MergeBathy (2015)

Zambo, Samantha; Holland, Todd; Plant, Nathaniel G.; Elmore, Paul; Avera, Will; Bourgeois, Brian S.; Perkins, A. Louise; Lalejini, D.

doi:10.1016/j.softx.2018.05.005

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…Appendix also substantiates the trigonometric construction arguments for the effect of seafloor slope on bathymetric uncertainty given in Zambo et al . [].…”

Section: Discussionmentioning

confidence: 99%

“…It is more computationally efficient to approximate

θ_{j} ≅ θ_{i} = arctan (|, (|||, \nabla {\overset{z}{true}}_{i}))

, where

{\overset{z}{true}}_{i}

is the gridded output of the estimated depth. Thus, to account for bottom slope influence on bathymetric uncertainty estimation, Zambo et al [] proposes that equation be augmented by adding

σ_{j H}^{2} \tan^{2} θ_{i}

as an additional variance term so that

σ_{i j}^{2} = σ_{j V}^{2} (|, \begin{matrix} 1 + {([]|, \begin{matrix} \frac{δ_{i j} + S_{H} σ_{j H}}{Δ_{min}} \end{matrix})}^{α} \end{matrix}) + σ_{j H}^{2} {tan}^{2} θ_{i} .

…”

Section: Obtaining Comparable Estimatesmentioning

confidence: 99%

See 1 more Smart Citation

Achieving comparable uncertainty estimates with Kalman filters or linear smoothers for bathymetry data

Bourgeois

Elmore

Avera

et al. 2016

Geochem Geophys Geosyst

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This paper examines and contrasts two estimation methods, Kalman filtering and linear smoothing, for creating interpolated data products from bathymetry measurements. Using targeted examples, we demonstrate previously obscured behavior showing the dependence of linear smoothers on the spatial arrangement of the measurements, yielding markedly different estimation results than the Kalman filter. For bathymetry data, we have modified the variance estimates from both the Kalman filter and linear smoothers to obtain comparable estimators for dense data. These comparable estimators produce uncertainty estimates that have statistically insignificant differences via hypothesis testing. Achieving comparable estimation is accomplished by applying the “propagated uncertainty” concept and a numerical realization of Tobler's principle to the measurement data prior to the computation of the estimate. We show new mathematical derivations for these modifications. In addition, we show test results with (a) synthetic data and (b) gridded bathymetry in the area of the Scripps and La Jolla Canyons. Our tenfold cross‐validation for case (b) shows that the modified equations create comparable uncertainty for both gridding algorithms with null hypothesis acceptance rates of greater than 99.95% of the data points. In contrast, bilinear interpolation has 10 times the amount of rejection. We then discuss how the uncertainty estimators are, in principle, applicable to interpolate geophysical data other than bathymetry.

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“…Appendix also substantiates the trigonometric construction arguments for the effect of seafloor slope on bathymetric uncertainty given in Zambo et al . [].…”

Section: Discussionmentioning

confidence: 99%

“…It is more computationally efficient to approximate

θ_{j} ≅ θ_{i} = arctan (|, (|||, \nabla {\overset{z}{true}}_{i}))

, where

{\overset{z}{true}}_{i}

is the gridded output of the estimated depth. Thus, to account for bottom slope influence on bathymetric uncertainty estimation, Zambo et al [] proposes that equation be augmented by adding

σ_{j H}^{2} \tan^{2} θ_{i}

as an additional variance term so that

σ_{i j}^{2} = σ_{j V}^{2} (|, \begin{matrix} 1 + {([]|, \begin{matrix} \frac{δ_{i j} + S_{H} σ_{j H}}{Δ_{min}} \end{matrix})}^{α} \end{matrix}) + σ_{j H}^{2} {tan}^{2} θ_{i} .

…”

Section: Obtaining Comparable Estimatesmentioning

confidence: 99%

Achieving comparable uncertainty estimates with Kalman filters or linear smoothers for bathymetry data

Bourgeois

Elmore

Avera

et al. 2016

Geochem Geophys Geosyst

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show abstract

“…After interpolation along the central fault strike of Longmenshan fault and using the nearest neighbor algorithm to calculate the weighted average of grid points, it is found that stress drop estimates largely constant within the upper 9 km and show a sharp increase at 10km from 3 MPa to 10 MPa. After Delaunay triangulations interpolation [50][51][52][53] of the whole area, the data results show that the high stress drop events are concentrated in the depth range of 20-24km. Even though our study regions in LMS host some of the deepest seismicity in Sichuan, observations of stress drop as a function of depth show considerable variability and the systematic variation of stress drop with depth is not particularly obvious.…”

Section: Spatial Variation Of Stress Dropsmentioning

confidence: 99%

The Small and Moderate Earthquake Parameters Training Catalog on the Main Faults in Sichuan, China

Wu,

Li,

et al. 2024

Preprint

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Numerous investigations have suggested that seismic source parameters and properties of the surrounding medium harbor valuable information regarding alterations in stress fields and medium properties at the focal depth. Monitoring the spatial and temporal evolution of these parameters can yield insights into variations in stress fields or medium properties within the seismogenic zone, offering a critical avenue to overcome the Earth's inaccessible nature. In recent years, modern seismic parameters such as seismic moment, focal mechanism solution, source stress drop, corner frequency, radiated seismic energy, rupture radius, and apparent stress have been increasingly used to characterize source characteristics. The Sichuan region is situated on the southeastern edge of the Qinghai-Tibet Plateau and is known for its strong eastward extrusion and structural deformation. The main fault zones in the area include the Xianshuihe Fault, Anninghe Zemuhe Fault, and Longmenshan Fault. This paper estimates source parameters of small to medium-sized earthquakes (ML 1.5-5.2) in the main fault zones and adjacent areas in Sichuan. A total of 4,310 earthquake stress drop measurements from 2019 to 2023 were analyzed to create a stress distribution image along the fault. This earthquake parameters training catalog provides insight into how coseismic stresses change and their relationship with other geophysical factors, as well as their spatial and temporal evolution.

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“…A technique that straddles both camps is the cube algorithm (Calder and Mayer, 2003), which is designed to compute the best estimate of depth at any given point in the area of interest, taking into account measurement uncertainty, which is often repeated over a regular grid to reconstruct the measurand. Modifications of the cube algorithm for sparse data have also been proposed (Bourgeois et al, 2016;Zambo et al, 2015). The cube algorithm has become a widely accepted approach for bathymetric data processing, being incorporated into a large majority of the software packages used for this purpose.…”

Section: Introductionmentioning

confidence: 99%