Spatial Point Process Theory Research Articles

Insights on the dip of fault zones in Southern California from modeling of seismicity with anisotropic point processes

Accurate models of fault zone geometry are important for scientific and hazard applications. While seismicity can provide high-resolution point measurements of fault geometry, extrapolating these measurements to volumes may involve making strong assumptions. This is particularly problematic in distributed fault zones, which are commonly observed in immature faulting regions. In this study, we focus on characterizing the dip of fault zones in Southern California with the goal of improving fault models. We introduce a novel technique from spatial point process theory to quantify the orientation of persistent surficial features in seismicity, even when embedded in wide shear zones. The technique makes relatively mild assumptions about fault geometry and is formulated with the goal of determining the dip of a fault zone at depth. The method is applied to 11 prominent seismicity regions in Southern California. Overall, the results compare favorably with the geometry models provided by the SCEC Community Fault Model and other focused regional studies. More specifically, we find evidence that the Southern San Andreas and San Jacinto fault zones are both northeast dipping at seismogenic depths at the length scales of 1.0–4.0 km. In addition, we find more limited evidence for some depth dependent variations in dip that suggest a listric geometry. The developed technique can provide an independent source of information from seismicity to augment existing fault geometry models.

Recent Co-occurring Expansion of Rubber Tree Plantations and Land Use/Land Cover Change in Luangnamtha District, Northern Laos

Monitoring land use/land cover change at various scales is of foremost importance for the management of natural resources and pivotal to achieve effective environmental governance. The purpose of this study was to classify land use/land cover and to quantify changes in land use/land cover in Luangnamtha district, northern Laos over the past two decades, using remote sensing and Geographic Information System technologies. We used Landsat 5 Thematic Mapper (TM) images from 2000, 2005, 2010 and Landsat 8 Operational Land Imager (OLI) images from 2017. A supervised classification was achieved by applying the maximum likelihood algorithm in the ENVI software. Five land cover classes, namely agriculture, forest, rubber tree, settlement and water were thus identified. The nature and extent of change detected was analyzed on the basis of the land use maps generated for years 2000, 2005, 2010 and 2017. We applied spatial point process theory to analyze spatial relationships between land use classes and with terrain covariables. The overall accuracy of our classifications were 86.8%, 89.3%, 90.4%, and 91.7% for the years 2000, 2005, 2010, and 2017, respectively and the Kappa coefficients were 0.76, 0.85, 0.85, and 0.89, respectively. The results of these classifications indicated that over the 2000 to 2017 period, settled areas increased by 2.35% (5,038 ha), water bodies increased very marginally (0.01% or 20 ha), but that rubber tree cover increased by as much as 7.60% (16,314 ha). During the same period, agricultural land decreased by 0.11% (224 ha) and the forested area shrunk by 9.84% (21,129 ha). Spatial analysis indicates that rubber tree plantations expanded from the lowest part of the landscape, in close spatial association with agricultural land, to increasingly higher locations where it most likely replaced forest. This study confirms that drivers such as government policies for permanent allocation of agricultural land poverty eradication, as well as foreign investments, had a major impact on the expansion of rubber tree plantation in Luangnamtha district from 2000 to 2017.

Likelihood based inference for partially observed renewal processes

This paper is concerned with inference for renewal processes on the real line that are observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point process theory to propose a Monte Carlo maximum likelihood estimator that takes into account the missing data. Its efficacy is assessed by means of a simulation study and the missing data reconstruction is illustrated on real data.

Microgeometry Modelling of Magnesium Alloy Polished Surfaces by Means of Cone-Based Manifolds

In this paper a new methology for surface microgeometry modelling is presented, taking the surface of a polished magnesium alloy as an example . The proposed method essentially is based on the usage of the mathematical concept of the continuous non-differentiable manifold composed of cones. The cones’ aperture, eccentricity, height and angular orientation are model parameters, as well as the cones spread over the modelled surface. The spread of cones might be of very different nature ranging from simple deterministic patterns to purely random distribution accordingly to the theory of spatial point processes. The statistical parameters estimated in the model are: Rp, Rv, Rt, Ra, Rq, Rskew, Rkurt, the roughness distribution histogram and the bearing curve. The geometrical parameters are: surface area, surface development, surface capacity and volume. All of the computational methods have been carefully examined from the perspective of use on discrete grids. The simulated surfaces have been compared with experimental results obtained with the used AFM technique on samples of the polished AZ31 magnesium alloy. The very high level of conformity achieved between the results from the modeled surface and the experimentally obtained results gives us a promising prognosis for further use.

Analysing the spatial patterns of erosion scars using point process theory at the coastal chalk cliff of Mesnil-Val, Normandy, northern France

Abstract. Over the last decade, many cliff erosion studies have focused on frequency-size statistics using inventories of sea cliff retreat sizes. By comparison, only a few paid attention to quantifying the spatial and temporal organisation of erosion scars over a cliff face. Yet, this spatial organisation carries essential information about the external processes and the environmental conditions that promote or initiate sea-cliff instabilities. In this article, we use summary statistics of spatial point process theory as a tool to examine the spatial and temporal pattern of a rockfall inventory recorded with repeated terrestrial laser scanning surveys at the chalk coastal cliff site of Mesnil-Val (Normandy, France). Results show that: (1) the spatial density of erosion scars is specifically conditioned alongshore by the distance to an engineered concrete groyne, with an exponential-like decreasing trend, and vertically focused both at wave breaker height and on strong lithological contrasts; (2) small erosion scars (10−3 to 10−2 m3) aggregate in clusters within a radius of 5 to 10 m, which suggests some sort of attraction or focused causative process, and disperse above this critical distance; (3) on the contrary, larger erosion scars (10−2 to 101 m3) tend to disperse above a radius of 1 to 5 m, possibly due to the spreading of successive failures across the cliff face; (4) large scars significantly occur albeit moderately, where previous large rockfalls have occurred during preceding winter; (5) this temporal trend is not apparent for small events. In conclusion, this study shows, with a worked example, how spatial point process summary statistics are a tool to test and quantify the significance of geomorphological observation organisation.

Analysis of Stochastic Radio Channels With Temporal Birth-Death Dynamics: A Marked Spatial Point Process Perspective

We employ the theory of spatial point processes to revisit and reinterpret a particular class of time-variant stochastic radio channel models. Common for all models in this class is that individual multipath components are emerging and vanishing in a temporal birth-death like manner, with the underlying stochastic birth-death mechanism governed by two facilitating assumptions. Well-known analytical properties of this class of channel models are reestablished by simple arguments and several new results are derived. The primary tool used to obtain these results is Campbell's Theorem which enables novel assessment of the autocorrelation functions of random processes used in the general channel model description. Under simplifying assumptions the channel transfer function is shown to be wide-sense stationary in both time and frequency (despite the birth-death behavior of the overall channel). The proof of this result is a consequence of the point process perspective, in particular by circumventing enumeration issues arising from the use of integer-indexed path components in traditional channel modeling approaches. The practical importance of being able to analytically characterize the birth-death channel models is clearly evidenced, e.g., by the fact that key parameters enter explicitly in measurable quantities such as the power-delay profile.

Characteristics of clustering extreme drought events in China during 1961–2010

Based on the Multi-Scale Standardized Precipitation Index (MSPI), extreme severe drought events in China during 1961–2010 were identified, and the seasonal, annual, and interdecadal variations of the clustering extreme drought events were investigated by using the spatial point process theory. It is found that severe droughts present a trend of gradual increase as a result of the significant increase and clustering tendency of severe droughts in autumn. The periodicity analysis of the clustering extreme droughts in different seasons suggests that there is a remarkable interdecadal change in the occurrence of clustering extreme droughts in winter. Meanwhile, it is revealed that the clustering extreme drought events exhibit greatly different annual mean spatial distributions during 1961–2010, with scattered and concentrated clustering zones alternating on the decadal timescale. Furthermore, it is found that the decadal-mean spatial distributions of extreme drought events in summer are correlated out of phase with those of the rainy bands over China in the past 50 years, and a good decadal persistence exists between the autumn and winter extreme droughts, implying a salient feature of consecutive autumn-winter droughts in this 50-yr period. Compared with other regions of China, Southwest China bears the most prominent characteristic of clustering extreme droughts.

Ecological information from spatial patterns of plants: insights from point process theory

Summary 1. This article reviews the application of some summary statistics from current theory of spatial point processes for extracting information from spatial patterns of plants. Theoretical measures and issues connected with their estimation are described. Results are illustrated in the context of specific ecological questions about spatial patterns of trees in two forests. 2. The pair correlation function, related to Ripley’s K function, provides a formal measure of the density of neighbouring plants and makes precise the general notion of a ‘plant’s-eye’ view of a community. The pair correlation function can also be used to describe spatial relationships of neighbouring plants with different qualitative properties, such as species identity and size class. 3. The mark correlation function can be used to describe the spatial relationships of quantitative measures (e.g. biomass). We discuss two types of correlation function for quantitative marks. Applying these functions to the distribution of biomass in a temperate forest, it is shown that the spatial pattern of biomass is uncoupled from the spatial pattern of plant locations. 4. The inhomogeneous pair correlation function enables first-order heterogeneity in the environment to be removed from second-order spatial statistics. We illustrate this for a tree species in a forest of high topographic heterogeneity and show that spatial aggregation remains after allowing for spatial variation in density. An alternative method, the master function, takes a weighted average of homogeneous pair correlation functions computed in subareas; when applied to the same data and compared with the former method, the spatial aggregations are smaller in size. 5. Synthesis. These spatial statistics, especially those derived from pair densities, will help ecologists to extract important ecological information from intricate spatially correlated plants in populations and communities.

Research on the validility of cluster delineation based on spatial point processes

On the basis of the two-dimensional Poisson process theory and spatial point process theory, we introduced the algorithm of cluster extraction which is based on k-th order distance, aiming at determining the valid range of the algorithm. We found that the ratio of cluster and cluster's densities and the number of data both have effect on the method. But the effect of the former much bigger than that of the latter. Furthermore, we introduced the concept of weight to extend the range of the simulated data, and gave the data different weights for delineating clusters, so that the range of this algorithm can be extended.

Modern Statistics for Spatial Point Processes*

Abstract. We summarize and discuss the current state of spatial point process theory and directions for future research, making an analogy with generalized linear models and random effect models, and illustrating the theory with various examples of applications. In particular, we consider Poisson, Gibbs and Cox process models, diagnostic tools and model checking, Markov chain Monte Carlo algorithms, computational methods for likelihood‐based inference, and quick non‐likelihood approaches to inference.