Splines under tension for gridding three-dimensional data

Brand, Hal R.; Frazer, Jack W.

doi:10.1021/ac00240a015

Cited by 4 publications

(6 citation statements)

References 2 publications

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“…that is, we calculate the traveltime perturbation Δ t i by integrating the slowness perturbations Δ s along the ray path L i ref in the unperturbed model. The slowness model is discretized by specifying the slowness on a 3‐D grid of nodes within a box enclosing the region of interest where the slowness between nodes is calculated using splines under tension (Brand & Frazer 1982).…”

Section: Methodsmentioning

confidence: 99%

P-wave velocity structure of the uppermost mantle beneath Hawaii from traveltime tomography

Tilmann

Benz

Okubo

2001

Geophysical Journal International

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SUMMARY We examine the P‐wave velocity structure beneath the island of Hawaii using P‐wave residuals from teleseismic earthquakes recorded by the Hawaiian Volcano Observatory seismic network. The station geometry and distribution of events makes it possible to image the velocity structure between ∼40 and 100 km depth with a lateral resolution of ∼15 km and a vertical resolution of ∼30 km. For depths between 40 and 80 km, P‐wave velocities are up to 5 per cent slower in a broad elongated region trending SE–NW that underlies the island between the two lines defined by the volcanic loci. No direct correlation between the magnitude of the lithospheric anomaly and the current level of volcanic activity is apparent, but the slow region is broadened at ∼19.8°N and narrow beneath Kilauea. In the case of the oceanic lithosphere beneath Hawaii, slow seismic velocities are likely to be related to magma transport from the top of the melting zone at the base of the lithosphere to the surface. Thermal modelling shows that the broad elongated low‐velocity zone cannot be explained in terms of conductive heating by one primary conduit per volcano but that more complicated melt pathways must exist.

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Section: Methodsmentioning

confidence: 99%

P-wave velocity structure of the uppermost mantle beneath Hawaii from traveltime tomography

Tilmann

Benz

Okubo

2001

Geophysical Journal International

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“…The number in parentheses is the total number of accepted estimates for that particular determination. 6 Excellent estimate, however, it is the mean of the only two estimates accepted in the entire set. Since these two estimates were from two adjacent analyses instead of from a single analysis the coresult rules rejected the mean.…”

Section: Methodsmentioning

confidence: 99%

“…A least-squares spline function is then fit to this new set of ordered pairs (5,6). This type of fit tends to follow the general Figure 4.…”

Section: Methodsmentioning

confidence: 99%

“…First, all the information which was in the set of ordered pairs, eq 4, is also in eq 5. In fact if one of the parameters in the least-squares spline fitting process is chosen properly, then E¡ = g{c¡) i = 1, 2.....N (6) This means that g goes through all the data points. Even if the parameter in the least-squares spline process is not chosen in this way, it will always by true that Ei » g(Ci) i = 1, 2.....N (7) The second thing to note is that g can be evaluated at any concentration value, not just at the C¡ values.…”

Section: Methodsmentioning

confidence: 99%

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Determination with ion selective electrodes in the low-level, non-Nernstian response region

Frazer¹,

Balaban²,

Brand³

et al. 1983

Anal. Chem.

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“…When T = 1, the tension reaches its maximum and the harmonic spline solution is obtained. The larger the value of the tension parameter, the smoother the result of the gridding [34]. For ocean bathymetric data, the tension factor is generally chosen to be between 0.32 and 0.4 [16].…”

Section: ) Multisource Data Griddingmentioning

confidence: 99%

Construction of High-Resolution Bathymetric Dataset for the Mariana Trench

Liu

Zhao

et al. 2019

IEEE Access

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Access to reliable and accurate bathymetric data is fundamental to many marine activities. This paper proposes a merge-normalization (MN) method that is suitable for multisource bathymetric data fusion in deep ocean areas, to solve the problem of difficult to integrate high-precision digital bathymetric model (DBM) for complex sources and various resolutions of global deep ocean bathymetric data. Then we apply it to the DBM construction of the Mariana Trench. The method combines multibeam, singlebeam, and electronic navigational chart data with Shuttle Radar Topography Mission (SRTM) dataset by using the workflow of merging and normalizing, which can fill the data gaps while preserving topographic details in high-resolution bathymetric data. Compared with the widely used General Bathymetric Chart of the Oceans (GEBCO) dataset, the Mariana Trench dataset constructed in this study demonstrated improved accuracy, resolution, and topographic detail, highlighting the value of the application of the method and of its development potential.

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Splines under tension for gridding three-dimensional data

Cited by 4 publications

References 2 publications

P-wave velocity structure of the uppermost mantle beneath Hawaii from traveltime tomography

P-wave velocity structure of the uppermost mantle beneath Hawaii from traveltime tomography

Determination with ion selective electrodes in the low-level, non-Nernstian response region

Construction of High-Resolution Bathymetric Dataset for the Mariana Trench

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