phase velocity” anisotropy appears to increase from 6 to 20% for P wave and 10 to 50% for SV wave with increasing amounts of calcareous material and shale in the rock. (Percentage anisotropy is defined as the ratio of the horizontal to vertical velocity for P waves and the ratio of velocity at 45° to vertical velocity for SV waves.) Sandstones and chalk exhibit the least amount of anisotropy, while the shales and calcareous shales exhibit the most.