Spatial Autocorrelation Techniques Research Articles

Suitability of 10 Hz vertical geophones for seismic noise array measurements based on frequency‐wavenumber and extended spatial autocorrelation analyses

ABSTRACTMicrozonation studies using ambient noise measurements constitute a promising way for seismic hazard evaluation in urban areas. Among the existing techniques, seismic noise array measurements have become a valuable tool for estimating Vs profiles and thus, the characteristics of a soil structure. Although methods based on analysis of seismic noise are simpler, cheaper and faster than borehole drilling and down‐hole or cross‐hole logs to derive shear‐wave velocity profiles, array deployment requires the use of several stations (broadband or short‐period sensors) that are not always available. In this paper, we have compared the results obtained by 10 Hz‐vertical‐geophone arrays with the results provided by 1 Hz‐sensor arrays. Two sites in the Bajo Segura Basin (SE Spain), with different soil characteristics, were chosen for array deployment. The comparison is carried out in terms of dispersion curves by using frequency‐wavenumber (f‐k) and extended spatial autocorrelation (ESAC) techniques. Both analyses show a good agreement using either 1 Hz sensors or 10 Hz geophones; moreover, they demonstrate that it is possible to extend the analysis in a frequency range much below the natural frequency of the geophones. The results of our study confirm the suitability of standard seismic refraction/reflection equipment also for ambient noise array measurements, which constitutes a cheaper and faster way for investigating soil characteristics.

Three-dimensional shear wave velocity imaging by ambient seismic noise tomography

3-D shear wave velocity images are of particular interest for engineering seismology. To obtain information about the local subsoil structure, we present a one-step inversion procedure based on the computation of high-frequency correlation functions between stations of a small-scale array deployed for recording ambient seismic noise. The calculation of Rayleigh wave phase velocities is based on the frequency-domain SPatial AutoCorrelation technique. Constitutively, a tomographic inversion of the traveltimes estimated for each frequency is performed, allowing the laterally varying 3-D surface wave velocity structure below the array to be retrieved. We test our technique by using simulations of seismic noise for a simple realistic site and by using real-world recordings from a small-scale array performed at the Nauen test site (Germany). The results imply that the cross-sections from passive seismic interferometry provide a clear image of the local structural heterogeneities and the shear wave velocities are satisfactorily reproduced. The velocity structure is also found to be in good agreement with the results of geoelectrical measurements, indicating the potential of the method to be easily applied for deriving the shallow 3-D velocity structure in urban areas and for monitoring purposes.

Characterization of Forested Landscapes from Remotely Sensed Data Using Fractals and Spatial Autocorrelation

The characterization of forested landscapes is frequently required in civil engineering practice. In this study, some spatial analysis techniques are presented that might be employed with Landsat TM data to analyze forest structure characteristics. A case study is presented wherein fractal dimensions (FDs), along with a simple spatial autocorrelation technique (Moran’sI), were related to stand density parameters of the Oakmulgee National Forest located in the southeastern United States (Alabama). The results indicate that when smaller trees do not dominate the landscape (<50%), forested areas can be differentiated according to breast sizes and thus important flood plain characteristics such as ratio of obstructed area to total area can be estimated from remotely sensed data using the studied indices. This would facilitate the estimation of hydraulic roughness coefficients for computation of flood profiles needed for bridge design. FD and Moran’sIremained fairly constant around the values of 2.7 and 0.9 (resp.) for samples with either greater than 50% saplings or less than 50% sawtimber and with ranges of 2.7–2.9 and 0.6–0.9 as the saplings decreased or the sawtimber increased. Those indices can also distinguish hardwood and softwood species facilitating forested landscapes mapping for preliminary environmental impact analysis.

Plant dispersal in the sub‐Antarctic inferred from anisotropic genetic structure

Climatic conditions and landscape features often strongly affect species' local distribution patterns, dispersal, reproduction and survival and may therefore have considerable impacts on species' fine-scale spatial genetic structure (SGS). In this study, we demonstrate the efficacy of combining fine-scale SGS analyses with isotropic and anisotropic spatial autocorrelation techniques to infer the impact of wind patterns on plant dispersal processes. We genotyped 1304 Azorella selago (Apiaceae) specimens, a wind-pollinated and wind-dispersed plant, from four populations distributed across sub-Antarctic Marion Island. SGS was variable with Sp values ranging from 0.001 to 0.014, suggesting notable variability in dispersal distance and wind velocities between sites. Nonetheless, the data supported previous hypotheses of a strong NW-SE gradient in wind strength across the island. Anisotropic autocorrelation analyses further suggested that dispersal is strongly directional, but varying between sites depending on the local prevailing winds. Despite the high frequency of gale-force winds on Marion Island, gene dispersal distance estimates (σ) were surprisingly low (<10 m), most probably because of a low pollen dispersal efficiency. An SGS approach in association with isotropic and anisotropic analyses provides a powerful means to assess the relative influence of abiotic factors on dispersal and allow inferences that would not be possible without this combined approach.

Improved Methods for Survey of Carabid Beetles (Coleoptera: Carabidae) Using Pitfall Trapping and Spatial Autocorrelation Techniques

Ground beetles (Coleoptera: Carabidae) inhabiting a peach orchard were collected using pitfall traps placed adjacent to plastic barriers that were perpendicular to each other and crossed each other at their midpoints. Each array of traps contained 5 traps with 1 at the midpoint of each barrier and the other 4 at the ends of each plastic barrier. The trap located at the center of each array captured about 40% of the total beetles trapped by each array, thus suggesting that a single trap located at the center of the array could be a more efficient means of sampling. Using spatial autocorrelation techniques, the range of spatial dependence for the two herbivorous carabids collected in this study - Harpalus tschiliensis Schauberger and Harpalus griseus Panzer - ranged from 136.7 - 210.3 m, whereas that of the predatory carabid Calathus halensi Schailer ranged from 330.1 - 412.4 m. Based upon our results, we suggest that pitfall traps used for monitoring or sampling carabid beetles be set no further than 210 m apart for herbivorous species and 412 m apart for carnivorous species.

Design Earthquake Ground Motion Prediction for Perth Metropolitan Area with Microtremor Measurements for Site Characterization

Perth is the largest city in Western Australia and home to three-quarters of the state's residents. In recent decades, there have been a lot of earthquake activities just east of Perth in an area known as the South-West Seismic Zone. Previous numerical results of site response analyses based on limited available geology information for PMA indicated that Perth Basin might amplify the bedrock motion by more than 10 times at some frequencies and at some sites. Hence, more detailed studies on site characterization and amplification are necessary. The microtremor method using spatial autocorrelation (SPAC) processing is a useful tool for gaining thickness and shear wave velocity (SWV) of sediments and has been adopted in many previous studies. In this study, the response spectrum of rock site corresponding to the 475-year return period for PMA is defined according to the probabilistic seismic hazard analysis (PSHA) based on the latest ground motion attenuation model of Southwest Western Australia. Site characterization in PMA is performed using two microtremor measurements, namely SPAC technique and H/V method. The clonal selection algorithm (CSA) is introduced to perform direct inversion of SPAC curves to determine the soil profiles of representative PMA sites investigated in this study. Using the simulated bedrock motion as input, the responses of the soil sites are estimated using numerical method based on the shear-wave velocity vs. depth profiles determined from the SPAC technique. The response spectrum of the earthquake ground motion on surface of each site is derived from the numerical results of the site response analysis, and compared with the respective design spectrum defined in the Australian Earthquake Loading Code. The comparison shows that the code spectra are conservative in the short period range, but may slightly underestimate the response spectrum at some long period range.

Differentiating geology and tectonics using a spatial autocorrelation technique for the hypsometric integral

Hypsometry is thought to be sensitive to tectonic uplift rates and lithology differences. In this study we calculated hypsometric integrals (HIs) using as topographic sources two digital elevation models of 10 and 90 m of pixel resolution in the Granada basin (SE of Spain). The HI spatial distributions do not show clear spatial patterns and do not correlate with basin parameters as mean elevation or relief amplitude. However, when exploratory spatial data analysis is applied to the data distributions through local indices of spatial autocorrelation, clear hot spots are visible that improve the geologic meaning of the HI. The distributions are robust and independent of the model resolution but are scale influenced. The application of this new method to the Granada basin shows a strong correlation between the main distribution of active normal faults in the basin and the clusters of high or low HI values obtained in our analysis. Clusters with high HI values define the uplifted footwalls of these faults and regions uplifted in relation with rollover anticlines or where epeirogenic uplift has not been counteracted by local extension. Once the method was adjusted in the Granada basin, we tested its applicability in an area of known contractive tectonic activity, central Otago, New Zealand, showing that the meaning of HI values is improved by using the autocorrelation techniques.

A study of near source effects in array-based (SPAC) microtremor surveys

Array-based methods for exploiting ambient seismic noise are receiving increasing attention in the literature, particularly for use in providing shear wave velocity profiles to assist with simulation of site-specific earthquake responses. Many of these microtremor methods—such as the spatial autocorrelation technique (SPAC)—operate under the fundamental assumption of plane wave propagation of surface waves. However, when there are significant microtremor sources in close proximity to an array, wave front curvature becomes significant, and the plane wave assumption becomes a tenuous one. This paper explains the use of a simplified geometry-based approach to examine the effect of source distance on SPAC spectra for hexagonal (six-station) and triangular (three-station) arrays. The results suggest that near source effects are generally minimal provided that most of the sources are located a distance equal to at least two array radii from the centre of the array, although this distance increases when attenuation is considered. Results of a field trial involving the deliberate use of near-sources in proximity to a hexagonal (six-station) array support the findings of the theoretical model. Near source effects generally result in the measured SPAC curve being offset to lower frequencies for wavenumbers less than the first secondary maximum of the SPAC curve (kr < 7.0; λ > 0.86R), resulting in underestimates of shear velocity values in the inverted layered earth model. For the field example, shear velocity was underestimated by up to approximately 17 per cent. Studies of near source effects in a number of theoretical source distributions for hexagonal arrays revealed that cyclic variation in the imaginary SPAC coefficients are indicative of near source effects, although field examples indicate this effect is less significant than the geometric modelling suggests. Modelling of linear microtremor source distributions (intended to represent traffic travelling along a road) resulted in less severe near source effects than full (360°) azimuthal source coverage—a result confirmed by field data. Model and field studies also indicated that in situations of a dominant, close microtremor source of limited azimuthal extent, use of a hexagonal (six-station) array significantly mitigates near source effects compared with a similarly aligned triangular (three-station) array.

Rayleigh wave dispersion curves from seismological and engineering-geotechnical methods: a comparison at the Bornheim test site (Germany)

Active and passive procedures for estimating the local seismic response from surface-wave measurements are compared for a test site in the Bornheim area (Germany), where independent geophysical and geological information is available. Recording was done using geophones, as well as seismometers, in various configurations. Five popular and standardized techniques were used for analysing the data: multichannel analysis of surface waves (MASW), the refraction microtremor technique (ReMi), the extended spatial autocorrelation technique (ESAC) and frequency–wavenumber analysis (beam-forming and maximum likelihood methods). The resulting surface wave dispersion curves are largely consistent, but differ in their respective low-frequency ranges due to the resolving capabilities of the respective acquisition geometries. Two joint inversions of dispersion and H/V curves, one for the lower frequency range (2.3–9.2 Hz) and the other for the complete range (2.3–45 Hz) of the dispersion curves resulted in fairly similar S-wave profiles, but increasing the frequency range allowed better estimates for the lower velocities at shallow depths. The results also compare well with borehole information. The site responses obtained from the two S-wave profiles are very similar, even at higher frequencies. The use of combined procedures (geotechnical-engineering and seismological) allows a high quality estimation of the S-wave velocity structure to be obtained, both at shallow and large depth. However, if a combined approach is not possible, for site response estimation at sites with sedimentary cover thicker than 30 to 50 m and where knowledge of the average S-wave velocity is more important than higher resolution estimates at shallower depths, the use of passive seismological 2D arrays is strongly recommended.

Assessing the reliability of the modified three-component spatial autocorrelation technique

SUMMARY Analysis of seismic ambient vibrations is becoming a widespread approach to estimate subsurface shear wave velocity profiles. However, the common restriction to vertical component wavefield data does not allow investigations of Love wave dispersion and the partitioning between Rayleigh and Love waves. In this study we extend the modified spatial autocorrelation technique (MSPAC) to three-component analysis (3c-MSPAC). By determination of Love wave dispersion curves, this technique provides additional information for the determination of shear wave velocity–depth profiles. Furthermore, the relative fraction of Rayleigh waves in the total portion of surface waves on the horizontal components is estimated. Tests of the 3c-MSPAC method are presented using synthetic ambient vibration waveform data. Different types of surface waves are simulated as well as different modes. In addition, different spatial distributions of sources are used. We obtain Rayleigh and Love wave dispersion curves for broad frequency bands in agreement with the models used for waveform simulation. The same applies for the relative fraction of Rayleigh waves. Dispersion curves are observed at lower frequencies for Love waves than for Rayleigh waves. While 3c-MSPAC has clear advantages for determination of Love waves velocities, 3c-MSPAC and conventional vertical frequency–wavenumber analysis complement each other in estimating the Rayleigh wave dispersion characteristics. Inversions of the dispersion curves for the shear wave velocity–depth profile show that the use of Love wave velocities confirms the results derived from Rayleigh wave velocities. In the presence of higher mode surface waves, Love waves even can improve results. Application of 3c-MSPAC to ambient vibration data recorded during field measurements (Pulheim, Germany) show dominance of Love waves in the wavefield. Existing shear wave profiles for this site are consistent with models obtained from inversion of Rayleigh and Love wave dispersion curves.

Direct estimation of the Rayleigh wave phase velocity in microtremors

We present a new estimation technique using a circular array for the Rayleigh wave phase velocity in microtremors. This technique allows us to employ more flexible sensor arrangements than that of Aki's spatial autocorrelation(SPAC) technique. One of the features is that the array output is represented by simultaneous equations consisting of complex coherence functions(CCFs). A CCF consists of two components:the Bessel function J0(r/c)(ω:angular frequency, r:radius, c:phase velocity) and an error term that varies with the azimuth of the sources. An analysis of the SPAC operation has demonstrated that the azimuthal averaging of the CCFs reduces the error term, and the average value can be approximated to J0(r/c). This result suggests the phase velocity can be determined by extracting J0(r/c) from the CCFs. Therefore, we tried to directly estimate J0(r/c) without the azimuthal averaging and developed a solution method referred to as the direct estimation method(DEM).

Regional and local factors in attenuation modelling: Hong Kong case study

Seismic attenuation behaviour is controlled by a large number of wave modification mechanisms. The characteristics of some of these mechanisms are specific to a local area, whilst the remainder can be generalised to the entire seismic region. Factors representing these mechanisms are often not resolved. A new attenuation modelling approach is demonstrated in this paper (using Hong Kong as a case study), to evaluate individual regional and local wave modification factors. Shear wave velocity (SWV) information for the four prevalent geological formations found in Hong Kong was first obtained: (a) at shallow depths from instrumented boreholes; (b) at depths of up to 100–200 m from measurements using the Microtremor SPatial Auto-Correlation (SPAC) technique; (c) at depths of up to 1.5 km from the monitoring of quarry blasts; and (d) at depths from 1.5 to 8 km in the hard basement rock layers from results of seismological refraction surveys. The upper-crust amplification factor calculated from the four modelled rock SWV profiles was then combined with predicted attenuation parameters to determine the upper-crust modification factor (filter function) incorporating the local wave modification characteristics associated with Hong Kong geological formations. Such functions may then be combined with the regional attenuation characteristics in that part of the South China region. A seismic attenuation model was developed by combining the upper-crust modification factor with the regional source function of intra-plate earthquakes, based on stochastic simulations. The ground shaking model developed from the presented methodology is supported by the comparison with macro-seismic data of seven historical earthquake events affecting Hong Kong.

Examining Lacunarity Approaches in Comparison with Fractal and Spatial Autocorrelation Techniques for Urban Mapping

The conventional spectral-based classification techniques have often been criticized due to the lack of consideration of images’ spatial properties. This study evaluates and compares two lacunarity methods, fractal triangular prism, spatial autocorrelation, and original spectral band approaches in classifying urban images. Results from this study show that the traditional spectral-based classification approach is inappropriate in classifying urban categories from highresolution data. The fractal triangular prism approach was also found to be ineffective in classifying urban features. Spatial autocorrelation was more accurate than the fractal approach. The overall accuracies in this study for the fractal, conventional spectral, spatial autocorrelation, lacunarity binary, and lacunarity gray-scale approaches were 52 percent, 55 percent, 78 percent, 81 percent, and 92 percent, respectively. These findings suggest that the lacunarity approaches are far more effective than the other approaches tested and can be used to drastically improve urban classification accuracy.

Wavelets for Urban Spatial Feature Discrimination

Traditional image processing techniques have proven inadequate for urban mapping using high spatial resolution remotesensing images. This study examined and evaluated wavelet transforms for urban texture analysis and image classification using high spatial resolution ATLAS imagery. For the purpose of comparison and to evaluate the effectiveness of the wavelet approaches, two different fractal approaches (isarithm and triangular prism), spatial autocorrelation (Moran’s I and Geary’s C), and spatial co-occurrence matrix of the selected urban classes were examined using 65 � 65, 33 � 33, and 17 � 17 samples with a pixel size of 2.5 m. Results from this study suggest that a multi-band and multi-level wavelet approach can be used to drastically increase the classification accuracy. The fractal techniques did not provide satisfactory classification accuracy. Spatial autocorrelation and spatial co-occurrence techniques were found to be relatively effective when compared to the fractal approaches. It can be concluded that the wavelet transform approach is the most accurate of all four approaches.

Resolving a velocity inversion at the geotechnical scale using the microtremor (passive seismic) survey method

High levels of ambient noise and safety factors often limit the use of "active-source" seismic methods for geotechnical investigations in urban environments. As an alternative, shear-wave velocity-depth profiles can be obtained by treating the background microtremor wave field as a stochastic process, rather than adopting the traditional approach of calculating velocity based on ray path geometry from a known source. A recent field test in Melbourne demonstrates the ability of the microtremor method, using only Rayleigh waves, to resolve a velocity inversion resulting from the presence of a hard, 12 m thick basalt flow overlying 25 m of softer alluvial sediments and weathered mudstone. Normally the presence of the weaker underlying sediments would lead to an ambiguous or incorrect interpretation with conventional seismic refraction methods. However, this layer of sediments is resolved by the microtremor method, and its inclusion is required in one-dimensional layered-earth modelling in order to reproduce the Rayleigh-wave coherency spectra computed from observed seismic noise records.Nearby borehole data provided both a guide for interpretation and a confirmation of the usefulness of the passive Rayleigh-wave microtremor method. Sensitivity analyses of resolvable modelling parameters demonstrate that estimates of shear velocities and layer thicknesses are accurate to within approximately 10% to 20% using the spatial autocorrelation (SPAC) technique. Improved accuracy can be obtained by constraining shear velocities and/or layer thicknesses using independent site knowledge. Although there exists potential for ambiguity due to velocity-thickness equivalence, the microtremor method has significant potential as a site investigation tool in situations where the use of traditional seismic methods is limited.

New insights from fine‐scale spatial genetic structure analyses in plant populations

Many empirical studies have assessed fine-scale spatial genetic structure (SGS), i.e. the nonrandom spatial distribution of genotypes, within plant populations using genetic markers and spatial autocorrelation techniques. These studies mostly provided qualitative descriptions of SGS, rendering quantitative comparisons among studies difficult. The theory of isolation by distance can predict the pattern of SGS under limited gene dispersal, suggesting new approaches, based on the relationship between pairwise relatedness coefficients and the spatial distance between individuals, to quantify SGS and infer gene dispersal parameters. Here we review the theory underlying such methods and discuss issues about their application to plant populations, such as the choice of the relatedness statistics, the sampling scheme to adopt, the procedure to test SGS, and the interpretation of spatial autocorrelograms. We propose to quantify SGS by an 'Sp' statistic primarily dependent upon the rate of decrease of pairwise kinship coefficients between individuals with the logarithm of the distance in two dimensions. Under certain conditions, this statistic estimates the reciprocal of the neighbourhood size. Reanalysing data from, mostly, published studies, the Sp statistic was assessed for 47 plant species. It was found to be significantly related to the mating system (higher in selfing species) and to the life form (higher in herbs than trees), as well as to the population density (higher under low density). We discuss the necessity for comparing SGS with direct estimates of gene dispersal distances, and show how the approach presented can be extended to assess (i) the level of biparental inbreeding, and (ii) the kurtosis of the gene dispersal distribution.

Planes, Trains, and Automobiles: The Impact of Traffic Noise on House Prices

Because of large planned infrastructural projects like expansion of the main airport and construction of high-speed railways, noise nuisance has become a national social topic in the Netherlands. Moreover, according to EU-guidelines, determination and enforcement of differentiated noise limits will be delegated from national to local governments in the near future. The value of noise has never been this important. In this paper, we estimate the non-linear impact of traffic noise on property prices. The used data set is very extensive; over 100,000 sales transactions are studied, with many individual property characteristics, combined with noise levels for 2 million small 100 by 100 m areas. We use spatial autocorrelation techniques to overcome the regular problems of traditional NIMBY-analysis performed by hedonic regression. In a rising market, we find that the impact of traffic noise ranges to 12 percent, with an average of about 5 percent. The discount varies across sub-markets, and is a non-linear function of the noise level.

Spatial analysis of genetic diversity as a tool for plant conservation

Development of suitable approaches to the analysis of genetic diversity in a spatial context, where factors such as pollination, seed dispersal, breeding system, habitat heterogeneity and human influence are appropriately integrated, can provide new insights in the understanding of the mechanisms of maintenance and dynamics of populations. In this sense, it is important to recognise that patterns and processes may take place at different scales at the same time, and that the scales of a study must be chosen in accordance with the objectives pursued. Apart from conventional approaches to genetic structure, spatial autocorrelation and related techniques, such as Mantel test, correlograms, Mantel correlograms, join-counts, variograms and point pattern analysis, can detect and characterise the existence of spatial genetic structures and lead the way to discussing the environmental and biological factors responsible for them. An alternative way of including spatial variability in modelling approaches that deal with genetic patterns or processes is through the use of constrained ordinations. Although scarcely used at present, these methodologies have great applicability in conservation biology and can lead a way to an effective integration of genetic, demographic and ecological perspectives.

Fractal approaches in texture analysis and classification of remotely sensed data: Comparisons with spatial autocorrelation techniques and simple descriptive statistics

There has been growing interest in the application of fractal geometry to observe spatial complexity of natural features at different scales. This study utilized three different fractal approaches--isarithm, triangular prism, and variogram--to characterize texture features of urban land-cover classes in high-resolution image data. For comparison purpose and to better evaluate the efficiency of fractal approaches in image classification, spatial autocorrelation techniques (Moran's I and Geary's C ), simple standard deviation, and mean of the selected features were also examined in this study. The discriminant analysis was carried out to discriminate between classes of urban land cover on the basis of texture measures (variables). This study demonstrated that the spatial autocorrelation approach was superior to the fractal approaches. In some cases, simple standard deviation and mean value of the samples gave better accuracy than all or some of the fractal approaches. The results obtained from this analysis suggest that fractal-based textural discrimination methods are applicable but these methods alone may be ineffective in extracting texture features or identifying different land-use and land-cover classes in remotely sensed images.

An Evaluation of Four Different Wavelet Decomposition Procedures for Spatial Feature Discrimination in Urban Areas

Texture or spatial arrangement of neighborhood objects and features plays an important role in the human visual system for pattern recognition and image classification. The traditional spectral–based image processing techniques have proven inadequate for urban land use and land cover mapping from images acquired by the current generation of fine–resolution satellites. This is because of the high frequency spatial arrangements or complex nature of urban features. There is a need for an effective algorithm to digitally classify urban land use and land cover categories using high–resolution image data. Recent studies using wavelet transforms for texture analysis have generally reported better accuracy. Based on a high–resolution ATLAS image, this study illustrates four different wavelet decomposition procedures – the standard, horizontal, vertical, and diagonal decompositions – for urban land use and land cover feature extraction with the use of 33×33 pixel samples. The standard decomposition approach was found to be the most efficient approach in urban texture analysis and classification. For comparison purposes and to better evaluate the accuracy of wavelet approaches in image classification, spatial autocorrelation techniques (Moran’s I and Geary’s C) and the spatial co–occurrence matrix method were also examined. The results suggest that the wavelet transform approach is superior to all other approaches.