Geographical information science

Abstract. Research papers at conferences such as EGIS and the International Symposia on Spatial Data Handling address a set of intellectual and scientific questions which go well beyond the limited technical capabilities of current technology in geographical information systems. This paper reviews the topics which might be included in a science of geographical information. Research on these fundamental issues is a better prospect for long-term survival and acceptance in the academy than the development of technical capabilities. This paper reviews the current state of research in a series of key areas and speculates on why progress has been so uneven. The final section of the paper looks to the future and to new areas of significant potential in this area of research.     

The continuation inverse problem revisited

The non-uniqueness of the continuation of a finite collection of harmonic potential field data to a level surface in the source-free region forces its treatment as an inverse problem. A formalism is proposed for the construction of continuation functions which are extremal by various measures. The problem is cast in such a form that the inverse problem solution is the potential function on the lowest horizontal surface above all sources, serving as the boundary function for the Dirichlet problem in the upper half-plane. The desired continuation, at the higher level of interest, must then be in the range of the upward continuation operator acting on this boundary function, rather than being allowed the full freedom of itself being part of a Dirichlet problem boundary function. Extremal solutions minimize non-linear functionals of the continuation function, which are re-expressed as different functionals of the boundary function. A crux of the method is that there is no essential distinction between the upward and downward continuation inverse problems to levels above or below data locations. Casting the optimization as a Lagrange multiplier problem leads to an integral equation for the boundary function, which is readily solved in the Fourier domain for a certain class of functionals. The desired extremal continuation is then given by upward continuation. It is found that for some functionals, application of the Lagrange multiplier theorem requires a further restriction on the set of allowable boundary functions: bandlimitedness is a natural choice for the continuation problem. With this imposition, the theory is developed in detail for semi-norm functionals penalizing departure from a constant potential, in the 2-norm and Sobelev norm senses, and illustrated by application for a small synthetic Deep Tow magnetic field data set.     

Split-step complex Padé-Fourier depth migration

We present a split-step complex Padé-Fourier migration method based on the one-way wave equation. The downward-continuation operator is split into two downward-continuation operators: one operator is a phase-shift operator and the other operator is a finite-difference operator. A complex treatment of the propagation operator is applied to mitigate inaccuracies and instabilities due to evanescent waves. It produces high-quality images of complex structures with fewer numerical artefacts than those obtained using a real approximation of a square-root operator in the one-way wave equation. Tests on zero-offset data from the SEG/EAGE salt data show that the method improves the image quality at the cost of an additional 10 per cent computational time compared to the conventional Fourier finite-difference method.     

珠江口伶仃洋海平面变化趋势研究

根据珠江口伶仃洋三灶,赤湾,香港三个站的验潮记录,应用傅氏变换方法对月均潮序列先做离散傅氏变换,并将周期小于４ａ的波动幅设为零,再进行反傅氏变换,以消除小于４ａ的周期波动对确定海平面变化趋势的影响,最后由低通序列一元线性回归分析确定穆江口各站的海平面变化趋势。     

Automated landslide mapping using spectral analysis and high-resolution topographic data: Puget Sound lowlands, Washington, and Portland Hills, Oregon

Landslide inventory maps are necessary for assessing landslide hazards and addressing the role slope stability plays in landscape evolution over geologic timescales. However, landslide inventory maps produced with traditional methods — aerial photograph interpretation, topographic map analysis, and field inspection — are often subjective and incomplete. The increasing availability of high-resolution topographic data acquired via airborne Light Detection and Ranging (LiDAR) over broad swaths of terrain invites new, automated landslide mapping procedures. We present two methods of spectral analysis that utilize LiDAR-derived digital elevation models of the Puget Sound lowlands, Washington, and the Tualatin Mountains, Oregon, to quantify and automatically map the topographic signatures of deep-seated landslides. Power spectra produced using the two-dimensional discrete Fourier transform and the two-dimensional continuous wavelet transform identify the characteristic spatial frequencies of deep-seated landslide morphologic features such as hummocky topography, scarps, and displaced blocks of material. Spatial patterns in the amount of spectral power concentrated in these characteristic frequency bands highlight past slope instabilities and allow the delineation of landslide terrain. When calibrated by comparison with detailed, independently compiled landslide inventory maps, our algorithms correctly classify an average of 82% of the terrain in our five study areas. Spectral analysis also allows the creation of dominant wavelength maps, which prove useful in analyzing meter-scale topographic expressions of landslide mechanics, past landslide activity, and landslide-modifying geomorphic processes. These results suggest that our automated landslide mapping methods can create accurate landslide maps and serve as effective, objective, and efficient tools for digital terrain analysis.     

基于形态学及傅里叶分析对两种南极冰鱼耳石外型的研究

根据2014年3—4月以及2015年4—9月在南设得兰群岛以及南乔治亚群岛周边水域采集的裘氏鳄头冰鱼(Champsocephalus gunnari)及雪冰(Chionobathyscus dewitti)样本,对其耳石进行5种基础形态参数测量并转换为7种形态学参数,比较分析了两种冰鱼间的耳石形态学差异,再利用傅里叶分析法选取两种耳石的77个傅里叶系数进行判别。结果表明,两种冰鱼耳石长、高、周长、面积及质量均与体长呈显著的幂指数关系(P0.01)。由形态指标分析可知,裘氏鳄头冰鱼较雪冰耳石环率更低,即更趋近于圆,更为规则,且耳石厚度上略薄。两者各项形态参数间均存在显著性差异(P0.01)。对耳石77个傅里叶谐值进行主成分分析,其中前20个主成分解释总变异的82.491%,两种冰鱼的因子分布图上重叠量较少,可见区分度较好,判别分析选取了其中的6个傅里叶值建立了判别函数,总体判别率为96.15%。总体而言,可利用耳石外型对两种冰鱼进行种类判别,傅里叶分析更为直观清晰且较为准确。本研究可为南极冰鱼耳石形态学研究提供基础数据,并就其种类鉴别提供备选方法。     

Spectral estimation on a sphere in geophysics and cosmology

We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are considered: (i) the spherical analogue of the one-dimensional (1-D) periodogram, (ii) the maximum-likelihood method and (iii) a spherical analogue of the 1-D multitaper method. The periodogram exhibits strong spectral leakage, especially for small regions of area   A ≪ 4π  , and is generally unsuitable for spherical spectral analysis applications, just as it is in 1-D. The maximum-likelihood method is particularly useful in the case of nearly-whole-sphere coverage,   A ≈ 4π  , and has been widely used in cosmology to estimate the spectrum of the cosmic microwave background radiation from spacecraft observations. The spherical multitaper method affords easy control over the fundamental trade-off between spectral resolution and variance, and is easily implemented regardless of the region size, requiring neither non-linear iteration nor large-scale matrix inversion. As a result, the method is ideally suited for most applications in geophysics, geodesy or planetary science, where the objective is to obtain a spatially localized estimate of the spectrum of a signal from noisy data within a pre-selected and typically small region.