John A. Hole

Nonlinear high‐resolution three‐dimensional seismic travel time tomography

A tomographic inversion procedure is described and applied to a synthetic three-dimensional (3-D) seismic refraction data set, demonstrating that tomography is capable of determining a densely sampled velocity model with large velocity contrasts. Forward and inverse modeling procedures are chosen to minimize the computational costs of the inversion. Parameterizing the linearized inversion using functions defined along the ray paths, simple backprojection with zero pixel size is shown to exactly solve the linear problem, producing the smallest model for the slowness perturbation. For small grid cells, simple backprojection closely approximates the exact solution and is a sufficient solution for an iterative nonlinear inversion. This eliminates the need to store or solve a large system of linear equations. Accurate first arrival travel times are rapidly computed using a finite difference algorithm. Forward modeling between each simple backprojection allows the procedure to correctly account for the locations of the rays. This becomes more important as the spatial resolution of the model is improved. The computational efficiency of the entire nonlinear procedure allows the model to be densely sampled, providing a spatially well-resolved 3-D tomographic image. The synthetic refraction survey is designed to be similar to a published 3-D survey over the East Pacific Rise. Tests based on this example and others show that 3-D tomography is capable of inverting a large travel time data set for detailed earth structure with large lateral velocity variations and is stable in the presence of noisy data.

Three-dimensional P and S wave velocity structure of Redoubt Volcano, Alaska

The three-dimensional P and S wave structure of Redoubt Volcano, Alaska, and the underlying crust to depths of 7–8 km is determined from 6219 P wave and 4008 S wave first-arrival times recorded by a 30-station seismograph network deployed on and around the volcano. First-arrival times are calculated using a finite-difference technique, which allows for flexible parameterization of the slowness model and easy inclusion of topography and source-receiver geometry. The three-dimensional P wave velocity structure and hypocenters are determined simultaneously, while the three-dimensional S wave velocity model is determined using the relocated seismicity and an initial S wave velocity model derived from the P wave velocity model assuming an average Vp/Vs ratio of 1.78. Convergence is steady with approximately 73% and 52% reduction in P and S wave arrival time RMS, respectively, after 10 iterations. The most prominent feature observed in the three-dimensional velocity models derived for both P and S waves is a relative low-velocity, near-vertical, pipelike structure approximately 1 km in diameter that extends from 1 to 6 km beneath sea level. This feature aligns axially with the bulk of seismicity and is interpreted as a highly fractured and altered zone encompassing a magma conduit. The velocity structure beneath the north flank of the volcano between depths of 1 and 6 km is characterized by large lateral velocity variations. High velocities within this region are interpreted as remnant dikes and sills and low velocities as regions along which magma migrates. No large low-velocity body suggestive of a magma chamber is resolved in the upper 7–8 km of the crust.

Crustal structure of a transform plate boundary: San Francisco Bay and the central California continental margin

Wide-angle seismic data collected during the Bay Area Seismic Imaging Experiment provide new glimpses of the deep structure of the San Francisco Bay Area Block and across the offshore continental margin. San Francisco Bay is underlain by a veneer (<300 m) of sediments, beneath which P wave velocities increase rapidly from 5.2 km/s to 6.0 km/s at 7 km depth, consistent with rocks of the Franciscan subduction assemblage. The base of the Franciscan at 15–18 km depth is marked by a strong wide-angle reflector, beneath which lies an 8- to 10-km-thick lower crust with an average velocity of 6.75 ± 0.15 km/s. The lower crust of the Bay Area Block may be oceanic in origin, but its structure and reflectivity indicate that it has been modified by shearing and/or magmatic intrusion. Wide-angle reflections define two layers within the lower crust, with velocities of 6.4–6.6 km/s and 6.9–7.3 km/s. Prominent subhorizontal reflectivity observed at near-vertical incidence resides principally in the lowermost layer, the top of which corresponds to the “6-s reflector” of Brocher et al. [1994]. Rheological modeling suggests that the lower crust beneath the 6-s reflector is the weakest part of the lithosphere; the horizontal shear zone suggested by Furlong et al. [1989] to link the San Andreas and Hayward/Calaveras fault systems may actually be a broad zone of shear deformation occupying the lowermost crust. A transect across the continental margin from the paleotrench to the Hayward fault shows a deep crustal structure that is more complex than previously realized. Strong lateral variability in seismic velocity and wide-angle reflectivity suggests that crustal composition changes across major transcurrent fault systems. Pacific oceanic crust extends 40–50 km landward of the paleotrench but, contrary to prior models, probably does not continue beneath the Salinian Block, a Cretaceous arc complex that lies west of the San Andreas fault in the Bay Area. The thickness (10 km) and high lower-crustal velocity of Pacific oceanic crust suggest that it was underplated by magmatism associated with the nearby Pioneer seamount. The Salinian Block consists of a 15-km-thick layer of velocity 6.0–6.2 km/s overlying a 5-km-thick, high-velocity (7.0 km/s) lower crust that may be oceanic crust, Cretaceous arc-derived lower crust, or a magmatically underplated layer. The strong structural variability across the margin attests to the activity of strike-slip faulting prior to and during development of the transcurrent Pacific/North American plate boundary around 29 Ma.

Seismic Evidence for a Lower-Crustal Detachment Beneath San Francisco Bay, California

Results from the San Francisco Bay area seismic imaging experiment (BASIX) reveal the presence of a prominent lower crustal reflector at a depth of ∼15 kilometers beneath San Francisco and San Pablo bays. Velocity analyses indicate that this reflector marks the base of Franciscan assemblage rocks and the top of a mafic lower crust. Because this compositional contrast would imply a strong rheological contrast, this interface may correspond to a lower crustal detachment surface. If so, it may represent a subhorizontal segment of the North America and Pacific plate boundary proposed by earlier thermo-mechanical and geological models.

Crustal structure of the Colorado Plateau, Arizona: Application of new long‐offset seismic data analysis techniques

The Colorado Plateau is a large crustal block in the southwestern United States that has been raised intact nearly 2 km above sea level since Cretaceous marine sediments were deposited on its surface. Controversy exists concerning the thickness of the plateau crust and the source of its buoyancy. Interpretations of seismic data collected on the plateau vary as to whether the crust is closer to 40 or 50 km thick. A thick crust could support the observed topography of the Colorado Plateau isostatically, while a thinner crust would indicate the presence of an underlying low-density mantle. This paper reports results on long-offset seismic data collected during the 1989 segment of the U.S. Geological Survey Pacific to Arizona Crustal Experiment that extended from the Transition Zone into the Colorado Plateau in northwest Arizona. We apply two new methods to analyze long-offset data that employ finite difference travel time calculations: (1) a first-arrival time inverter to find upper crustal velocity structure and (2) a forward-modeling technique that allows the direct use of the inverted upper crustal solution in modeling secondary reflected arrivals. We find that the crustal thickness increases from 30 km beneath the metamorphic core complexes in the southern Basin and Range province to about 42 km beneath the northern Transition Zone and southern Colorado Plateau margin. We observe some crustal thinning (to ∼37 km thick) and slightly higher lower crustal velocities farther inboard; beneath the Kaibab uplift on the north rim of the Grand Canyon the crust thickens to a maximum of 48 km. We observe a nonuniform crustal thickness beneath the Colorado Plateau that varies by ∼15% and corresponds approximately to variations in topography with the thickest crust underlying the highest elevations. Crustal compositions (as inferred from seismic velocities) appear to be the same beneath the Colorado Plateau as those in the Basin and Range province to the southwest, implying that the plateau crust represents an unextended version of the Basin and Range. Some of the variability in crustal structure appears to correspond to preserved lithospheric discontinuities that date back to the Proterozoic Era.

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.

Three‐dimensional seismic velocity structure of the San Francisco Bay area

Seismic travel times from the northern California earthquake catalogue and from the 1991 Bay Area Seismic Imaging Experiment (BASIX) refraction survey were used to obtain a three-dimensional model of the seismic velocity structure of the San Francisco Bay area. Nonlinear tomography was used to simultaneously invert for both velocity and hypocenters. The new hypocenter inversion algorithm uses finite difference travel times and is an extension of an existing velocity tomography algorithm. Numerous inversions were performed with different parameters to test the reliability of the resulting velocity model. Most hypocenters were relocated 12 km under the Sacramento River Delta, 6 km beneath Livermore Valley, 5 km beneath the Santa Clara Valley, and 4 km beneath eastern San Pablo Bay. The Great Valley Sequence east of San Francisco Bay is 4–6 km thick. A relatively high velocity body exists in the upper 10 km beneath the Sonoma volcanic field, but no evidence for a large intrusion or magma chamber exists in the crust under The Geysers or the Clear Lake volcanic center. Lateral velocity contrasts indicate that the major strike-slip faults extend sub vertically beneath their surface locations through most of the crust. Strong lateral velocity contrasts of 0.3–0.6 km/s are observed across the San Andreas Fault in the middle crust and across the Hayward, Rogers Creek, Calaveras, and Greenville Faults at shallow depth. Weaker velocity contrasts (0.1–0.3 km/s) exist across the San Andreas, Hayward, and Rogers Creek Faults at all other depths. Low spatial resolution evidence in the lower crust suggests that the top of high-velocity mafic rocks gets deeper from west to east and may be offset under the major faults. The data suggest that the major strike-slip faults extend sub vertically through the middle and perhaps the lower crust and juxtapose differing lithology due to accumulated strike-slip motion. The extent and physical properties of the major geologic units as constrained by the model should be used to improve studies of seismicity, strong ground motion, and regional stress.

Wide‐angle seismic constraints on the evolution of the deep San Andreas plate boundary by Mendocino triple junction migration

Recent, wide-angle seismic observations that constrain the existence and structure of a mafic layer in the lower crust place strong constraints on the evolution of the San Andreas plate boundary system in northern and central California. Northward migration of the Mendocino Triple Junction and the subducted Juan de Fuca lithospheric slab creates a gap under the continent in the new strike-slip system. This gap must be filled by either asthenospheric upwelling or a northward migrating slab attached to the Pacific plate. Both processes emplace a mafic layer, either magmatic underplating or oceanic crust, beneath the California Coast Ranges. A slab of oceanic lithosphere attached to the Pacific plate is inconsistent with the seismic observation that the strike-slip faults cut through the mafic layer to the mantle, detaching the layer from the Pacific plate. The layer could only be attached to the Pacific plate if large vertical offsets and other complex structures observed beneath several strike-slip faults are original oceanic structures that are not caused by the faults. Otherwise, if oceanic slabs exist beneath California, they do not migrate north to fill the growing slab gap. The extreme heat pulse created by asthenospheric upwelling is inconsistent with several constraints from the seismic data, including a shallower depth to the slab gap than is predicted by heat flow models, seismic velocity and structure that are inconsistent with melting or metamorphism of the overlying silicic crust, and a high seismic velocity in the upper mantle. Yet either the Pacific slab model or the asthenospheric upwelling model must be correct. While the mafic material in the lower crust could have been emplaced prior to triple junction migration, the deeper slab gap must still be filled. A preexisting mafic layer does not reduce the inconsistencies of the Pacific slab model. Such material could, however, compensate for the decrease in mafic magma that would be produced if asthenospheric upwelling occurred at a lower temperature. These low temperatures, however, may be inconsistent with asthenospheric rheology.

Interface inversion using broadside seismic refraction data and three‐dimensional travel time calculations

A procedure has been developed to interpret densely sampled broadside seismic refraction data recorded from a large air gun array. First arrival travel times are inverted to find the structure on an interface beneath the shot line. Travel times are calculated for three-dimensional velocity models using a rapid finite difference algorithm, adapted to allow variable sampling of the model and the determination of rays. A simple inversion parameterization eliminates the need for matrix inversion. The complete inversion procedure is computationally rapid yet allows the determination of detailed three-dimensional structure. Broadside refraction data recorded in the Queen Charlotte Basin, offshore western Canada, during a multichannel reflection experiment are used to demonstrate the procedure. The data are inverted for the basement interface beneath the shot line, defining a rapidly varying thickness of sedimentary basin fill. The results of the inversion stimulate a reinterpretation of the reflection data and identify a new major basement fault. Structure out of the plane of the reflection section is determined, including the strike of the fault and other nearby features.

Seismic reflections from the near‐vertical San Andreas Fault

An electric motive device includes two pairs of magnets, movable in pairs relative to each other. The magnets of each pair have pole faces positioned normally to cause the magnets of the respective pair to repel each other. The pole faces of each magnet are spaced to form an air gap through which magnetic flux flows between the pole faces of each magnet. A shuttle moves relative to the pairs of magnets into and out of the air gaps. The shuttle includes a magnetic core and a coil which is driven by a current source to enable the core to be saturated. The shuttle and magnets are interconnected with each other and a commutator by a lever arm system and a snap action device so that current is supplied only intermittently to the coil. When no current is supplied to the coil, the core provides a low reluctance path for fluxes of the magnets to enable the magnets to be drawn towards the shuttle. In response to movement of the magnets into close proximity with the shuttle, current is supplied to the coil, causing the core to become saturated and increase the reluctance thereof. Thereby, the adjacent pole faces of the magnets repel each other. The coil, when energized, functions as an electromagnet that is repelled from the air gap of one pair of magnets to the other pair of magnets.