Scalar- and planar-valued curve fitting using splines under tension

Cline, Alan

doi:10.1145/360924.360971

Cited by 220 publications

(76 citation statements)

References 2 publications

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“…Travel time inversion is a nonlinear problem which can be linearized to obtain an iterative solution of the equation First arrival times were sampled for all 21 shots with reciprocity points embedded within the set of picks. A onedimensional spline routine [Cline, 1974] …”

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confidence: 99%

Seismic imaging of upper crustal structure using travel times from the PASSCAL Ouachita Experiment

Lutter¹,

Nowack²,

Braile³

1990

J. Geophys. Res.

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A first arrival travel time inversion applied to the 1986 PASSCAL Ouachita experiment has been used to image upper crustal structure. Twenty-one shot points every 10 km were recorded along two 100-km-long segments with 400 seismographs on each segment. A splined velocity model parameterization allowed for the inversion of laterally inhomogeneous models but not velocity discontinuities. Over 800 travel times were used in the inversion with a variable data covariance weighting. The multiple source nature of the experiment design allowed the use of reciprocity relationships among the 21 shot points to enhance data correlation. A succession of models with velocities specified at 30, 90, 171, and 221 nodes were inverted for whose horizontal node spacing decreased from 100 to 12.5 km in the final 221 node model. Vertical node spacings of 3.0 and 1.5 km were used. The results of the inversions indicate changes in depth of isovelocity lines which are interpreted as Triassic fault structure based on nearby well data. The final RMS travel time residual is 0.045 s. Resolution using first arrivals deteriorates rapidly below 9 km depth. Three distinct velocity gradients can be correlated with geologic units. Surface exposed Cretaceous and Jurassic sediments with velocities from 2.0 to 3.5 km/s extend to 1.5 km depth. Triassic rift fill sediments, which do not outcrop, have inverted velocities ranging from 3.5 to 4.75 km/s between depths of 1.5-3.0 km. Paleozoic sediments are imaged by a decreased velocity gradient below a depth of 3.0 km. Lack of resolution at depths greater than 9 km necessitates detailed modeling of wide-angle reflected phases to further constrain deeper crustal structure.

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mentioning

confidence: 99%

Seismic imaging of upper crustal structure using travel times from the PASSCAL Ouachita Experiment

Lutter¹,

Nowack²,

Braile³

1990

J. Geophys. Res.

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“…This data grid was then extended 15 minutes of latitude and longitude beyond the quadrangle boundaries in order to attenuate unwanted edge effects which inevitably result from further mathematical operations on the grid. This grid enlargement was accomplished by merging similarly projected and gridded data sets immediately adjacent to the quadrangle using analytical continuation and smoothing techniques, including application of an algorithm for splining under tension (Cline, 1974;Bhattacharyya and others, 1979;Hildenbrand, 1983).…”

Section: Geophysical Datamentioning

confidence: 99%

Map showing mineral resource assessment for vein and replacement deposits of gold, silver, copper, lead, zinc, manganese, and tungsten in the Butte 1° x 2° quadrangle, Montana

Elliott¹,

Wallace²,

Lee³

et al. 1992

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“…For both programs, the velocity model was described by a three dimensional grid. A cubic spline under tension (Cline, 1974) was used to interpolate the velocity and fi rst and second deri vat i ves between the nodes of the grid. In the central part of the transform, the model of Figure 5.11 simulates a crustal magma chamber.…”

Section: Structuresmentioning

confidence: 99%

Seismicity and structure of the Orozco transform fault from ocean bottom seismic observations

Tréhu¹

1982

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jIn this thesis, seismic waves generated by sources rangi ng from 2.7 kg shots of TNT to magni tude 5 earthquakes are studied in order to determine the seismic activity and crustal structure of the Orozco transform fault. Most of the data were coll ected by a network of 29 ocean bottom seismometers (OBS) and hydrophones (OBH) which were deployed as part of project ROSE (Rivera Ocean Seismic Experiment). Additional information is provided by magnetic anomaly and bathymetric data collected during and prior to ROSE and by teleseismic earthquakes recorded by the WWSSN (Worldwide Seismic Station Network).In Chapter II, the tectonic setting, bathymetry and teleseismic history of the Orozco Fracture Zone are summari zed. Coveri ng an area of 90 x 90 km whi ch i ncl udes ridges and troughs trending both parallel and perpendicular to the present spreading direction (approximately east-west), the bathymetry of the transform portion of the fracture zone does not resemble that of other transform faults which have been studied in detail. A detailed study of one of the largest teleseismic earthquakes (mb=5.1) indicates right lateral strike-slip faulting with a strike parallel to the present spreading direction and a focal depth of less than 5 km. The moment sum from teleseismic earthquakes suggests an average fault width of at most a few kilometers. Because the teleseismic earthquake locations are too imprecise to define the present plate boundary and the magnetic anomaly data are too sparse to resolve the recent tectonic history, more questions are raised than are answered by the results in this chapter. These questions provide the focus for the study of the ROSE data. Chapter III contains an examination of the transfer function between seafloor motion and data recorded by the MIT OBS. The response of the recordi ng system is determi ned and the coupl i ng of the OBS to the seafloor duri ng tests at two nearshore sites is analysed. Applying these results to the ROSE data, we conclude that the ground motion in the absence of the instrument can be adequately determi ned for at 1 east one of the MIT OBS deployed duri ng ROSE.Hypocentral parameters for 70 earthquakes, calculated for a n ass u m ê d 1 ate r a 11 y h 0 m 0 g e n e 0 u s vel 0 city s t r u c t u r e w h i c h was adapted from the results of several refraction surveys in the area, are presented in Chapter iv. Because of the large number of stations in the ROSE network, the epicentral 1 ocati ons, focal depths and source mechani sms are determi ned with a precision unprecedented in marine microseismic work.Relative to the assumed model, most horizontal errors are less than I1 km; vertical errors are somewhat larger. All epicenters are within the transform region of the Orozco Fracture Zone. About half of the epicenters define a narrow 1 i n e 0 f act i vi ty par a 11 e 1 to the s p rea din g d ire c t i ~ n and situated along a deep topographic trough which forms the northern boundary of the transform zone (region 1). Most well determined depths are very sha...

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Scalar- and planar-valued curve fitting using splines under tension

Cited by 220 publications

References 2 publications

Seismic imaging of upper crustal structure using travel times from the PASSCAL Ouachita Experiment

Seismic imaging of upper crustal structure using travel times from the PASSCAL Ouachita Experiment

Map showing mineral resource assessment for vein and replacement deposits of gold, silver, copper, lead, zinc, manganese, and tungsten in the Butte 1° x 2° quadrangle, Montana

Seismicity and structure of the Orozco transform fault from ocean bottom seismic observations

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