• Zelt, C. A. and R. M. Ellis, Practical and efficient ray tracing in two-dimensional media for rapid traveltime and amplitude forward modelling, Canadian Journal of Exploration Geophysics, 24, 16-31, 1988.

  • Download PDF file of the paper.

    An algorithm for tracing rays and calculating amplitudes in two-dimensional media based on a new velocity-model parameterization has been developed. The simple, layered, large-block parameterization in which velocity is an analytic function of position allows for computationally efficient ray tracing. The user's ability to specify simple kinematically similar ray families permits practical and rapid forward modelling of refraction data. In addition, the routine allows for S- wave propagation including converted phases, multiple and surface reflections, approximate attenuation, head waves, and a reverse ray-direction amplitude calculation important for the interpretation of common-receiver profiles. The source may emit both P- and S type rays and the ratio of P-wave to S-wave amplitude at the source may be specified. Amplitude calculations are based on zero- and first-order asymptotic ray theory. The velocity model is parameterized in terms of a sequence of quasi-horizontal layers, each layer separated by a boundary consisting of straight-line segments. Layer thicknesses may be reduced to zero to model pinch-outs or isolated bodies. Each layer is broken up laterally into a series of large trapezoidal blocks with vertical left and right sides and upper and lower boundaries of arbitrary dip. The velocity structure within each trapezoid is defined by a single upper and lower velocity such that the velocity varies linearly from the upper to lower boundary along a vertical path. The major attributes of the routine are illustrated with four examples: a comparison of efficiency and accuracy with the Spence et al. algorithm, a practical application to the interpretation of observed crustal refraction profiles from the Peace River Arch region, a complex subduction zone model to illustrate the degree of lateral inhomogeneity possible with the routine's model parameterization, and a demonstration of how the routine may be used to study the effects of near-surface velocity anomalies on CMP data.
  • Zelt, C. A. and R. M. Ellis, Seismic structure of the crust and upper mantle in the Peace River Arch region, Canada, Journal of Geophysical Research, 94, 5729-5744, 1989.
    Four intersecting ~300-km-long reversed refraction lines within northwestern Alberta and northeastern British Columbia have been interpreted for crustal and upper mantle seismic velocity structure in the Peace River Arch (PRA) region of the Western Canada Sedimentary Basin. The data have been modeled using a two-dimensional ray trace forward modeling approach based on asymptotic ray theory to match travel times and amplitudes of first and coherent later arrivals. In addition, an inversion of first arrival travel times along a fan shot profile has been performed to constrain crustal thickness northwest of the arch in a region not sampled by the reversed profiles. The major features of the structural models are (1) weak to moderate lateral variations in crustal structure with no evidence of significant layering or thick low-velocity zones within the crust, (2) an average sub-basement RMS crustal velocity of 6.6 km/s, average upper mantle velocity of 8.25 km/s and average crustal thickness of 40 km, (3) regional variations in structure which appear related to the dominant N-S trending cratonic structure, including crustal thickness, upper crustal and upper mantle velocities and PmP character, and (4) subtle variations in structure that may be associated with the E-W trending Devonian axis of the PRA, including a shallowing of high lower crustal velocities, thickening of the crust, and an anisotropic PmP character beneath the arch and a weak trend in the dip of intracrustal reflectors away from the center of the PRA region. Evidence from the refraction and other geophysical data for the presence of a local crustal expression of the PRA is weak, but suggests a thermal as opposed to flexural origin for its anomalous vertical movements.
  • Zelt, C. A. and R. M. Ellis, Comparison of near-coincident crustal refraction and extended Vibroseis reflection data: Peace River region, Canada, Geophysical Research Letters, 16, 843-846, 1989.
    A 10-km-long uncorrelated Vibroseis data set was processed to test the feasibility of using industry reflection data for deep crustal imaging in the Peace River region and elsewhere in the Western Canada Sedimentary Basin. These results were compared with a crustal refraction interpretation of a line ~10 km to the north. The Vibroseis data were extended from a conventional 3 s to 14 s two-way travel time using the self-truncating-sweep method. The reflection section contains a prominent eastward-dipping event at ~9.4 s (29 km depth) which corresponds to the zero-offset two-way travel time of an intracrustal boundary in the refraction model. This may represent the Riel discontinuity imaged at similar depths in southern Alberta. A series of near-vertical incidence reflections over 1-1.5 s terminating at 13 s corresponds well with the refraction Moho at 12.8 s (41 km depth). This suggests that locally, the crust-mantle boundary is a complex, possibly layered transition zone of 3 5 km thickness.
  • Zelt, C. A. and R.M. Ellis, Crust and upper mantle Q from seismic refraction data: Peace River region, Canadian Journal of Earth Sciences, 27, 1040-1047, 1990.
    Crustal refraction data from the Peace River region of Alberta, Canada have been analysed using the spectral ratio method to obtain Q. A total of 1205 first and later arrivals corresponding to turning and reflected P-waves within the crust and upper mantle were studied. Source spectra were estimated from near-offset traces assuming typical sedimentary Q values. The large scatter of measured spectral ratios restricted the resolution to a three-layer model of the crust and upper mantle with Q constant in each layer. This model was obtained using a linear inverse method since the measured spectral ratios and known travel times in each layer are linearly related through the attenuation (Q-1) in each layer. A weighted L1 norm was minimized using linear programming, the weights being a measure of the certainty of each spectral ratio. The inversion was performed using the 25% most certain spectral ratios, regardless of magnitude or sign. Model bounds which account for the scattered data were estimated. The results suggest that Q is between 200-500 in the upper crust and Q is greater than 600 in the lower crust and upper mantle. This model is generally consistent with nearby crustal Q studies.
  • Zelt, C. A. and R. B. Smith, Seismic traveltime inversion for 2-D crustal velocity structure, Geophysical Journal International, 108, 16-34, 1992.
    A method of seismic traveltime inversion for simultaneous determination of 2-D velocity and interface structure is presented that is applicable to any type of body-wave seismic data. The advantage of inversion, as opposed to trial-and-error forward modeling, is that it provides estimates of model parameter resolution, uncertainty and non-uniqueness, and an assurance that the data have been fit according to a specified norm. In addition, the time required to interpret data is significantly reduced. The inversion scheme is iterative and is based on a model parameterization and a method of ray tracing suited to the forward step of an inverse approach. The number and position of velocity and boundary nodes can be adapted to the shot-receiver geometry and subsurface ray coverage, and to the complexity of the near-surface. The model parameterization also allows ancillary amplitude information to be used to constrain model features not adequately resolved by the traveltime data alone. The method of ray tracing uses an efficient numerical solution of the ray tracing equations, an automatic determination of take-off angles, and a simulation of smooth layer boundaries that yields more stable inversion results. The partial derivatives of traveltime with respect to velocity and the depth of boundary nodes are calculated analytically during ray tracing and a damped least-squares technique is used to determine the updated parameter values, both velocities and boundary depths simultaneously. The stopping criteria and optimum number of velocity and boundary nodes are based on the trade-off between RMS traveltime residual and parameter resolution, as well as the ability to trace rays to all observations. Methods for estimating spatial resolution and absolute parameter uncertainty are presented. An example using synthetic data demonstrates the algorithm's accuracy, rapid convergence and sensitivity to realistic noise levels. An inversion of refraction and wide-angle reflection traveltimes from the 1986 IRIS-PASSCAL Nevada, U.S.A. (Basin and Range province) seismic experiment illustrates the methodology and practical considerations necessary for handling real data. A comparison of our final 2-D velocity model with results from studies using other 1-D and 2-D forward and inverse methods serves as a check on the validity of the inversion scheme and provides estimates of parameter uncertainties that account for the bias introduced by the modeling approach and the interpreter.
  • Zelt, C. A., D. A. Forsyth, B. Milkereit, D. J. White, I. Asudeh and R. M. Easton, Seismic structure of the Central Metasedimentary Belt, southern Grenville Province, Canadian Journal of Earth Sciences, 31, 243-254, 1994.
    Crust and upper mantle structure interpreted from wide-angle seismic data along a 260-km profile across the Central Metasedimentary Belt of the southern Grenville Province in Ontario and New York state shows (i) relatively high average crustal and uppermost mantle velocities of 6.8 and 8.3 km/s, (ii) east-dipping reflectors extending to 24 km depth in the Central Metasedimentary Belt, (iii) weak lateral velocity variations beneath 5 km, (iv) a mid-crustal boundary at 27 km depth, and (v) a depth to Moho of 43-46 km. The wide-angle model is generally consistent with the vertical-incidence reflectivity of an intersecting Lithoprobe reflection line. The mid-crustal boundary correlates with a crustal detachment zone in the Lithoprobe data and the depth extent of east-dipping wide-angle reflectors. Regional structure and aeromagnetic anomaly trends support the southwest continuity of Grenville terranes and their boundaries from the wide-angle profile to two reflection lines in Lake Ontario. A zone of wide-angle reflectors with an average apparent eastward dip of 13 degrees has a surface projection that correlates spatially with the boundary between the Elzevir and Frontenac terranes of the Central Metasedimentary Belt and resembles reflection images of a crustal-scale shear zone beneath Lake Ontario. A high-velocity upper-crustal anomaly beneath the Elzevir-Frontenac boundary zone is positioned in the hanging wall associated with the concentrated zone of wide-angle reflectors. The high-velocity anomaly is coincident with a gravity high and increased metamorphic grade suggesting northwest transport of mid-crustal rocks by thrust faulting consistent with the mapped geology. The seismic data suggest (i) a reflective, crustal-scale structure has accommodated northwest-directed tectonic transport within the Central Metasedimentary Belt, (ii) this structure continues southwest from the exposed Central Metasedimentary Belt to at least southern Lake Ontario, and (iii) crustal reflectivity and complexity within the eastern Central Metasedimentary Belt is similar to that observed at the Grenville Front and the western Central Metasedimentary Belt boundary.
  • Zelt, C. A. and D. A. Forsyth, Modeling wide-angle seismic data for crustal structure: southeastern Grenville province, Journal of Geophysical Research, 99, 11687-11704, 1994.
    A modeling methodology for obtaining two-dimensional (2-D) crustal structure from wide-angle seismic data is applied to data from the southeastern Grenville Province. Pre-modeling steps include (1) assignment of arrival pick uncertainties for appropriate data fitting and weighting using an empirical relationship based on signal-to-noise ratio, (2) using a modified form of travel time reciprocity to avoid unreasonable levels of model heterogeneity, and (3) identifying data unsuitable for 2-D modeling. The goal of the travel time inversion-amplitude modeling approach is to obtain a minimum-structure and minimum-parameter model that takes into account both horizontal and vertical variations in the resolution of typical wide-angle data. Each step of a layer-stripping procedure involves a series of inversions in which a one-dimensional or simple starting model is improved with additional velocity and/or interface nodes until a satisfactory trade-off between travel time fit, parameter resolution and complete ray coverage of all source-receiver pairs is achieved. Using zero vertical-velocity gradient layers and head waves during preliminary first-arrival inversion can (1) decrease the number of intermediate models, (2) allow greater lateral heterogeneity to be imaged, and (3) simplify incorporation of amplitude modeling constraints into the final model. Using amplitude-distance curves allows quantitative modeling of the relative amplitude and offset variations of phases. Discrepancies between observed and calculated reflection amplitudes are used to infer fundamental, non step-like velocity changes at layer boundaries. Later arrivals due to unresolved velocity anomalies are modeled using reflecting segments that ``float" within the model without an associated velocity structure. These reflectors provide a spatial image like that obtained from vertical-incidence reflection data, as opposed to a velocity image. The model of Grenville crustal structure is more detailed than a model obtained from a previous interpretation of the data and includes elements analogous to those imaged in nearby deep reflection data. A crustal-scale zone of wide-angle reflectors with an average easterly apparent dip of 13 degrees defines a major Grenvillian terrane boundary.
  • Zelt, C. A., 3-D velocity structure from simultaneous traveltime inversion of in-line seismic data along intersecting profiles, Geophysical Journal International, 118, 795-801, 1994.
    A method for simultaneously inverting in-line seismic traveltime data recorded along a network of intersecting linear profiles is presented. Consistency of the models at the intersection points is assured and permits 3-D structural and velocity variations to be inferred by interpolation between the profiles. Common model parameters are used at the intersection points, thereby minimizing the number of independent model parameters and maximizing the degree of constraint of each 2-D model. The method has two main application: (1) to obtain the most constrained set of 2-D models for each profile if subsequent 3-D modelling is not possible, and (2) to provide a 3-D starting model for subsequent 3-D modelling if there is sufficient azimuthal data coverage. Some ideal line geometries are suggested, but the method is applicable to any set of two or more lines with one or more intersection point. A new interpretation of crustal seismic data from the Peace River Arch region of the Western Canada Sedimentary Basin consisting of four profiles is presented using the simultaneous inversion method for both refracted and reflected arrivals. The results are generally consistent with a previous interpretation of the data in which each profile was modelled independently of the others using 2-D forward modelling. However, the models obtained by inversion contain less lateral heterogeneity that more accurately reflects the resolution limits of the data. This illustrates the need to reconsider data that have only been analyzed by forward modelling.
  • O'Leary, D. M., R. M. Ellis, R. A. Stephenson, L. S. Lane and C. A. Zelt, Crustal structure of the northern Yukon and MacKenzie Delta, northwestern Canada, Journal of Geophysical Research, 100, 9905-9920, 1995.
    Travel time inversion and amplitude forward modeling have been applied to two seismic refraction profiles from the northern Yukon-Mackenzie Delta region of northwestern Canada. The two-dimensional crustal P wave velocity models feature a near-surface layer which is 1-7 km thick and has an average velocity of 4 km/s; this overlies three crustal units, each having an average thickness of 11-15 km and with average velocities of 5.9, 6.1, and 7.1 km/s. The Moho is at ~37 km with little relief and overlies an upper mantle with a poorly constrained velocity. Tectonically, the study area lies between cratonic and Cordilleran North America and adjacent Mesozoic polar continental margin. The velocity models clearly illustrate a domainal crustal structure in the study area. A cratonic domain is characterized by a middle and lower crust with homogeneous velocities of 6.6-6.8 km/s. The other domain ("Yukon domain") is characterized by midcrustal velocities near 6 km/s and a lower crustal layer with velocities near 7.1 km/s. The transition zone between these domains is well-defined and is interpreted as a Proterozoic paleocontinental margin, supporting previous interpretations based on geological trends and potential field data. Lateral homogeneity of the crustal velocity structure within Yukon domain supports interpretations that Arctic Alaska was not emplaced into its present position on strike-slip faults. Local variations in lower crustal thickness, together with clear wide-angle Moho reflections, suggest a lower crustal and Moho signature possibly related to rifting, crustal extension, and magmatic intrusion and underplating during the Jura-Cretaceous development of the Arctic Ocean and polar continental margin.
  • Zelt, C. A. and D. J. White, Crustal structure and tectonics of the southeastern Canadian Cordillera, Journal of Geophysical Research, 100, 24255-24273, 1995.
    The crustal structure of the Omineca (OB) and Foreland (FB) belts of the southeastern Canadian Cordillera are interpreted from the inversion of seismic refraction/reflection traveltimes and amplitudes, and modeling of the Bouguer gravity data from a 350-km east-west wide-angle profile. The main features of the resultant velocity and density models include (i) a low average crustal velocity of 6.2 km/s, (ii) variable upper crustal velocities (5.6--6.3 km/s) within the FB and Purcell Anticlinorium as compared to further west in the OB (6.1--6.2 km/s), (iii) a mid-crustal (~20 km depth) 0.4--0.5 km/s velocity increase within the OB, (iv) eastward crustal thickening from 35 to 42 km over 80 km distance beneath the OB-FB boundary, (v) the Slocan Lake fault (SLF) dipping east at 15--20 degrees to at least 35 km depth, (vi) decreased lower crustal velocities (6.7 to 6.4 km/s) across the SLF from the OB into the FB, (vii) increased uppermost mantle velocities (7.9 to 8.0 km/s) from the OB into the FB, and (viii) an average crustal density increase of 40 kg/m**3 from the OB into the FB. Lower velocities, higher conductances and increased densities within the upper crust (0--10 km depth) of the Purcell Anticlinorium appear to be associated with Middle and Upper Proterozoic rift-related metasediments and gabbroic dikes (35--55% by volume) in contrast to the mainly Mesozoic felsic intrusives and metamorphic rocks that dominate further west in the OB. Elevated crustal temperatures within the OB (a high heat flow province) are responsible for low velocity gradients to 20 km depth. A more mafic lower crust beneath the OB (inferred from higher velocities) and the westward decrease in crustal thickness are interpreted as resulting primarily from Middle and/or Late Proterozoic extension and rifting of the craton. Penetration of the SLF into the lower crust may be controlled by lateral strength contrasts at the edge of the craton. Farther west, a mid-crustal strength contrast (a velocity boundary at 20--25 km depth), may have acted as a regional detachment zone during compressional and extensional tectonic episodes.
  • Clowes, R. M., C. A. Zelt, J. R. Amor and R.M. Ellis, Lithospheric structure in the southern Canadian Cordillera from a network of seismic refraction lines, Canadian Journal of Earth Sciences, 32, 1485-1513, 1995.
    Lithospheric velocity structure and its relationship to regional tectonics and development of the southern Canadian Cordillera are derived from a synthesis of interpretations from nine in-line seismic refraction-wide-angle reflection profiles and broadside data recorded during the Lithoprobe Southern Cordillera Refraction Experiment (SCoRE) and other refraction experiments across southern British Columbia, and one profile in northwestern Washington. Consistency of the SCoRE two-dimensional models at their intersection positions is achieved through application of a simultaneous inversion of all relevant traveltime data. The cross-sectional and map presentations demonstrate the strong degree of three-dimensional heterogeneity within the crust and upper mantle. A first-order characteristic is the continuous increase in crustal velocities westward from the Foreland belt to the Insular belt. The variations do not correlate with the morphogeological belts; they do correspond with large-scale geological and (or) tectonic features and seismic reflection results. Crustal thickness varies from 30 to 48 km; a lack of comparable variation in Bouguer gravity anomalies requires significant density changes in the crust. Variations in the seismic parameters do not correlate well with variations in crustal resistivity or heat flow, suggesting that generalizations relating low resistivities, high temperatures, and low seismic velocities must be treated with caution. Seismic heterogeneities are due primarily to lithological and (or) structural variations and are superimposed on the generally low velocities attributed to the thermal regime. An upper mantle reflector beneath the mainland Cordillera is inferred to be the top of a shallow asthenosphere. Westward flow in the warm asthenosphere interacts with the cold lithosphere of the subducting Juan de Fuca plate below the central Coast belt, forming a "sink" that could provide a driving mechanism for the flow.
  • Zelt, C. A. and B. C. Zelt, Study of out-of-plane effects in the inversion of refraction/wide-angle reflection traveltimes, Tectonophysics, 286, 209-221, 1998.
    In the presence of three-dimensional (3D) inhomogeneous structure, the results of 2D traveltime inversion will be in error since the effects of "out-of-plane" or 3D ray sampling are ignored. We have inverted synthetic data using 2D and 3D algorithms to examine the errors caused by 3D inhomogeneities which produce significant out-of-plane ray bending. The results of inverting data from 2D experiments are compared with vertical slices through 3D models obtained by inverting data using a number of recently-employed 3D recording geometries. Our results show that, even for strong 3D inhomogeneities, out-of-plane effects are relatively small, with crustal velocity errors of less than 0.15 km/s, and intra-crustal boundary depth errors generally less than 2 km. These errors are approximately equal to the uncertainties commonly assigned to crustal models derived from traveltime inversion. The artifacts are also similar in magnitude to the lateral smearing that occurs in 3D models when using relatively coarse 3D geometries. Only for a dense network of profiles will a 3D inversion using off- and in-line data provide greater lateral resolution than a 2D independent or simultaneous inversion of in-line data along each profile. 2D and 2.5D inversion of crooked-line data in the presence of strong velocity variations produces erroneous small-scale velocity structure. We conclude that most 3D crustal experiments cannot be justified on the basis that the results from a 2D experiment or a network of 2D profiles will be significantly in error due to out-of-plane effects. 3D experiments can be justified when a dense grid of shots and receivers is used or if a volume image, as opposed to a cross-sectional image, is required.
  • Zelt, B. C., M. Talwani and C. A. Zelt, Prestack depth migration of dense wide-angle seismic data, Tectonophysics, 286, 193-208, 1998.
    Prestack depth migration of wide-angle seismic data represents an extension of traditional imaging with near-vertical incidence data because it includes a larger component of the recorded wave field. To date, however, previous studies that have employed wide- angle migration have suffered because only widely spaced data were available and because only very simple synthetic tests were performed. Although wide-angle migration has the potential to increase our ability to image deep crustal structures, particularly when closely spaced data are collected, a thorough study of this technique has been lacking. To address this, we present a study of prestack depth migration of relatively dense synthetic wide- angle marine data. The objectives are to identify potential benefits and limitations of this approach and answer such fundamental questions as how close the receiver spacing must be for a typical survey to effectively image with wide-angle data. This will facilitate the design of better seismic experiments. Our study employs Kirchhoff prestack depth migration of variably spaced full wave-field synthetic wide-angle marine ocean bottom hydrophone (OBH) data generated using a realistic velocity model based on models for the passive eastern margin of the United States. We show how an increase in OBH density improves the migration by increasing the lateral resolution and signal-to-noise ratio. We also investigate the contribution of various offset ranges to the migrated image and show how the wider angle components contribute primarily to the deepest parts of the image with relatively low spatial frequency compared to the near-vertical incidence components. To investigate how errors in the velocity model affect imaging as a function of offset range we migrate the data using velocity models derived from refraction and reflection traveltime inversion. These examples demonstrate the need to obtain an increasingly accurate model as increasingly wider-angle data are migrated. To effectively image structures in our 200 x 40 km synthetic velocity model, an OBH spacing of approximately 2 km is required.
  • Zelt, C. A. and P. J. Barton, 3D seismic refraction tomography: A comparison of two methods applied to data from the Faeroe Basin, Journal of Geophysical Research, 103, 7187-7210, 1998.
    This paper presents a comparison of two tomographic methods for determining three- dimensional (3D) velocity structure from first-arrival traveltime data. The first method is backprojection in which traveltime residuals are distributed along their raypaths independently of all other rays. The second method is regularized inversion in which a tradeoff between data misfit and model roughness is minimized. Both methods are non-linear in that a starting model is required and new raypaths are calculated at each iteration. Both methods are applied to 3D ocean bottom seismometer (OBS) data from the Faeroe Basin, consisting of 53,479 traveltimes recorded at 29 OBSs. Different starting models and values for the free parameters of each method are tested. The results of a new form of backprojection compare favorably with regularized inversion, but the latter method provides a slightly simpler model for relatively little additional computational expense. The uniqueness of two model features is assessed using regularized inversion with combined smoothness and flatness constraints. An inversion of synthetic data corresponding to 100% data recovery from the real experiment shows a marked improvement in lateral resolution at certain depths, and demonstrates the potential of currently-feasible 3D refraction experiments. The similarity of the final models from the two tomographic methods suggests that the results from backprojection can be relied on when computational resources rule out regularized inversion. Two isovelocity surfaces representing a major intra-basin boundary and the basement correspond closely with thickened isopachs, a prominent basement ridge, and a large normal fault interpreted from a regional network of commercial reflection profiles.
  • Zelt, C. A., Lateral velocity resolution from 3-D seismic refraction data, Geophyscal Journal International, submitted, 1998.
    A method for estimating the lateral velocity resolution from 3-D seismic refraction traveltimes is presented. The method is nonlinear in that synthetic data calculated from "checkerboard" models are inverted using an iterative tomographic approach incorporating smoothness constraints and updated raypaths at each iteration. Two applications are presented: (1) the real data from the Faeroe Basin experiment using the ray coverage and noise level of the ~50,000 picks, and (2) the ideal data from the same experiment corresponding to 100% data recovery, equivalent to about three times as many raypaths. The refraction data constrain the sedimentary and basement structure to ~12 km depth. A comparison of the results from the two data sets provides a qualitative check on the resolution method, illustrates the pitfalls of using ray coverage as an indicator of resolution, and demonstrates the potential resolution of currently feasible 3-D refraction experiments. Thirty- two checkerboard models consisting of alternating positive and negative velocity anomalies superimposed on the preferred final model of the basin were tested, each with a different cell size, position or orientation. The problem of ray bending associated with the 5% checkerboard anomalies is shown to be small. Using models with four cell sizes allowed for resolution estimates from 3 to 15 km, this range being imposed by the frequency content of the data and the areal dimensions of the study area (44x26 km). An operator centered on each model node measures the local semblance between the known and recovered checkerboard models. A determination of the smallest well-resolved cell size at each model node is then made using a 0.7 semblance threshold to provide a spatially-dependent lateral resolution estimate. Resolution for the real data set varies from an average of just over 3 km at 2 km depth, to 10 km at 10 km depth, where there is a local maxima in ray coverage due to a concentration of ray bottoming points. For the ideal data set, the average lateral resolution drops off roughly linearly from better than 3 km at 2 km depth, to 6.3 km at 10 km depth. The largest difference between the ideal and real data's resolution occurs at 7.2 km depth where it averages 4.6 km for the former and 10.8 km for the latter due to the near absence of ray bottoming points between 7 and 9 km. The results show that the final model for the Faeroe Basin obtained by regularized inversion with smoothness constraints is consistent with the resolution estimates in the sense that the model does not contain structure with a wavelength smaller than the resolution estimate at any point. The results for the ideal data show that good quality 3-D refraction experiments can provide a lateral resolution of no worse than the receiver spacing (shot spacing for land data) throughout most of the sampled volume.
  • Condi, F. J., C. A. Zelt, D. S. Sawyer, and G. J. Hirasaki, Gravity inversion for rifted margin deep structure using extension and isostatic constraints, Geophysical Journal International, 138, 435-446, 1999.
    We present a gravity inversion method for determining the deep structure of rifted margins. It uses a two dimensional earth model parameterized as multiple, irregularly shaped, polygonal bodies, each of uniform density. The method has three novel features. First, it links parameters in the shallow parts of the model to those in the deep parts, by using a uniform extension model as a constraint in the inversion. The shallow structure will typically be known with greater certainty than the deep structure based on shallow seismic and borehole data. Second, it provides for variable weighting of prior information on densities, shapes, the extension model, and smoothing, to find geologically reasonable models. Third, it estimates densities and shapes simultaneously. The first two features are used to compensate for the inherent deficiencies of poor depth resolution and non-uniqueness in gravity modeling. The last two make the method an efficient way to explore a range of models. Synthetic tests of sensitivity to noise indicate that the isostatic extension constraint promotes the recovery of the short wavelength Moho topography and eliminates spatial undulations in deep structure due to noise in the data. Synthetic tests of sensitivity to untrue prior information show that the isostatic extension constraint increases the range of acceptable recovered models over no isostatic extension constraint. The range of recovered Moho positions suggests a vertical resolution of about 2 km. Although many recovered models fit the data, the results imply a methodology for choosing a best set of models and we suggest guidelines for applying the method to real margins.
  • Zelt, C.A., A. M. Hojka, E. R. Flueh and K. D. McIntosh, 3D simultaneous seismic refraction and reflection tomography of wide-angle data from the central Chilean margin, Geophysical Research Letters, 26, 2577-2580, 1999.
    We present an application of three-dimensional (3D) simultaneous seismic refraction and reflection tomography for velocity and interface structure. The inversion technique and method for developing the starting model are specifically designed for relatively sparse wide-angle data acquired across strongly-varying structure. The data were recorded in a region of seamount subduction on the Chilean margin and consist of seven receivers and ten intersecting airgun profiles over a 90x90 km area providing constraint to 25 km depth. The tomographic method and the final model are assessed through a comparison with the large-scale geologic features of the margin and a resolution test. The 3D model shows the Valparaiso forearc basin, the accretionary wedge, the subducting plate, and possibly a subducted seamount. Our results show the potential of relatively sparse 3D wide-angle data.
  • Zelt, C. A., Modelling strategies and model assessment for wide-angle seismic traveltime data, Geophysical Journal International, 139, 183-204, 1999.
    Strategies for modelling seismic refraction/wide-angle reflection traveltimes to obtain 2-D velocity and interface structure are presented along with methods for assessing the reliability of the results. Emphasis is placed on using inverse methods, but a discussion of pre-modelling considerations such as arrival picking and classification, data uncertainties and fitting, traveltime reciprocity, crooked line geometry, and the selection of a starting model is also applicable to trial-and-error forward modelling. The most important advantages of an inverse method are the ability to derive simpler models for the appropriate level of fit to the data, and the ability to assess the final model in terms of resolution, parameter bounds and non-uniqueness. Given the unique characteristics of each dataset and the local earth structure, there is no single approach to modelling wide-angle data that is best. This paper describes the best modelling strategies according to the (1) model parameterization, (2) inclusion of prior information, (3) complexity of the earth structure, (4) characteristics of the data, and (5) utilisation of coincident seismic reflection data. There are two natural end member inversion styles: (1) a regular, fine-grid parameterization when seeking a minimum-structure model, and (2) an irregular grid, minimum-parameter model when considering certain forms of prior information. The former style represents the "pure" tomography approach. The latter style is closer to automated forward modelling, and can be applied best with a parameter- selective algorithm, that is, one that allows any subset of model parameters to be selected for inversion. Data from regions with relatively strong lateral heterogeneity in the near-surface are best treated using layer stripping, whereas data from regions that are generally complex throughout are best treated using whole-model inversion, that is, determining all model parameters simultaneously after careful construction of a starting model that allows the appropriate rays to be traced to all pick locations. The lateral spacing of model nodes will depend on the type of inversion and whether detailed prior information, such as from reflection data, is included, but a general guideline is the shot spacing (receiver spacing for typical marine data), except perhaps in the upper layers where about half this may be necessary. Traveltimes picked from pre-stack, unmigrated or migrated coincident reflection data can be (1) used to develop the starting model, (2) inverted simultaneously with the wide-angle data, or (3) inverted after modelling the wide-angle data to constrain interfaces that "float" within the velocity model. Model assessment establishes the reliability of the final model. Presenting model statistics, traveltime fits, ray diagrams, and resolution kernels is useful, but can only indirectly address this issue. Direct model assessment techniques that derive alternate models that satisfactorily fit both the real data and prior information are the best means for establishing the absolute bounds on model parameters and if a particular model feature is required by the data.
  • Zelt, C. A., K. Sain, J. V. Naumenko, and D. S. Sawyer, Assessment of crustal velocity models using seismic refraction and reflection tomography, Geophysical Journal International, 153, 609-626, 2003.
    Two tomographic methods for assessing velocity models obtained from wide-angle seismic traveltime data are presented through four case studies. The modeling/inversion of wide-angle traveltimes usually involves some aspects that are quite subjective. For example: (1) identifying and including later phases that are often difficult to pick within the seismic coda, (2) assigning specific layers to arrivals, (3) incorporating pre-conceived structure not specifically required by the data, and (4) selecting a model parameterization. These steps are applied to maximize model constraint and minimize model non-uniqueness. However, these steps may cause the overall approach to appear ad hoc, and thereby diminish the credibility of the final model. The effect of these subjective choices can largely be addressed by estimating the minimum model structure required by the least subjective portion of the wide-angle dataset: the first-arrival times. For datasets with Moho reflections, the tomographic velocity model can be used to invert the PmP times for a minimum-structure Moho. In this way, crustal velocity and Moho models can be obtained that require the least amount of subjective input, and the model structure that is required by the wide-angle data with a high degree of certainty can be differentiated from structure that is merely consistent with the data. The tomographic models are not intended to supersede the preferred models, since the latter model is typically better resolved and more interpretable. This form of tomographic assessment is intended to lend credibility to model features common to the tomographic and preferred models. Four case studies are presented in which a preferred model was derived using one or more of the subjective steps described above. This was followed by conventional first-arrival and reflection traveltime tomography using a finely-gridded model parameterization to derive smooth, minimum-structure models. The case studies are from the SE Canadian Cordillera across the Rocky Mountain Trench, central India across the Narmada-Son lineament, the Iberia margin across the Galicia Bank, and the central Chilean margin across the Valparaiso Basin and a subducting seamount. These case studies span the range of modern wide-angle experiments and datasets in terms of shot/receiver spacing, marine and land acquisition, lateral heterogeneity of the study area, and availability of wide-angle reflections and coincident near-vertical reflection data. The results are surprising given the amount of structure in the smooth, tomographically-derived models that is consistent with the more subjectively-derived models. The results show that exploiting the complementary nature of the subjective and tomographic approaches is an effective strategy for the analysis of wide-angle traveltime data.