Smoothing Three-Dimensional Manifold Data, with Application to Tectonic Fault Detection
Three-dimensional manifold data arise in many contexts of geoscience, such as laser scanning, drilling surveys and seismic catalogs. They provide point measurements of complex surfaces, which cannot be fitted by common statistical techniques, like kriging interpolation and principal curves. This paper focuses on iterative methods of manifold smoothing based on local averaging and principal components; it shows their relationships and provides some methodological developments. In particular, it develops a kernel spline estimator and a data-driven method for selecting its smoothing coefficients. It also shows the ability of this approach to select the number of nearest neighbors and the optimal number of iterations in blurring-type smoothers. Extensive numerical applications to simulated and seismic data compare the performance of the discussed methods and check the efficacy of the proposed solutions.
KeywordsBandwidth selection Kernel splines Local averaging Principal surfaces New Madrid earthquakes Sliced scanning Stopping criteria
A sincere thank to the Editors and Reviewers for their useful comments.
- Biedermann S, Yang M (2015) Designs for selected nonlinear models. In: Dean A, Morris M, Stufken J, Bingham D (eds) Handbook of design and analysis of experiments. Chapman & Hall, London, pp 515–547Google Scholar
- Carreira-Perpiñán MÁ (2006) Fast nonparametric clustering with Gaussian blurring mean-shift. In: Proceedings of 23rd international conference on machine learning. Pittsburgh, pp 153–160Google Scholar
- Forte AM, Mitrovica JX, Moucha R, Simmons RA, Grand SP (2007) Descent of the ancient Farallon slab drives localized mantle flow below the New Madrid seismic zone. Geophys Res Lett 34(4):L04308. doi: 10.1029/2006GL027895
- Jordan TH (2014) Faults in focus: 20 years of earthquake science accomplishments. SECS: Southern California Earthquake CenterGoogle Scholar
- Ozertem U, Erdogmus D (2011) Locally defined principal curves and surfaces. J Mach Learn Res 12:1249–1286Google Scholar
- Park JH, Zhang Z, Zha H, Kasturi R (2004) Local smoothing for manifold learning. In: Proceedings of 2004 IEEE conference on computer vision and pattern recognition Vol 2. Washington, pp 452–459Google Scholar
- Wang W, Carreira-Perpiñán MÁ (2010) Manifold blurring mean shift algorithms for manifold denoising. In: Proceedings of 2010 IEEE conference on computer vision and pattern recognition. San Francisco, pp 1759–1766Google Scholar