R. G. Pratt

The University of Western Ontario, London, Ontario, Canada

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Publications (34)35.95 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: We apply Laplace-Fourier 2D and 2.5D waveform tomography to a challenging wide-angle land data set from a geologically complex region in Japan. The survey line is crooked (up to 500 m deviation from the 2D line over the 16 km line length), and the area contains significant topographic relief (up to 400 m) and near-surface weathering layers. The lack of reflections previously prevented conventional reflection processing. We demonstrate that 2D acoustic waveform tomography is capable of extracting a reliable velocity model from refractions and wide-angle reflections with carefully designed data-preconditioning and inversion strategies. Sources and receivers are projected onto a 2D plane without preserving offsets: we eliminate traces where errors in offsets are large. We restrict the inversion to phase information at lowest frequencies, and discretize the model with a fine grid, in order to minimize the effects of the crooked line and the topography. We use balanced data amplitudes (using surface-consistent static deconvolution) to conduct the source estimation. We extensively validate the obtained velocity model by comparisons with a well log and observed waveforms, through scrutiny of the resulting reverse-time-migration image. An additional test with 2.5D waveform tomography demonstrates that 2D waveform inversion is adequate for these data.
    06/2014;
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    Rie Kamei, R. Gerhard Pratt, Takeshi Tsuji
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    ABSTRACT: In seismic waveform inversion, non-linearity and non-uniqueness require appropriate strategies. We formulate four types of L2 normed misfit functionals for Laplace-Fourier domain waveform inversion: i) subtraction of complex-valued observed data from complex-valued predicted data (the ‘conventional phase-amplitude’ residual), ii) a ‘conventional phase-only’ residual in which amplitude variations are normalized, iii) a ‘logarithmic phase-amplitude’ residual and finally iv) a ‘logarithmic phase-only’ residual in which the only imaginary part of the logarithmic residual is used. We evaluate these misfit functionals by using a wide-angle field Ocean Bottom Seismograph (OBS) data set with a maximum offset of 55 km. The conventional phase-amplitude approach is restricted in illumination and delineates only shallow velocity structures. In contrast, the other three misfit functionals retrieve detailed velocity structures with clear lithological boundaries down to the deeper part of the model. We also test the performance of additional phase-amplitude inversions starting from the logarithmic phase-only inversion result. The resulting velocity updates are prominent only in the high-wavenumber components, sharpening the lithological boundaries. We argue that the discrepancies in the behaviours of the misfit functionals are primarily caused by the sensitivities of the model gradient to strong amplitude variations in the data. As the observed data amplitudes are dominated by the near-offset traces, the conventional phase-amplitude inversion primarily updates the shallow structures as a result. In contrast, the other three misfit functionals eliminate the strong dependence on amplitude variation naturally and enhance the depth of illumination. We further suggest that the phase-only inversions are sufficient to obtain robust and reliable velocity structures and the amplitude information is of secondary importance in constraining subsurface velocity models.
    Geophysical Prospecting 04/2014; · 1.36 Impact Factor
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    Takeshi Tsuji, Rie Kamei, R. Gerhard Pratt
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    ABSTRACT: We use the pore pressure distribution predicted from a waveform tomography (WT) velocity model to interpret the evolution of the mega-splay fault system in the Nankai Trough off Kumano, Japan. To map pore pressure around the mega-splay fault and plate boundary décollement, we integrate the high-resolution WT velocities with laboratory data and borehole well log data using rock physics theory. The predicted pore pressure distribution shows that high pore pressures (close to lithostatic pressure) along the footwall of the mega-splay fault extend seaward to the trough region, and the normalized pore pressure ratio is nearly constant over that extent. This continuity of the overpressured zone indicates that a coseismic rupture can potentially propagate nearly to the trough axis. We interpret a high-pressure belt within an accretionary wedge on the landward side of the present mega-splay fault as evidence of the ancient mega-splay fault. Because the ancient mega-splay fault soles into the active mega-splay fault, the active mega-splay fault may function as a basal detachment fault and is directly connected to the seaward plate boundary décollement.
    Earth and Planetary Science Letters 01/2014; 396:165–178. · 4.72 Impact Factor
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    R. Kamei, R. G. Pratt, T. Tsuji
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    ABSTRACT: We successfully apply the acoustic Laplace-Fourier waveform tomography method to delineate P-wave velocity structures of the mega-splay fault system in the central part of the seismogenic Nankai subduction zone offshore Japan, using densely sampled wide-angle ocean bottom seismograph (OBS) data originally acquired in 2004. Our success is due to new and carefully designed data preconditioning and inversion strategies to mitigate (i) the well-known non-linearity of waveform inversion, (ii) the challenges arising from crustal-scale survey designs (e.g. undersampling of the OBSs), and (iii) modelling errors due to the use of the acoustic assumption. We identify a sixfold set of key components that together lead to the success of the high-resolution waveform tomography image: (i) Availability of low-frequency components (starting at 2.25 Hz) reducing the non-linearity, and access to large offset data (up to 55 km) increasing the depth of illumination and the recovery of low wavenumber components. (ii) A highly accurate traveltime tomography result (with an rms error of approximately 60 ms) that further mitigates the non-linearity. (iii) A hierarchical inversion approach in which phase spectra are inverted first to reduce artefacts from the acoustic assumption, and amplitude information is only incorporated in the final stages. (iv) A Laplace-Fourier domain approach that facilitates a multiscale approach to mitigate non-linearity by restricting the inversion to the low frequency components and early arrivals first, and sequentially including higher frequencies and later arrivals. (v) A pre-conditioning strategy for eliminating undesirable high wavenumber components from the the gradient. (vi) A strategy for source estimation that reduce the influence of the instrumental design. In the OBS case study used for illustration purposes, Laplace-Fourier waveform tomography retrieves velocity anomalies as small as 700 m (horizontally) and 350 m (vertically) above the top of the Philippine Sea Plate. The resulting velocity structures include low-velocity zones and thrust structures which have not been previously identified clearly. The velocity models are validated by scrutiny of synthetic and observed waveforms, by evaluating the coherency of source estimates, and by comparison with 3-D pre-stack migrated (PreSDM) images. Chequerboard tests and point-scatter tests demonstrate both the reliability and the limitations of the acoustic implementation.
    Geophysical Journal International 08/2013; 194(2):1250-1280. · 2.85 Impact Factor
  • R. Kamei, R. G. Pratt
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    ABSTRACT: Visco-acoustic waveform inversion can potentially yield quantitative images of the distribution of both velocity and the attenuation parameters from seismic data. Intrinsic P-wave attenuation has been of particular interest, but has also proven challenging. Frequency-domain inversion allows attenuation and velocity relations to be easily incorporated, and allows a natural multiscale approach. The Laplace-Fourier approach extends this to allow the natural damping of waveforms to enhance early arrivals. Nevertheless, simultaneous inversion of velocity and attenuation leads to significant `cross-talk' between the resulting images, reflecting a lack of parameter resolution and indicating the need for pre-conditioning and regularization of the inverse problem. We analyse the cross-talk issue by partitioning the inversion parameters into two classes; the velocity parameter class, and the attenuation parameter class. Both parameters are defined at a reference frequency, and a dispersion relation is assumed that describes these parameters at any other frequency. We formulate the model gradients at a forward modelling frequency, and convert them to the reference frequency by employing the Jacobian of the coordinate change represented by the dispersion relation. We show that at a given modelling frequency, the Fréchet derivatives corresponding to these two parameter classes differ only by a 90° phase shift, meaning that the magnitudes of resulting model updates will be unscaled, and will not reflect the expected magnitudes in realistic (Q-1 ≪ 1) media. Due to the lack of scaling, cross-talk will be enhanced by poor subsurface illumination, by errors in kinematics, and by data noise. To solve these issues, we introduce an attenuation scaling term (the inverse of a penalty term) that is used to pre-condition the gradient by controlling the magnitudes of the updates to the attenuation parameters. Initial results from a suite of synthetic cross-hole tests using a three-layer randomly heterogenous model with both intrinsic and extrinsic (scattering) attenuation demonstrate that cross-talk is a significant problem in attenuation inversion. Using the same model, we further show that cross-talk can be suppressed by varying the attenuation scaling term in our pre-conditioning operator. This strategy is effective for simultaneous inversion of velocity and attenuation, and for sequential inversion (a two-stage approach in which only the velocity models are recovered in the first stage). Further regularization using a smoothing term applied to the attenuation parameters is also effective in reducing cross-talk, which is often highly oscillatory. The sequential inversion approach restricts the search space for attenuation parameters, and appears to be important in retrieving a reliable attenuation model when strong time-damping is applied. In a final test with our synthetic model, we successfully carry out visco-acoustic inversions of noise-contaminated data.
    Geophysical Journal International 08/2013; 194(2):859-884. · 2.85 Impact Factor
  • Rie Kamei, R. Gerhard Pratt
    SEG Technical Program Expanded Abstracts 2012; 09/2012
  • SEG Technical Program Expanded Abstracts 2012; 09/2012
  • Rie Kamei, R. Gerhard Pratt, Takeshi Tsuji
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    ABSTRACT: We apply Frequency-domain Waveform Tomography to form quantitative, high-resolution P-wave velocity images of a megasplay fault system within the central Nankai subduction zone offshore of southwest Japan, using controlled source Ocean Bottom Seismometer (OBS) data originally acquired in 2004. The Waveform Tomography method exploits recorded seismic waveforms beyond their first arrivals, and thus achieves a much higher resolution (of the order of a wavelength) than that of conventional Traveltime Tomography methods. Frequency-domain Waveform Tomography facilitates a multi-scale approach to stabilize the inversion, in which initial Traveltime Tomography results are sequentially improved on by first fitting low frequency components of the seismic records (starting at 2.25 Hz); higher frequency components (up to 8.5 Hz) are then introduced progressively.Our final Waveform Tomography image allows velocity anomalies as small as 700 m (horizontally) and 350 m (vertically) to be discerned and interpreted, as confirmed by checkerboard modeling tests. The improved explanatory power of the final images is verified by observing that synthetic waveforms calculated from the final results yield much better fit to the observed waveforms than those estimated from the original Traveltime Tomography image. Apparent lithological boundaries from Waveform Tomography agree well with corresponding reflections on seismic migration images, providing further confidence in the validity of the results.The megasplay fault is evident on the final Waveform Tomography image as a sharp velocity discontinuity, delineating the upper surface of a velocity reduction of nearly 1 km/s with respect to the regional 1D velocity trend. The megasplay fault can be traced continuously throughout the entire image, from a nearly horizontal section at the landward extent, moving seaward through to a steeper angle penetrating the old accretionary prisms, with several additional splays appearing to branch in the shallow subsurface. The location of the low-velocity zones imaged by our waveform tomography method coincides with two-previously-identified low velocity zones. The image reveals a low velocity zone that is continuous from deeper to shallower portions of the subsurface, suggesting that pore-fluids may be transported from the inner wedge, to the transition zone, and to the surface, through fluid conduits associated with the megasplay fault system.
    Earth and Planetary Science Letters 02/2012; s 317–318:343–353. · 4.72 Impact Factor
  • R. Kamei, R. G. Pratt, T. Tsuji
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    ABSTRACT: We apply Frequency-domain Waveform Tomography to form quantitative, high-resolution P-wave velocity images of a megasplay fault system within the central Nankai subduction zone offshore of southwest Japan using controlled source Ocean Bottom Seismometer (OBS) data originally acquired in 2004. Waveform Tomography attempts to fit recorded waveforms rather than just first arrivals, and thus generates a high-resolution velocity structure in a scale of a wavelength, while the conventional Traveltime Tomogrpahy is limited to the scale of the Fresnel zone. The frequency-domain implementation facilitates a multi-scale approach, in which initial results are matlabgenerated using low frequencies (starting at 2.25 Hz), and higher frequencies (up to 8.5 Hz) are introduced progressively. These results also yield significant improvements in the data fit to the OBS data, in comparison with those obtained from Traveltime Tomography conducted by Nakanishi et al., 2008. A remarkable agreement of apparent lithological boundaries from Waveform Tomography with corresponding reflections on seismic migration images (Moore et al., 2009, Park et al., 2010) provides further confidence in the validity of the results. The megasplay fault is evident on the final image as a sharp velocity discontinuity, delineating the upper surface of a velocity reduction of nearly 1 km/s with respect to the regional 1D velocity trend. The megasplay fault can be traced continuously throughout the entire system, from a nearly horizontal section at the landward extent, moving seaward through to a steeper angle penetrating the old accretionary prisms, with several additional splays appearing to branch in the shallow subsurface. The Waveform Tomography images further confirms a connection zone 1.5 km thick between two potentially over-pressured low velocity zones in the system, suggesting that pore-fluids may be transported from the inner wedge, to the transition zone and to the surface through fluid conduits associated with the megasplay fault system.
    AGU Fall Meeting Abstracts. 12/2011;
  • Rie Kamei, Andrew J. Brenders, R. Gerhard Pratt
    SEG Technical Program Expanded Abstracts 2011; 01/2011
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    ABSTRACT: Waveform tomography can generate velocity models with significantly higher resolution than travel time tomography. While this has been demonstrated for synthetic data sets, there are only a few successfull applications for real data. In 1998 the land-based SIMBA (Seismic Investigations of the Messum and Brandberg Areas) experiment was carried out in Namibia to study the deep structure of the Messum intrusive complex. As the geometry of this experiment (roll-along) was designed for near-vertical incidence reflection processing, the data are exceptional in comparison with oher data sets used for waveform tomography. Messum is a composite ring intrusion, with a central pipe of syenites surrounded by concentric gabbroic and granite layers, which cannot resolved in detail with travel time tomography. The aim of this work is to resolve these thin (tens to hundreds of m) gabbro and granite structures using waveform tomography. First, a theoretical velocity model was created based on geological interpretations of the present sub-volcanic exposure of the ring complex. A synthetic data set with 22500 traces was then generated based on the source and receiver geometry of the SIMBA project. Travel time picking and inversion provided the starting model for the waveform tomography in the frequency domain. For the inversion several parameters and the influence of noise were tested to choose the optimal parameters. With nearly the same parameters the inversion of the real data has been carried out to resolve more details of the internal structure of the complex. Furthermore we tested the influence of different approaches to consider crooked line geometry in the straight line inversion. The models derived by waveform tomography reveal detailed shallow features within the Messum Complex which are not resolved by travel time tomography.
    AGU Fall Meeting Abstracts. 12/2010;
  • R. Kamei, R. G. Pratt
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    ABSTRACT: Seismic waveforms contain the information not only about velocity, but also various parameters, such as attenuation (or Q factor), density, and anisotropic parameters. The Q values can provide the useful information about rheology, pore fluid, and fluid flow information. Attenuation has conventionally been imaged from the first arrival waveforms (amplitudes and/or spectra) using with ray theoretical methods. Although these methods are simple and fast, the method does not use the full record of observed waves, and the resolution is limited. By using a greater portion of the waveforms, frequency domain full waveform inversion has resulted in the improved velocity and attenuation images (Hicks and Pratt, 2001). Challenges remain regarding attenuation imaging, including the estimation of source signatures, source and receiver coupling effects, geometrical spreading, etc. Our previous work with synthetic data showed that it is critical to obtain accurate velocity images prior to attenuation imaging, in order to enhance parameter resolution (Kamei and Pratt, 2008). Inaccurate velocity structures lead to instable attenuation imaging. However the work focused on parameter separation between attenuation and velocity, and the results were limited to noise-free synthetic data. In this study we first investigate the tradeoff between the amplitudes of estimated source signatures, and attenuation models. There is inverse proportionality between Q values and source amplitudes.. Apparently waveform inversion provides relative attenuation images, and some other information is required to obtain absolute Q values. We also compare two objective function; the standard and the logarithmic L2 objective function proposed by Shin and Min (2006). The logarithmic L2 objective function enabled to recover higher wavenumber components of the attenuation model, than the standar L2 objective function, since the logarithmic function enhanced the contribution from small-valued data. Then, the waveform inversion technique is applied to the synthetic data contaminated with Gaussian noise. The attenuation imaging is severely affected by inadequate amplitude information at low and middle frequencies, although the standard L2 function showed more robustness. The noise test revealed that it is essential to use a group of frequencies to stabilize the inversion.
    AGU Fall Meeting Abstracts. 12/2009;
  • R. G. Pratt, R. Kamei, B. Smithyman
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    ABSTRACT: Waveform Tomography, when implemented in the frequency-domain, potentially yields images of the intrinsic attenuation from seismic waveform data (Pratt et al., 1998). The attenuation (or its inverse, the seismic Q value) is strongly related to rheology, fluid flow, pore fluid content and fractures. Since phase and amplitude anomalies are also caused by velocity structure (due to geometrical and scattering effects), it is critical to assess inversion strategies as to their ability to resolve these effects. We compared two sets of strategies: first, velocity and attenuation models were updated jointly at each iteration ("simultaneous inversio"). In a second test, ("sequential inversion"), a velocity model alone was first inverted, followed by simultaneous inversion. While the predicted waveforms from both strategies agreed with the observed data, only the sequential inversion strategy imaged attenuation structure well in the presence of small-scale velocity heterogeneities. This highlights the strong dependence of attenuation imaging on the quality of the velocity model. We then tested the approach using a shallow seismic dataset collected on an engineered clay embankment at Seven Sisters Falls, Manitoba. The test embankment contained three targets composed of granitic rip- rap; these corresponded to higher velocities and higher scattering potential than the surrounding in-situ clays. Waveform Tomography was applied to long-offset refraction data collected over the embankment using 70 weight-drop shots and 48 geophones. The starting model was developed with traveltime tomography on the hand-picked first arrivals. The data were inverted between 20 Hz and 150 Hz, corresponding to wavelengths between approximately 100 m and 13 m. We were able to resolve sub- wavelength targets on the order of 3-4 m in cross-section using the final velocity model. Interpretation of the seismic-Q images along with the velocity allowed us to define the target positions. In order to assess the quality of our model fit, we compared synthetic results with the real data. A very good fit between model and observed data was achieved, indicating the reliability of the results.
    AGU Fall Meeting Abstracts. 12/2008;
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    K. Bauer, R. G. Pratt, C. Haberland, M. Weber
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    ABSTRACT: Crosshole seismic experiments were conducted to study the in-situ properties of gas hydrate bearing sediments (GHBS) in the Mackenzie Delta (NW Canada). Seismic tomography provided images of P velocity, anisotropy, and attenuation. Self-organizing maps (SOM) are powerful neural network techniques to classify and interpret multi-attribute data sets. The coincident tomographic images are translated to a set of data vectors in order to train a Kohonen layer. The total gradient of the model vectors is determined for the trained SOM and a watershed segmentation algorithm is used to visualize and map the lithological clusters with well-defined seismic signatures. Application to the Mallik data reveals four major litho-types: (1) GHBS, (2) sands, (3) shale/coal interlayering, and (4) silt. The signature of seismic P wave characteristics distinguished for the GHBS (high velocities, strong anisotropy and attenuation) is new and can be used for new exploration strategies to map and quantify gas hydrates.
    Geophysical Research Letters 01/2008; 35(19). · 3.98 Impact Factor
  • R. Kamei, R. G. Pratt
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    ABSTRACT: Seismic inversion is a multiparameter problem: the observed waveforms contain information not only on velocity structure, but also on various other parameters, including attenuation and density (and the possibility of anisotropy). Among these parameters, the attenuation (or its inverse, the seismic Q value) is strongly related to useful geological variables such as rheology, fluid flow, pore fluid content and fractures. In this work, we investigate methodologies for obtaining velocity and attenuation images simultaneously. In contrast to ray-based inversions of first arrival times and/or amplitudes, Full Waveform Inversion incorporates scattered, refracted and reflected waves, and consequently improves image resolution and accuracy. In frequency domain implementations, instead of inverting Q values directly, complex valued velocities are estimated using steepest descent algorithms. The real and imaginary parts of the velocity fields, (vr, vi), have differing sensitivities, making the simultaneous inversion of (vr, vi) with steepest descent methods difficult. Although Newton methods may enable a true simultaneous inversion, these are computationally expensive, and the instability of the Hessian matrix remains problematic. A possible solution to the simultaneous inverse problem is the subspace method (a Newton method in a chosen subspace), in which we search for an optimal update direction in a 2D subspace spanned by each of the two model type steepest descent vectors: P-wave velocity and Q values. The proposed 2D subspace method requires only one additional forward modelling over the steepest descent method, and inverting the 2 × 2 projected Hessian is trivial. The off-diagonal terms of the projected Hessian matrix indicate the coupling of data sensitivities to the two model parameter types. In this study, we implemented the subspace method into frequency-domain full waveform inversion, and compared the results to the standard steepest descent method. Because the model parameterization may influence robustness and resolution of the inversion procedure, we also examined several model parameterizations, including (vr, vi), (vr, Q), and their respective inverses.
    AGU Fall Meeting Abstracts. 12/2007;
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    ABSTRACT: We have applied acoustic-waveform tomography to 45 2D seismic profiles to image the 3D geometry of a buried pale-ochannel at a groundwater-contamination site at Hill Air Force Base in Utah. The paleochannel, which is incised into an alluvium-covered clay aquitard, acts as a trap for dense nonaqueous-phase liquids DNAPLs that contaminate the shallowest groundwater system in the study area. The 2D profiles were extracted from a 3D surface reflection data set. First-arrival traveltime tomography provided initial velocity models for the waveform tomography. We inverted for six frequency components in the band 30–90 Hz of the direct and refracted waves to produce 45 2D velocity models. The flanks and bottom of a channel with a maximum depth of about 15 m were well modeled in most of the 45 parallel 2D slices, which allowed us to construct a 3D image of the chan-nel by combining and interpolating between the 45 image slices. The 3D model of the channel will be useful for siting extraction wells within the site remediation program. The al-luvium that fills the channel showed marked vertical and lat-eral velocity heterogeneity. Traveltime tomography and waveform tomography can be complementary approaches. Used together, they can provide high-resolution images of complicated shallow structures.
    Geophysics. 01/2007; 72(5).
  • A. J. Brenders, R. Gerhard Pratt
    SEG Technical Program Expanded Abstracts 01/2007; 26(1).
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    A. J. Brenders, R. G. Pratt
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    ABSTRACT: SUMMARYA comprehensive validation of 2-D, frequency-domain, acoustic wave-equation tomography was undertaken in a ‘blind test’, using third-party, realistic, elastic wave-equation data. The synthetic 2-D, wide-angle seismic data were provided prior to a recent workshop on the methods of controlled source seismology; the true model was not revealed to the authors until after the presentation of our waveform tomography results. The original model was specified on a detailed grid with variable P-wave velocity, S-wave velocity, density and viscoelastic Q-factor structure, designed to simulate a section of continental crust 250 km long and 40 km deep. Synthetic vertical and horizontal component data were available for 51 shot locations (spaced every 5 km), recorded at 2779 receivers (spaced every 90 m), evenly spread along the surface of the model. The data contained energy from 0.2 to 15 Hz.Waveform tomography, a combination of traveltime tomography and 2-D waveform inversion of the early arrivals of the seismic waveforms, was used to recover crustal P-velocity structure from the vertical component data, using data from 51 sources, 1390 receivers and frequencies between 0.8 and 7.0 Hz. The waveform tomography result contained apparent structure at wavelength-scale resolution that was not evident on the traveltime tomography result. The predicted (acoustic) waveforms in the final result matched the original elastic data to a high degree of accuracy.During the workshop, the exact model was revealed; over much of the model the waveform tomography results provided a good correspondence with the true model, from large- to intermediate-(wavelength) scales, with a resolution limit on the order of 1 km. A significant, near-surface low-velocity zone, invisible to traveltime methods, was correctly recovered; the results also provided a high-resolution image of the complex structure of the entire crust, and the depth and nature of the crust–mantle transition. Some inaccuracies were observed near the edges of the images due to the limited ray coverage inherent to the footprint of the survey geometry.Several aspects of the waveform tomography strategy were critical to the success of the acoustic method with realistic, synthetic, viscoelastic data: (i) the accuracy of the starting model from traveltime tomography, (ii) implementation in the frequency domain, (iii) the use of complex-valued frequencies to effect time damping of the data residuals, (iv) the selection of a suitable subset of data and data frequencies, (v) progressive inversion of low- to high-frequency components of the data, (vi) initial, pre-inversion matching of the amplitudes between observed and modelled data, and (vii) sufficient preconditioning of both the data and the update images. Combined, these strategies were effectively equivalent to a multiscale approach that mitigated the non-linearity of the seismic inverse problem. During the inversion we carried out repeated forward modelling to ensure our modelled waveforms matched the observed data as closely as possible in both frequency and time domains.The synthetic data set used in this paper provides a benchmark for future testing of modelling, inversion, and imaging algorithms for wide-angle lithospheric imaging.
    Geophysical Journal International 12/2006; 168(1):133 - 151. · 2.85 Impact Factor
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    A. J. Brenders, R. G. Pratt
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    ABSTRACT: We provide a series of numerical experiments designed to test waveform tomography under (i) a reduction in the number of input data frequency components (‘efficient’ waveform tomography), (ii) sparse spatial subsampling of the input data and (iii) an increase in the minimum data frequency used. These results extend the waveform tomography results of a companion paper, using the same third-party, 2-D, wide-angle, synthetic viscoelastic seismic data, computed in a crustal geology model 250 km long and 40 km deep, with heterogeneous P-velocity, S-velocity, density and Q-factor structure.Accurate velocity models were obtained using efficient waveform tomography and only four carefully selected frequency components of the input data: 0.8, 1.7, 3.6 and 7.0 Hz. This strategy avoids the spectral redundancy present in ‘full’ waveform tomography, and yields results that are comparable with those in the companion paper for an 88 per cent decrease in total computational cost. Because we use acoustic waveform tomography, the results further justify the use of the acoustic wave equation in calculating P-wave velocity models from viscoelastic data.The effect of using sparse survey geometries with efficient waveform tomography were investigated for both increased receiver spacing, and increased source spacing. Sampling theory formally requires spatial sampling at maximum interval of one half-wavelength (2.5 km at 0.8 Hz): For data with receivers every 0.9 km (conforming to this criterion), artefacts in the tomographic images were still minimal when the source spacing was as large as 7.6 km (three times the theoretical maximum). Larger source spacings led to an unacceptable degradation of the results.When increasing the starting frequency, image quality was progressively degraded. Acceptable image quality within the central portion of the model was nevertheless achieved using starting frequencies up to 3.0 Hz. At 3.0 Hz the maximum theoretical sample interval is reduced to 0.67 km due to the decreased wavelengths; the available sources were spaced every 5.0 km (more than seven times the theoretical maximum), and receivers were spaced every 0.9 km (1.3 times the theoretical maximum). Higher starting frequencies than 3.0 Hz again led to unacceptable degradation of the results.
    Geophysical Journal International 12/2006; 168(1):152 - 170. · 2.85 Impact Factor
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    ABSTRACT: Application of 2D frequency-domain waveform to-mography to a data set from a high-resolution vertical seismic profiling (VSP) experiment at a groundwater contamination site in Hill Air Force Base (HAFB), Utah, reveals a surprisingly complicated shallow sub-structure with a resolution of approximately 1.5 m. Vari-ance in the waveform misfit function is reduced 69.4% by using an initial velocity model from first-arrival trav-eltime tomography. The waveform tomography model suggests (1) a low-velocity layer at 1 to 4 m depth, (2) a high-vertical-velocity gradient of 80 m/s/m on average, and (3) severe lateral variations — velocity contrasts as large as about 200 m/s occur in a distance as short as 1.5 m. The model is well correlated with lithologic logs and is interpreted geologically. A Q-value of 20 is esti-mated for the target area. The extreme lateral and verti-cal variations of the subsurface compromise many stan-dard seismic processing methods.
    Geophysics 01/2006; 71(10). · 1.72 Impact Factor