Fractal Correlation Research Articles

Detecting fractal power-law long-range dependence in pre-sliced cooked pork ham surface intensity patterns using Detrended Fluctuation Analysis

The visual texture of pork ham slices reveals information about the different qualities and perceived image heterogeneity, which is encapsulated as spatial variations in geometry and spectral characteristics. Detrended Fluctuation Analysis (DFA) detects long-range correlations in nonstationary spatial sequences, by a self-similarity scaling exponent alpha. In the current work, the aim is to investigate the usefulness of alpha, using different colour channels (R, G, B, L*, a*, b*, H, S, V, and Grey), as a quantitative descriptor of visual texture in sliced ham surface patterns for the detection of long-range correlations in unidimensional spatial series of greyscale intensity pixel values at 0 degrees , 30 degrees , 45 degrees , 60 degrees , and 90 degrees rotations. Images were acquired from three qualities of pre-sliced pork ham, typically consumed in Ireland (200 slices per quality). Results indicated that the DFA approach can be used to characterize and quantify the textural appearance of the three ham qualities, for different image orientations, with a global scaling exponent. The spatial series extracted from the ham images display long-range dependence, indicating an average behaviour around 1/f-noise. Results indicate that alpha has a universal character in quantifying the visual texture of ham surface intensity patterns, with no considerable crossovers that alter the behaviour of the fluctuations. Fractal correlation properties can thus be a useful metric for capturing information embedded in the visual texture of hams.

Fractal correlation of heart rate variability in obese children

Background The loss of variability and fractal properties in the heart rate is related to greater morbidity and mortality rates. Objective The aim of the present study was to analyze heart rate dynamics in obese children by measuring short and long-term fractal exponents and heart rate variability (HRV) indices. Materials and methods 112 male and female children aged 8 to 12 years were divided into two groups based on body mass index: obese ( n = 51) and normal weight range ( n = 61). Heart rate was monitored beat-to-beat in the dorsal decubitus position for 20 min, analyzing the low frequency (LF) and high frequency (HF) spectral indices in normalized units and ms² as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). The non-paired Student's t-test and Mann–Whitney test were used for the statistical analysis, with the level of significance set at P ≤ 0.05. Results The following were lower in the obese children: alpha-1 exponent value (0.930 ± 0.14 vs. 0.992 ± 0.11; P = 0.012), LF index (219.0 vs. 361.0; P = 0.001) and HF index (175.0 vs. 227.0; P = 0.019) in ms 2. No significant differences between groups were found for the alpha-2 exponent, LF and HF indices in normalized units or LF/HF ratio. Conclusion The obese children exhibited a reduction in short-term fractal correlation properties in heart frequency dynamics associated to a reduction in both sympathetic and parasympathetic activities, thereby demonstrating a need for early treatment for these children in order to avoid future complications.

Heart Rate Nonlinear Dynamics During Sudden Hypoxia at 8230 m Simulated Altitude

Acute hypobaric hypoxia is associated with autonomic changes that bring a global reduction of linear heart rate variability (HRV). Although changes in nonlinear HRV can be associated with physiologic stress and are relevant predictors of fatal arrhythmias in ischemic heart disease, to what extent these components vary in sudden hypobaric hypoxia is not known. Twelve military pilots were supplemented with increasing concentrations of oxygen during decompression to 8230 m in a hypobaric chamber. Linear and nonlinear HRV was evaluated at 8230 m altitude before, during, and after oxygen flow deprivation. Linear HRV was assessed through traditional time-domain and frequency-domain analysis. Nonlinear HRV was quantified through the short-term fractal correlation exponent alpha (alphas) and the Sample Entropy index (SampEn). Hypoxia was related to a decrease in linear HRV indexes at all frequency levels. A non-significant decrease in alphas (basal, 1.39 +/- 0.07; hypoxia, 1.11 +/- 0.13; recovery, 1.41 +/- 0.05; P = .054) and a significant increase in SampEn (basal, 1.07 +/- 0.11; hypoxia, 1.45 +/- 0.12; recovery, 1.43 +/- 0.09; P = .018) were detected. The observed pattern of diminished linear HRV and increased nonlinear HRV is similar to that seen in subjects undergoing heavy exercise or in patients with ischemic heart disease at high risk for ventricular fibrillation.

Arrhythmic Rats after SCN Lesions and Constant Light Differ in Short Time Scale Regulation of Locomotor Activity

Circadian rhythm disruption (i.e., arrhythmicity) in motor activity is an abnormal behavioral pattern. In rats, it can be caused by the lesion of the hypothalamic suprachiasmatic nucleus (SCN) and by prolonged exposure to constant light (LL). We carried out a comparative study of these arrhythmic phenotypes to assess the role of the SCN in the regulation of the motor output beyond circadian rhythmicity. Motor activity series were studied in rats that had become arrhythmic as a result of 1) LL exposure at 2 light intensities: 300 lux (LL(300)) and 1.3 lux (LL(1.3)), and 2) SCN lesion (SCNx). The Fourier spectra, the fractal Hurst coefficient (H) from the autocorrelation function, and the beta slope from the power spectral density were calculated in data sections at baseline, when the rats were still rhythmic, and later at stages with undetectable circadian rhythms. In the LL(300) group, high power content was detected at frequencies of 8 to 4 h (i.e., ultradian). Lower power content for these harmonics was found in the LL(1.3) group, whereas no dominant harmonics appeared in the SCNx group. Independently of the manifestation of circadian rhythm, H values were higher and more sustained in time in rats exposed to LL( 300) but gradually decreased in rats exposed to LL(1.3). Fractal correlation was found in control DD group but was absent in the SCNx group. We conclude that scale-invariant regulation of the motor pattern by SCN activity is dependent on light intensity but independent of the circadian rhythm output. Adjusting the light intensity by modifying the coupling degree between the population of oscillations could affect the dynamics of each individual oscillator in the SCN, making it less predictable.

Fractal and b-Value Mapping in Eastern Himalaya and Southern Tibet

Abstract Fractal (correlation) dimension and b -value are determined from ∼1300 well-located earthquakes recorded at 32 seismic stations in eastern Himalaya and southern Tibet during 1993–2003. The spatial correlation of 0.9 is indicative of more clustered events in the region, while a b -value of 1.02 implies a highly active seismic region. A detailed study of the frequency–magnitude distribution and fractal dimension as a function of depth is also made. The results suggest structural variability at different depth levels in the Tibet–Himalaya collision zone that reflects highly heterogeneous and high-grade metamorphism in the region.

Long-Range Correlations in Rectal Temperature Fluctuations of Healthy Infants during Maturation

BackgroundControl of breathing, heart rate, and body temperature are interdependent in infants, where instabilities in thermoregulation can contribute to apneas or even life-threatening events. Identifying abnormalities in thermoregulation is particularly important in the first 6 months of life, where autonomic regulation undergoes critical development. Fluctuations in body temperature have been shown to be sensitive to maturational stage as well as system failure in critically ill patients. We thus aimed to investigate the existence of fractal-like long-range correlations, indicative of temperature control, in night time rectal temperature (Trec) patterns in maturing infants.Methodology/Principal FindingsWe measured Trec fluctuations in infants every 4 weeks from 4 to 20 weeks of age and before and after immunization. Long-range correlations in the temperature series were quantified by the correlation exponent, α using detrended fluctuation analysis. The effects of maturation, room temperature, and immunization on the strength of correlation were investigated. We found that Trec fluctuations exhibit fractal long-range correlations with a mean (SD) α of 1.51 (0.11), indicating that Trec is regulated in a highly correlated and hence deterministic manner. A significant increase in α with age from 1.42 (0.07) at 4 weeks to 1.58 (0.04) at 20 weeks reflects a change in long-range correlation behavior with maturation towards a smoother and more deterministic temperature regulation, potentially due to the decrease in surface area to body weight ratio in the maturing infant. α was not associated with mean room temperature or influenced by immunizationConclusionsThis study shows that the quantification of long-range correlations using α derived from detrended fluctuation analysis is an observer-independent tool which can distinguish developmental stages of night time Trec pattern in young infants, reflective of maturation of the autonomic system. Detrended fluctuation analysis may prove useful for characterizing thermoregulation in premature and other infants at risk for life-threatening events.

Breathing frequency bias in fractal analysis of heart rate variability

Detrended Fluctuation Analysis (DFA) is an algorithm widely used to determine fractal long-range correlations in physiological signals. Its application to heart rate variability (HRV) has proven useful in distinguishing healthy subjects from patients with cardiovascular disease. In this study we examined the effect of respiratory sinus arrhythmia (RSA) on the performance of DFA applied to HRV. Predictions based on a mathematical model were compared with those obtained from a sample of 14 normal subjects at three breathing frequencies: 0.1 Hz, 0.2 Hz and 0.25 Hz. Results revealed that: (1) the periodical properties of RSA produce a change of the correlation exponent in HRV at a scale corresponding to the respiratory period, (2) the short-term DFA exponent is significantly reduced when breathing frequency rises from 0.1 Hz to 0.2 Hz. These findings raise important methodological questions regarding the application of fractal measures to short-term HRV.

Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution

Abstract. Lovejoy and Schertzer (1990a) presented a statistical analysis of blotting paper observations of the (two-dimensional) spatial distribution of raindrop stains. They found empirical evidence for the fractal scaling behavior of raindrops in space, with potentially far-reaching implications for rainfall microphysics and radar meteorology. In particular, the fractal correlation dimensions determined from their blotting paper observations led them to conclude that "drops are (hierarchically) clustered" and that "inhomogeneity in rain is likely to extend down to millimeter scales". Confirming previously reported Monte Carlo simulations, we demonstrate analytically that the claims based on this analysis need to be reconsidered, as fractal correlation dimensions similar to the ones reported (i.e. smaller than the value of two expected for uniformly distributed raindrops) can result from instrumental artifacts (edge effects) in otherwise homogeneous Poissonian rainfall. Hence, the results of the blotting paper experiment are not statistically significant enough to reject the Poisson homogeneity hypothesis in favor of a fractal description of the discrete nature of rainfall. Our analysis is based on an analytical expression for the expected overlap area between a circle and a square, when the circle center is randomly (uniformly) distributed inside the square. The derived expression (πr2−8r3/3+r4/2, where r denotes the ratio between the circle radius and the side of the square) can be used as a reference curve against which to test the statistical significance of fractal correlation dimensions determined from spatial point patterns, such as those of raindrops and rainfall cells.

Fractal dynamics of human gait: a reassessment of the 1996 data of Hausdorff et al.

We propose in this paper a reassessment of the original data of Hausdorff et al. (Hausdorff JM, Purdon PL, Peng C-K, Ladin Z, Wei JY, Goldberger AR. J Appl Physiol 80: 1448-1457, 1996). We confirm, using autoregressive fractionally integrated moving average modeling, the presence of genuine fractal correlations in stride interval series in self-paced conditions. In contrast with the conclusions of the authors, we show that correlations did not disappear in metronomic conditions. The series of stride intervals presented antipersistent correlations, and 1/f fluctuations were evidenced in the asynchronies to the metronome. We show that the super central pattern generator model (West B, Scafetta N. Phys Rev E Stat Nonlin Soft Matter Phys 67: 051917, 2003) allows accounting for the experimentally observed correlations in both self-paced and metronomic conditions, by the simple setting of the coupling strength parameter. We conclude that 1/f fluctuations in gait are not overridden by supraspinal influences when walking is paced by a metronome. The source of 1/f noise is still at work in this condition, but expressed differently under the influence of a continuous coupling process.

Optical characterization of the nanoscale organization of mineral deposits on silk films

The alignment of deposited minerals in tissues such as bone and teeth plays a critical role in the mechanical properties of these tissues. Therefore, assessment of features that are characteristic of aligned biominerals could aid in the development of novel biomaterials and engineered tissues that can be used to replace damaged or defective human tissues. In this study, we demonstrate that light scattering spectroscopy can serve as a useful tool for the noninvasive characterization of mineralization on aligned organic substrates. Specifically, we used silk films with oriented and nonoriented secondary structures as a protein matrix for control of mineralization. The mineral deposits displayed self-affine fractal morphologies with the oriented films yielding a significantly higher Hurst parameter, which in turn suggests higher levels of fractal organization. In addition, the value of the upper bound of fractal correlation lengths was significantly smaller for the oriented than for the nonoriented films and correlated well with the size of the corresponding nanocrystalline mineral beads identified by scanning electron microscope imaging.

Assessment of Nonlinear Heart Rate Dynamics after Beating-Heart Revascularization

Advanced nonlinear methods of measuring heart rate variability (HRV) derived from the mathematics of complex dynamics and fractal geometry have provided new insights into the abnormalities of heart rate behavior in various pathologic conditions. These methods have provided additional prognostic information compared with traditional HRV measures and clearly have complemented the conventional linear methods. Knowledge about the behavior of complex cardiac dynamics indices after different cardiac procedures is very limited, however. We aimed to clarify how nonlinear heart rate dynamics are affected by beating-heart revascularization (off-pump coronary artery bypass graft [CABG] surgery) within the first week after the procedure. Included in the study were 66 patients who had isolated stable multivessel coronary artery disease and were in normal sinus rhythm. The patients were on chronic beta-blocker therapy and were scheduled for off-pump CABG. We performed 15-minute high-resolution electrocardiographic recordings preoperatively and on the third and seventh postoperative days to assess linear and nonlinear heart rate dynamics. Frequency-domain measurements, detrended fluctuation analysis (DFA) with short-term (<or=11 beats, alpha1) and long-term (>11 beats, alpha2) correlation properties of RR-intervals, and fractal dimension (FD) measurements (average, high, and low) were made. Arrhythmia was monitored preoperatively with 24-hour Holter recordings, postoperatively by continuous monitoring for the first 4 days after the procedure, and subsequently by clinical monitoring; 24-hour Holter recordings were obtained again on the seventh postoperative day. We used the paired-samples Student t test, the Mann-Whitney U test, and the Fisher exact test for statistical analyses. Differences in arrhythmia occurrence before and after the procedure were tested with the Wilcoxon signed rank test and the McNemar test. A P level < .05 was considered statistically significant. Values for all frequency-domain parameters decreased significantly after off-pump CABG (P< .001). Values for the alpha1 and high FD parameters decreased significantly after the procedure (P= .028 and .001, respectively), whereas alpha2 increased significantly (P= .023). DFA alpha1 was significantly lower in patients with postoperative atrial fibrillation than in patients remaining in sinus rhythm (mean +/- SD, 0.79+/-0.32 versus 1.13+/-0.45 [P= .003] on the third postoperative day; 0.89+/-0.31 versus 1.22+/-0.34 [P< .001] on the seventh postoperative day), whereas low and average FDs were significantly higher (1.84+/-0.16 versus 1.68+/-0.19 [P= .003] on the third postoperative day and 1.77+/-0.18 versus 1.66+/-0.17 [P= .01] on the seventh postoperative day for the low FD; 1.83+/-0.09 versus 1.76+/-0.10 [P= .011] on the third postoperative day and 1.80+/-0.11 versus 1.73+/-0.10 [P= .014] on the seventh postoperative day for the average FD). The low FD was significantly higher on the third postoperative day in patients with postoperative deterioration of ventricular ectopy than in patients with improved ventricular ectopy (1.74+/-0.17 versus 1.48+/-0.08, [P= .03]). The decreases in alpha1, average FD, and high FD indicate that a profound decay of cardiac complexity and fractal correlation can be observed after off-pump CABG. Furthermore, a more extensive impairment of nonlinear indices was observed in patients who developed postoperative arrhythmias than in those who remained in stable sinus rhythm. Our findings suggest that the postoperative hyperadrenergic setting acts as a preliminary condition in which both reduced and enhanced vagal activity may predispose patients to arrhythmia, indicating that postoperative rhythm disturbances are an end point associated with divergent autonomic substrates.

Computer simulation of model cohesive powders: Plastic consolidation, structural changes, and elasticity under isotropic loads

The quasistatic behavior of a simple two-dimensional model of a cohesive powder under isotropic loads is investigated by discrete element simulations. We ignore contact plasticity and focus on the effect of geometry and collective rearrangements on the material behavior. The loose packing states, as assembled and characterized in a previous numerical study [Gilabert, Roux, and Castellanos, Phys. Rev. E 75, 011303 (2007)], are observed, under growing confining pressure P , to undergo important structural changes, while solid fraction Phi irreversibly increases (typically, from 0.4-0.5 to 0.75-0.8). The system state goes through three stages, with different forms of the plastic consolidation curve, i.e., Phi as a function of the growing reduced pressure P;{*}=PaF_{0} , defined with adhesion force F0 and grain diameter a . In the low-confinement regime (I), the system undergoes negligible plastic compaction, and its structure is influenced by the assembling process. In regime II the material state is independent of initial conditions, and the void ratio varies linearly with lnP [i.e., Delta(1Phi)=lambdaDelta(lnP;{*}) ], as described in the engineering literature. Plasticity index lambda is reduced in the presence of a small rolling resistance (RR). In the last stage of compaction (III), Phi approaches an asymptotic, maximum solid fraction Phi_{max} , as a power law Phi_{max}-Phi proportional, variant(P;{*});{-alpha} , with alpha approximately 1 , and properties of cohesionless granular packs are gradually retrieved. Under consolidation, while the range xi of fractal density correlations decreases, force patterns reorganize from self-balanced clusters to force chains, with correlative evolutions of force distributions, and elastic moduli increase by a large amount. Plastic deformation events correspond to very small changes in the network topology, while the denser regions tend to move like rigid bodies. Elastic properties are dominated by the bending of thin junctions in loose systems. For growing RR those tend to form particle chains, the folding of which, rather than tensile ruptures, controls plastic compaction.

Area-scaling of interferometric and fluorescent detection of protein on antibody microarrays

The sensitivity limits for an in-line interferometric (IL)/fluorescent (FL) dual-channel BioCD are established as a function of spatial averaging. Forward-phase and sandwich assays at 10 ng/ml were performed on large-scale antibody microarrays (6800-spot) and detected using in-line interferometry and fluorescence channels. The interferometric channel has an extrapolated label-free limit-of-detection (LOD) of 250 pg/ml in a forward-phase assay for which the fluorescent channel is inapplicable. In the sandwich assay, the extrapolated limit-of-detection is 70 pg/ml for the interferometric channel, and for the fluorescent channel it is 30 pg/ml. Intrinsic scale-free sensitivities for the detection channels are defined assuming spatially uncorrelated fluctuations with sensitivities of S′ = 13 pg/mm for interferometric detection and 7 pg/mm for sandwich fluorescent detection. The intrinsic sensitivities become weakly scale dependent in the presence of fractal spatial correlations among the antibody spots.

Heart Rate and Blood Pressure Variability and Baroreflex Sensitivity in Patients With Anorexia Nervosa

Anorexia nervosa (AN) is considered to have a significant risk for sudden death because of cardiac complications, and abnormalities of the autonomic nervous system might be a cause of cardiac dysfunction. The aim of this study was to investigate autonomic nervous system function in AN patients by analyzing heart rate variability (HRV), blood pressure variability (BPV), and baroreflex sensitivity (BRS). The subjects were 32 AN patients without other psychiatric comorbidities and 37 healthy controls. Beat-to-beat R-R interval and systolic blood pressure recorded in the supine position were analyzed using power spectral analysis and cross-spectrum analysis to quantify the frequency domain properties of HRV, BPV, and BRS. In addition, detrended fluctuation analysis was used to quantify the fractal correlation properties from the scaling exponent alpha1 of HRV. High frequency power and total power of HRV and BRS were significantly higher in AN patients and low frequency power of BPV, low frequency/High frequency ratio of HRV, and the scaling exponent alpha1 of HRV were significantly lower in AN patients, compared with controls. These findings suggest that AN patients have reduced cardiovascular sympathetic nervous responsiveness, increased parasympathetic nervous responsiveness, and increased complexity of the interbeat interval time series compared with healthy controls. Regarding the relationship to prognosis of AN, the study showed conflicting results, and further prospective studies are needed to determine if these results are related to high mortality in AN patients.

Fractal scaling properties of heart rate dynamics following resistance exercise training

With aging and disease, there is a breakdown of the natural fractal-like organization of heart rate (HR). Fractal-like correlation properties of HR can be assessed with detrended fluctuation analysis (DFA). A short-time scaling exponent (alpha(s)) value of 1 is associated with healthy HR dynamics, whereas values that deviate away from 1, in either direction, indicate fractal collapse. The purpose of this study was to examine the effect of resistance exercise training (RT) on fractal correlation properties of HR dynamics. Resting ECG was collected at baseline, following a 4-wk time control period and 6 wk of RT (3 days per wk) in 34 men (23 +/- 1 years of age). Fractal properties of HR were assessed with DFA. There was no change in alpha(s) following either the time control period or RT (1.01 +/- 0.06 to 0.98 +/- 0.06 to 0.93 +/- 0.04, P > 0.05). Given the potential bidirectional nature of fractal collapse, subjects were retrospectively separated into two groups (higher alpha(s) and lower alpha(s)) on the basis of the initial alpha(s) by using cluster analysis. An interaction was detected for alpha(s) following RT (P < 0.05). There was no change in alpha(s) in either group following the time control, but alpha(s) increased following RT in the lower alpha(s) group (n = 18; 0.73 +/- 0.04 to 0.69 +/- 0.04 to 0.88 +/- 0.04) and alpha(s) decreased following RT in the higher alpha(s) group (n = 16; 1.20 +/- 0.04 to 1.24 +/- 0.04 to 0.98 +/- 0.04). In conclusion, RT improves fractal properties of HR dynamics.

1D-based defect detection in patterned TFT-LCD panels using characteristic fractal dimension and correlations

Thin film transistor-liquid crystal display (TFT-LCD) is a major technology for flat panel display used in a wide range of electronic devices. As the TFT-LCD panel becomes dense, small defects can only be observed at an extremely high resolution. For fast imaging of a large-sized TFT-LCD panel at a high resolution, a one-dimensional (1D) line scan system is demanded. A TFT-LCD panel image at a fine resolution presents very complicated repetitive patterns, which increases the difficulty of the defect detection task. In this paper, we propose a 1D self-comparison defect detection scheme that directly works on the 1D line images of a TFT-LCD panel. The proposed method first uses the fractal transformation to enhance the periodicity and regularity of a 1D gray-level line image, and then divides the resulting fractal signal into small segments, each of the length of the repeated period. By calculating each divided segment’s normalized cross correlation with its neighboring segments and comparing the resulting correlation value with a predetermined threshold, the segments containing a defect can be effectively identified. Since the proposed method does not require a reference template, it is invariant to changes in illumination and image translation. Experimental results on a number of microdefects in patterned TFT-LCD panel surfaces show that the proposed method can well detect various ill-defined defects and is computationally very efficient.

Development of more erratic heart rate patterns is associated with mortality post–myocardial infarction

Cardiac patients often have sinus arrhythmia of nonrespiratory origin (erratic sinus rhythm [ESR]). ESR was quantified using hourly Poincaré and power spectral heart rate variability plots from normal-to-normal interbeat intervals and hourly values of the short-term fractal scaling exponent and correlations of normal-to-normal intervals in n = 60 nonsurvivors and n = 66 randomly selected survivors in the Cardiac Arrhythmia Suppression Trial. Hours were coded (ABN) as normal (0), borderline (0.5), or ESR (1). t Tests compared ABN for n = 2413 paired hours at baseline and on therapy. ABN was higher in nonsurvivors (0.38 ± 0.44 vs 0.28 ± 0.40, baseline, and 0.51 ± 0.45 vs 0.34 ± 0.43, on therapy, P < .001). Increased ABN with treatment were greater in nonsurvivors. Normal hours at baseline (relative risk = 0.77; 095% confidence interval, 0.62-0.96, P = .018) and on treatment (relative risk = 0.47; 95% confidence interval, 0.39-0.58) were significantly associated with decreased mortality compared with ESR. Quantification of ESR may identify more vulnerable patients or help monitor the effects of pharmacologic treatment.

Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes

We investigate how simultaneously recorded long-range power-law correlated multivariate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which are at the same time long-range cross-correlated. We study how the degree of cross-correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals. Our findings have relevance when studying parallel outputs of multiple component of physical, physiological and social systems.

Wavelet transform modulus maxima based fractal correlation analysis

The wavelet transform modulus maxima (WTMM) used in the singularity analysis of one fractal function is extended to study the fractal correlation of two multifractal functions. The technique is developed in the framework of joint partition function analysis (JPFA) proposed by Meneveau et al. [1] and is shown to be equally effective. In addition, we show that another leading approach developed for the same purpose, namely, relative multifractal analysis, can be considered as a special case of JPFA at a particular parameter setting.

Earthquake hazard zonation of Sikkim Himalaya using a GIS platform

An earthquake hazard zonation map of Sikkim Himalaya is prepared using eight thematic layers namely Geology (GE), Soil Site Class (SO), Slope (SL), Landslide (LS), Rock Outcrop (RO), Frequency–Wavenumber (F–K) simulated Peak Ground Acceleration (PGA), Predominant Frequency (PF), and Site Response (SR) at predominant frequencies using Geographic Information System (GIS). This necessitates a large scale seismicity analysis for seismic source zone classification and estimation of maximum earthquake magnitude or maximum credible earthquake to be used as a scenario earthquake for a deterministic or quasi-probabilistic seismic scenario generation. The International Seismological Center (ISC) and Global Centroid Moment Tensor (GCMT) catalogues have been used in the present analysis. Combining b-value, fractal correlation dimension (Dc) of the epicenters and the underlying tectonic framework, four seismic source zones are classified in the northeast Indian region. Maximum Earthquake of MW 8.3 is estimated for the Eastern Himalayan Zone (EHZ) and is used to generate the seismic scenario of the region. The Geohazard map is obtained through the integration of the geological and geomorphological themes namely GE, SO, SL, LS, and RO following a pair-wise comparison in an Analytical Hierarchy Process (AHP). Detail analysis of SR at all the recording stations by receiver function technique is performed using 80 significant events recorded by the Sikkim Strong Motion Array (SSMA). The ground motion synthesis is performed using F–K integration and the corresponding PGA has been estimated using random vibration theory (RVT). Testing for earthquakes of magnitude greater than MW 5, a few cases presented here, establishes the efficacy and robustness of the F–K simulation algorithm. The geohazard coverage is overlaid and sequentially integrated with PGA, PF, and SR vector layers, in order to evolve the ultimate earthquake hazard microzonation coverage of the territory. Earthquake Hazard Index (EHI) quantitatively classifies the terrain into six hazard levels, while five classes could be identified following the Bureau of Indian Standards (BIS) PGA nomenclature for the seismic zonation of India. EHI is found to vary between 0.15 to 0.83 quantitatively classifying the terrain into six hazard levels as “Low” corresponding to BIS Zone II, “Moderate” corresponding to BIS Zone III, “Moderately High” belonging to BIS Zone IV, “High” corresponding to BIS Zone V(A), “Very High” and “Severe” with new BIS zones to Zone V(B) and V(C) respectively.