B. C. Zelt

Inversion of three‐dimensional wide‐angle seismic data from the southwestern Canadian Cordillera

Seismic refraction/wide-angle reflection data were recorded on a triangular array in southwestern British Columbia centered on the boundary between the Coast Belt to the southwest and the Intermontane Belt to the northeast. The experiment, part of the Lithoprobe Southern Cordillera transect, enabled determination of the three-dimensional (3-D) velocity structure of the crust and upper mantle. An algorithm for the inversion of wide-angle seismic data to determine 3-D velocity structure and depth to reflecting interfaces is developed. The algorithm is based on existing procedures for the inversion and forward modeling of first arrival travel times and forward modeling of reflection travel times, including (1) forward modeling using a 3-D finite difference algorithm; and (2) a simple velocity model parameterization for the inversion which eliminates the need to solve a large system of equations. The existing procedure is extended to allow (1) the inversion of reflection times to solve for depth to a reflecting interface and/or velocity structure; (2) the inversion of first arrival travel times to solve for depth to a refracting interface; and (3) layer stripping. Application of the algorithm to southern Cordillera data uses Pg to constrain upper crustal velocity structure, PmP to constrain lower crustal velocity structure and depth to Moho, and Pn to constrain upper mantle velocities and depth to Moho. The 3-D velocity model for the southwestern Canadian Cordillera is characterized by (1) significant lateral velocity variations at all depths that do not, in general, correlate with surface geological features or gravity data; (2) a relatively high velocity middle and lower crust in the southwestern part of the study area which correlates with a strong relative gravity high and outlines the eastern extent of lower Wrangellia, an accreted terrane forming the Insular Belt to the west; (3) a narrow zone of slower velocity in the lower crust and change in crustal thickness associated with the Fraser Fault system, lending additional support to the view that it is a crustal penetrating fault; (4) an average upper mantle velocity of 7.85 km/s; and (5) a depth to Moho of 33–36 km in the Intermontane Belt and 36–38 km throughout most of the Coast Belt, decreasing in the west to 33 km near the Insular-Coast contact. Horizontal velocity structure slices and an interpreted cross section based on these and other results show the complexity of crustal structure in the region.

Seismic survey probes urban earthquake hazards in Pacific Northwest

A multidisciplinary seismic survey earlier this year in the Pacific Northwest is expected to reveal much new information about the earthquake threat to U.S. and Canadian urban areas there. A disastrous earthquake is a very real possibility in the region. The survey, known as the Seismic Hazards Investigation in Puget Sound (SHIPS), engendered close cooperation among geologists, biologists, environmental groups, and government agencies. It also succeeded in striking a fine balance between the need to prepare for a great earthquake and the requirement to protect a coveted marine environment while operating a large airgun array.

Prestack depth migration of dense wide-angle seismic data

Abstract 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, 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 case 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 image effectively 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 ocean-bottom hydrophone (OBH) data generated using a realistic velocity model based on 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 a velocity model derived from refraction and reflection traveltime inversion. This example demonstrates the need to obtain an increasingly accurate model as increasingly wider-angle data are migrated. To effectively image structures in our 200 × 40 km synthetic velocity model, an OBH spacing of approximately 2 km is required.

Study of out-of-plane effects in the inversion of refraction/wide-angle reflection traveltimes

Abstract 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.

Some recent developments in the acquisition and processing of seismic data

Abstract Industry-style 3-D surveys are different in the volume of data, processing techniques and expected results from ‘academic’ 3-D surveys. Industry has developed new acquisition techniques for marine 3-D surveys: multi-streamer seismic ships, vertical cables, and dual-sensor bottom cables. As opposed to 2-D post-stack time migration, new techniques involving 2-D and 3-D pre-stack depth migration are becoming important. Examples are given. Migration of wide-angle data to obtain subsurface imaging is discussed. Attribute analyses, including the use of wavelets to detect azimuthal anisotropy and lithologic contrasts are described. The use of the recent developments in wavelets in seismic analysis is introduced.

Truncated asymptotic representation of waves in a one-dimensional elastic medium

A new time‐domain method has been developed for solving for the stress and displacement of normally incident plane waves propagating in a smoothly varying one‐dimensional elastic medium. Both the Young’s modulus E and the density ρ are allowed to vary smoothly with depth. The restriction of geometrical optics, that the wavelength be much less than the material stratification length, is not required in this new method. We truncate the infinite geometrical‐optics asymptotic expansion after n terms (n = 2 in this paper), which imposes a condition on the acoustic impedance I for exact solutions to exist. The resultant expansion is uniform and exact for three general classes of impedance functions. Results are calculated for the case of a medium with a linear velocity gradient (for which there is an exact solution in the frequency domain); the results are compared with a two‐term WKBJ approximation and the new truncated expansion method. Since a linear velocity gradient is not one of the foregoing classes of i...

Risk assessment for unexploded ordnance remediation

We develop and compare methods for assessing the risk that unexploded ordnance (UXO) have been missed following prioritized digging. A random compliance sampling approach has been suggested for UXO risk assessment, and we extend this approach to account for the bias in prioritized digging, thereby reducing the number of excavations required to test for outlying UXO. We then discuss and compare methods for identification of outliers to the distribution of UXO via generative models of the receiver operating characteristic (ROC). Next, we consider how seeded items emplaced for quality control can be used to increase confidence in the classification process, and we model this process by constraining the ROC model. Finally, we turn to the problem of identifying novel, or unique, UXO with prioritized validation digs. We propose a metric that combines features of the geophysical model estimated for each detected target to identify novel UXO. The metric requires no prior information about the UXO present at a site.

Setting the stop dig point for unexploded ordnance remediation

We develop objective methods for determining whether advanced classification with geophysical data has identified all hazardous unexploded ordnance (UXO) at a site. We first propose a simple criterion for selection of the stop dig point: we can stop digging once a specified number (Nstop) of non-UXO are encountered in sequence during ordered excavation of targets. We then develop an objective method for determining Nstop that accounts for the difficulty of a given classification problem. Finally, we show how a binormal model can be fit to the receiver operating characteristic in order to estimate the posterior probability that each target is a UXO.

Two- and three-dimensional velocity structure of the southwestern Canadian Cordillera from seismic refraction data

Seismic refraction/wide-angle reflection data recorded on a triangular array in the southwestern Canadian Cordillera in 1989 as part of the Lithoprobe Southern Cordillera transect are analyzed to determine the twoand three-dimensional velocity structure of the crust and upper mantle. In-line data recorded along two sides of the triangle are interpreted for 2—D structure using an iterative combination of traveltime inversion and forward modelling of amplitudes. An algorithm for the inversion of wide-angle seismic data to determine 3—D velocity structure and depth to reflecting interfaces is developed. The algorithm is based on an existing procedure for the inversion of first arrival traveltimes which includes: (i) forward modelling of traveltimes using a 3—D finite-difference algorithm; and (ii) a simple velocity model parameterization for the inversion which eliminates the need to solve a large system of equations. The existing procedure is extended to allow: (i) fast and accurate forward modelling of reflection times; (ii) the inversion of reflection times to solve for depth to a reflecting interface and/or velocity structure; (iii) the inversion of first arrival traveltimes to solve for depth to a refracting interface; and (iv) layer stripping. Application of the algorithm for southern Cordillera data uses Pg to constrain upper crustal velocity structure, PmP to constrain lower crustal velocity structure and depth to Moho, and P to constrain upper mantle velocities and depth to Moho. Results for a line running along-strike in the southern Intermontane Belt (Quesnellia terrane) reveal low average vertical velocity gradients, average depth to Moho of 32 km, and an upper mantle reflector —16 km below the Moho that may represent the base of the lithosphere. The upper and middle crust of the refraction model comprise the upper part of the Quesnellia terrane; the lower crust probably comprises parautochthonous and cratonic North America, but does not show the division into two components that is inferred from reflection data, indicating that their physical properties are not significantly different within the resolution of the refraction data. The lower lithosphere of Quesnellia is absent and

Signal coherence in shallow water with rough boundaries

A normal mode model to predict signal coherence for a source moving in shallow water with rough boundaries has been described previously [J. M. Ozard, G. H. Brooke, M. J. Wilmut, and M. V. Greening, J. Acoust. Soc. Am. Suppl. I 69, S19 (1981)]. The model assumes that mode amplitude or mode phase fluctuate. We have extended this model to widely spaced sensors by permitting the fluctuations to be independent from sensor to sensor. This new model has been used to calculate signal coherence for a variety of sensor configurations. Coherences have been calculated for low frequencies for which only a few modes are present. When source receiver range is changing rapidly it is found that for closely spaced sensors coherence depends only on receiver separation, mode shape, and mode excitation. However, for widely spaced sensors or sources that maintain a constant source receiver range the roughness parameters have a profound effect on coherence. Sensor configurations that give consistently high signal coherence, an...