Observation and modelling of fault-zone fracture seismic anisotropy - I. P, SV and SH travel times

Summary. Three-component VSP borehole seismograms taken in the vicinity of an active normal fault in California show strong systematic shear-wave splitting that increases with proximity to the fault. Using Červený's method of characteristics for ray tracing in anisotropic heterogeneous media and Hudson's formulation of elastic constants for media-bearing aligned fractures, we have fitted a suite of P, SV and SH hanging-wall and foot-wall travel times with a simple model of aligned fractures flanking the fault zone. The dominant fracture set is best modelled as parallel to the fault plane and increasing in density with approach to the fault. The increase in fracture density is non-uniform (power law or Gaussian) with respect to distance to the fault. Although the hanging-wall and the foot-wall rock are petrologically the same unit, the fracture halo is more intense and extensive in the hanging wall than in the foot wall. Upon approach to the fault plane, the fracture density or fracture-density gradient becomes too great for the seismic response to be computed by Hudson–Červený procedures (the maximum fracture density that can be modelled is about 0.08). Within this 25 m fracture domain it appears more useful to model the fault and near field fractures as a low-velocity waveguide. We observe production of trapped waves within the confines of the intense fracture interval.     

Crosshole seismic waveform tomography – II. Resolution analysis

In an accompanying paper, we used waveform tomography to obtain a velocity model between two boreholes from a real crosshole seismic experiment. As for all inversions of geophysical data, it is important to make an assessment of the final model, to determine which parts of the model are well-resolved and can confidently be used for geological interpretation. In this paper we use checkerboard tests to provide a quantitative estimate of the performance of the inversion and the reliability of the final velocity model. We use the output from the checkerboard tests to determine resolvability across the velocity model. Such tests can act as good guides for designing appropriate inversion strategies. Here we discovered that, by including both reference-model and smoothing constraints in initial inversions, and then relaxing the smoothing constraint for later inversions, an optimum velocity image was obtained. Additionally, we noticed that the performance of the inversion was dependent on a relationship between velocity perturbation and checkerboard grid-size: larger velocity perturbations were better-resolved when the grid-size was also increased. Our results suggest that model assessment is an essential step prior to interpreting features in waveform tomographic images.     

Multiple scattering and energy transfer of seismic waves – separation of scattering effect from intrinsic attenuation – I. Theoretical modelling

Summary. In order to separate the scattering effect from the intrinsic attenuation, we need a multiple scattering model for seismic wave propagation in random heterogeneous media. In this paper, we apply radiative transfer theory to seismic wave propagation and formulate in the frequency domain the energy density distribution in space for a point source. We consider the cases of isotropic scattering and strong forward scattering. Some numerical examples are shown. It is seen that the energy density–distance curves have quite different shapes depending on the values of medium seismic albedo B ₀=η_s/(η_s+η_a) where η_s is the scattering coefficient and η_a is the absorption coefficient of the medium. For a high albedo ( B > 0.5) medium, the energy–distance curve is of arch shape and the position of the peak is a function of the extinction coefficient of the medium η_e=η_s+η_a. Therefore it is possible to separate the scattering effect and the absorption based on the measured energy density distribution curves.     

Shear-wave polarizations near the North Anatolian Fault – II. Interpretation in terms of crack-induced anisotropy

Summary. The polarizations of shear waves recorded by networks of digital three-component seismometers immediately above small earthquakes near the North Anatolian Fault in Turkey display shear-wave splitting on almost all shear-wave seismograms recorded within the shear-wave window. This splitting is incompatible with source radiation-patterns propagating through simple isotropic structures but is compatible with effective anisotropy of the internal structure of the rock along the ray paths. This paper interprets the phenomena in terms of widespread crack-induced anisotropy. Distributions of stress-induced cracks model many features of the observations, and synthetic polarization diagrams calculated for propagation through simulated cracked rock are similar to the observed patterns. This evidence for widespread crack-induced anisotropy lends strong support to the hypothesis of extensive-dilatancy anisotropy (EDA) suggested by laboratory experiments in subcritical crack-growth. The crucial evidence confirming some form of EDA would be observations of temporal changes in shear-wave splitting as the stress field alters the crack density and crack geometry. There is some weak evidence for such temporal changes at one site, but further analysis of suitable digital three-component seismometer networks in seismic areas is required to confirm EDA.     

P-wave traveltime and polarization tomography of VSP data

The presence of anisotropy requires that tomographic methods be generalized to account for anisotropy. This generalization allows geological structure to be correctly imaged and allows the anisotropic parameters to be estimated. Use of isotropic inversion for imaging anisotropic structures gives systematic trends in the traveltime and polarization residuals. However, due to the limited directional coverage, the traveltimes along may not be sufficient to study the anisotropic properties of the structure. Polarizations can provide independent information on the structure. Traveltime and polarization inversion are applied to synthetic examples simulating VSP experiments. Transverse isotropy and 1-D structure are assumed. Plots of traveltime and polarization residuals are an important tool to detect the anomalies due to the presence of anisotropy. For receivers located in anisotropic layers, polarization residuals display consistent anomalies of several degrees. The synthetic examples show that even the simple 1-D problem is difficult, when using direct arrivals only. Large a posteriori errors in anisotropic parameters are obtained by traveltime inversion in layers where available incidence angles are less than 45°. Resolution of the tomographic image of VSP data is greatly improved by a combination of traveltime and polarization information. In order to obtain accurate inversion results, the measurement error of polarization data should be kept to within a few degrees.     

Correlation between seismic anisotropy and Bouguer gravity anomalies in Tibet and its implications for lithospheric structures

As a baseline measurement for understanding the Himalayan–Tibetan orogen, a product of continent–continent collision between India and Eurasia, we analyse digital seismic data in order to constrain the seismic anisotropy of the Indian shield. Based on spatially sparse data that are currently available in the public domain, there is little shear-wave birefringence for SKS phases under the Indian shield, even though it is part of a fast-moving plate in the hotspot frame of reference. If most of the northern Indian mantle has little transverse anisotropy, the onset of significant anisotropy under Tibet marks the northern terminus of intact Indian lithosphere that is thrusting under the Himalayan–Tibetan orogen. Beyond this terminus, tectonic fabric such as that associated with the deforming lithospheric mantle of Eurasia must be present in the upper mantle. Along the profile from Yadong to Golmud, the only profile in Tibet where a number of shear-wave birefringence data are available, the amount of birefringence shows two marked increases, near 30° and 33°N, between which a local high in Bouguer gravity anomaly is observed. Such a correlation between patterns of shear-wave birefringence and gravity anomalies is explained by the juxtaposition of Indian lithosphere against the overlying Eurasian lithosphere: while the Eurasian lithospheric mantle appears only to the north of 30°N, the Indian lithospheric mantle extends northwards to near 33°N.     

Range of validity of seismic ray and beam methods in general inhomogeneous media – II. A canonical problem

Summary. The Green's function, in a constant gradient medium, is derived for an explosive point source, in the frequency and the time domains. The analytical dynamic ray tracing (DRT) solution is rederived with conditions stated in Part I. The Gaussian beam (GB) solution is investigated. New beam parameters and conditions are defined. Comparisons between exact and approximate solutions are undertaken.
For both methods, DRT and GB, conditions of validity are explicit and quantitative. An accuracy criterion is defined in the time domain, and measures a global relative error. The range of validity is expressed in the form of two inequalities for the dynamic ray tracing method and of five inequalities for the Gaussian beam method. Results remain accurate at ray turning points. For the types of medium considered, the breakdown of the dynamic ray tracing method is smoother and better behaved than that of Gaussian beams. As examples, a vertical seismic profiling configuration, and a shallow earthquake are modelled, using Gaussian beams.     

P-wave seismograms from continuously varying transition zones—II. Elastic media

Summary. A class of elastic transition zones are modelled by considering a homogeneous half space overlying an inhomogeneous half space with a bounded and monotonically increasing profile for the rigidity modulus and constant Poisson's ratio and density. Reflected P waves due to a compressional point source in the upper half space are studied in the frequency and time domains by means of numerical contour integration in the complex k plane and the Fast Fourier Transform (FFT). Results from the exact fourth-order elasticity theory are compared with those from the approximate decoupled equations for P and SV waves. Agreement is observed between the two theories at high frequencies beyond the caustic range.     

Crustal structure across the Grand Banks–Newfoundland Basin Continental Margin – II. Results from a seismic reflection profile

New multichannel seismic reflection data were collected over a 565 km transect covering the non-volcanic rifted margin of the central eastern Grand Banks and the Newfoundland Basin in the northwestern Atlantic. Three major crustal zones are interpreted from west to east over the seaward 350 km of the profile: (1) continental crust; (2) transitional basement and (3) oceanic crust. Continental crust thins over a wide zone (∼160 km) by forming a large rift basin (Carson Basin) and seaward fault block, together with a series of smaller fault blocks eastwards beneath the Salar and Newfoundland basins. Analysis of selected previous reflection profiles (Lithoprobe 85-4, 85-2 and Conrad NB-1) indicates that prominent landward-dipping reflections observed under the continental slope are a regional phenomenon. They define the landward edge of a deep serpentinized mantle layer, which underlies both extended continental crust and transitional basement. The 80-km-wide transitional basement is defined landwards by a basement high that may consist of serpentinized peridotite and seawards by a pair of basement highs of unknown crustal origin. Flat and unreflective transitional basement most likely is exhumed, serpentinized mantle, although our results do not exclude the possibility of anomalously thinned oceanic crust. A Moho reflection below interpreted oceanic crust is first observed landwards of magnetic anomaly M4, 230 km from the shelf break. Extrapolation of ages from chron M0 to the edge of interpreted oceanic crust suggests that the onset of seafloor spreading was ∼138 Ma (Valanginian) in the south (southern Newfoundland Basin) to ∼125 Ma (Barremian–Aptian boundary) in the north (Flemish Cap), comparable to those proposed for the conjugate margins.     

Surface wave array tomography in SE Tibet from ambient seismic noise and two-station analysis – II. Crustal and upper-mantle structure

We determine the 3-D shear wave speed variations in the crust and upper mantle in the southeastern borderland of the Tibetan Plateau, SW China, with data from 25 temporary broad-band stations and one permanent station. Interstation Rayleigh wave (phase velocity) dispersion curves were obtained at periods from 10 to 50 s from empirical Green's function (EGF) derived from (ambient noise) interferometry and from 20 to 150 s from traditional two-station (TS) analysis. Here, we use these measurements to construct phase velocity maps (from 10 to 150 s, using the average interstation dispersion from the EGF and TS methods between 20 and 50 s) and estimate from them (with the Neighbourhood Algorithm) the 3-D wave speed variations and their uncertainty. The crust structure, parametrized in three layers, can be well resolved with a horizontal resolution about of 100 km or less. Because of the possible effect of mechanically weak layers on regional deformation, of particular interest is the existence and geometry of low (shear) velocity layers (LVLs). In some regions prominent LVLs occur in the middle crust, in others they may appear in the lower crust. In some cases the lateral transition of shear wave speed coincides with major fault zones. The spatial variation in strength and depth of crustal LVLs suggests that the 3-D geometry of weak layers is complex and that unhindered crustal flow over large regions may not occur. Consideration of such complexity may be the key to a better understanding of relative block motion and patterns of seismicity.     

Crosshole seismic waveform tomography – I. Strategy for real data application

The frequency-domain version of waveform tomography enables the use of distinct frequency components to adequately reconstruct the subsurface velocity field, and thereby dramatically reduces the input data quantity required for the inversion process. It makes waveform tomography a computationally tractable problem for production uses, but its applicability to real seismic data particularly in the petroleum exploration and development scale needs to be examined. As real data are often band limited with missing low frequencies, a good starting model is necessary for waveform tomography, to fill in the gap of low frequencies before the inversion of available frequencies. In the inversion stage, a group of frequencies should be used simultaneously at each iteration, to suppress the effect of data noise in the frequency domain. Meanwhile, a smoothness constraint on the model must be used in the inversion, to cope the effect of data noise, the effect of non-linearity of the problem, and the effect of strong sensitivities of short wavelength model variations. In this paper we use frequency-domain waveform tomography to provide quantitative velocity images of a crosshole target between boreholes 300 m apart. Due to the complexity of the local geology the velocity variations were extreme (between 3000 and 5500 m s⁻¹), making the inversion problem highly non-linear. Nevertheless, the waveform tomography results correlate well with borehole logs, and provide realistic geological information that can be tracked between the boreholes with confidence.