A quantitative study of the energy release in the aftershocks of the Bhuj earthquake, 2001, India, using Lg phase

The devastating earthquake on 26 January 2001 at Bhuj, India, resulted in large-scale death and destruction of properties of several million US dollars. The moment magnitude of the earthquake was 7.7 and its maximum focal intensity exceeded X in MM scale. The rate of aftershocks of this earthquake, recorded at Gauribidanur seismic array station (GBA), shows a monotonic decay with time superposed with oscillations. For the Indian continent the Lg phase is a prominent arrival at regional distances. The estimate of Lg amplitude is obtained by optimally fitting the Lg wave train to a exponential decay curve. The logarithm of these amplitudes and logarithm of root mean square (rms) value of actual amplitudes of the Lg are calibrated with USGS m_b to create a local m_bLg magnitude scale. The energy released from these aftershocks is calculated from the rms value of Lg phase. The plot of cumulative energy release with time follows the power law of the form t^p, superposed with oscillations. The exponent of the power law, p, is estimated both by a time-window scanning method and by an interpolation method. The value of p is 0.434 for time-window scanning method and 0.432 for the interpolation method. The predominant periods found in the oscillatory part of the cumulative energy, obtained by differencing the observed from the power law fit, are 10.6, 7.9, 5.4, 4.6 and 3.5 h for time-window scanning method. The corresponding periods for interpolation method are 13.4, 11.5, 7.4, 4.2, 3.5, 2.6 and 2.4 h.     

Are sea-level-rise trends along the coasts of the north Indian Ocean consistent with global estimates?

Mean-sea-level data from coastal tide gauges in the north Indian Ocean were used to show that low-frequency variability is consistent among the stations in the basin. Statistically significant trends obtained from records longer than 40 years yielded sea-level-rise estimates between 1.06–1.75 mm yr^− 1, with a regional average of 1.29 mm yr^− 1, when corrected for global isostatic adjustment (GIA) using model data. These estimates are consistent with the 1–2 mm yr^− 1 global sea-level-rise estimates reported by the Intergovernmental Panel on Climate Change.     

Estimation of wave period statistics using numerical coastal wave model

We used field and model wave data to investigate that zero crossing and average wave period distribution follow Gamma distribution. Since Gamma CDF is an infinite power series, further mathematical treatment is difficult. Hence its shape parameter is approximated to the nearest integer to arrive at Erlang distribution. An expression is derived from Erlang distribution to estimate various mean wave periods and significant wave period and validated by relative root mean square (RRMS) error criteria. It is shown by mathematical logic that the significant wave period distribution follows Erlang (or Gamma) distribution and is validated. The average of one-third and one-tenth highest wave periods (T _s ) estimated from Erlang distribution are in accordance with the values computed from recorded buoy and numerical coastal wave model wave period data. The predicted T _s values from coastal wave model wave period data underestimates the values from buoy wave period data.     

Chaotic behaviour of interplanetary magnetic field under various geomagnetic conditions

In the present study, the deterministic chaotic behaviour of interplanetary magnetic field (IMF) under various geomagnetic conditions of low and high solar active periods was analyzed, using the time series of IMF |B| and B_z, by employing chaotic quantifiers like, Lyapunov exponent, Tsallis entropy, correlation dimension, and non-linear prediction error. We have investigated whether the chaotic behaviour of interplanetary magnetic field would modify, when it produces major geomagnetic storms, and how it depends on the phase of solar activity. The yearly average values of Lyapunov exponent for the time series of IMF |B| and B_z, show solar flux dependence, whereas those values of entropy, correlation dimension and non-linear prediction error had no significant solar flux dependence. The yearly average values of entropy for quiet periods are higher compared to those values for major storm periods belonging to low/high solar active conditions, for both the time series |B| and B_z.     

Trapped waves of the 27 November 1945 Makran tsunami: observations and numerical modeling

The 27 November 1945 earthquake in the Makran Subduction Zone triggered a destructive tsunami that has left important problems unresolved. According to the available reports, high waves persisted along the Makran coast and at Karachi for several hours after the arrival of the first wave. Long-duration sea-level oscillations were also reported from Port Victoria, Seychelles. On the other hand, only one high wave was reported from Mumbai. Tide-gauge records of the tsunami from Karachi and Mumbai confirm these reports. While the data from Mumbai shows a single high wave, Karachi data shows that high waves persisted for more than 7 h, with maximum wave height occurring 2.8 h after the arrival of the first wave. In this paper, we analyze the cause of these persistent high waves using a numerical model. The simulation reproduces the observed features reasonably well, particularly the persistent high waves at Karachi and the single high wave at Mumbai. It further reveals that the persistent high waves along the Makran coast and at Karachi were the result of trapping of the tsunami-wave energy on the continental shelf off the Makran coast and that these coastally-trapped edge waves were trapped in the along-shore direction within a ∼300-km stretch of the continental shelf. Sensitivity experiments establish that this along-shore trapping of the tsunami energy is due to variations in the shelf width. In addition, the model simulation indicates that the reported long duration of sea-level oscillations at Port Victoria were mainly due to trapping of the tsunami energy over the large shallow region surrounding the Seychelles archipelago.     

Application of Weibull model for redefined significant wave height distributions

It is well accepted that the parent distribution for individual ocean wave heights follows the Weibull model. However this model does not simulate significant wave height which is the average of the highest one-third of some ‘n’ (n- varies) wave heights in a wave record. It is now proposed to redefine significant wave height as average of the highest one-third of a constant number (n-constant, say,n = 100) of consecutive individual wave heights. The Weibull model is suggested for simulating redefined significant wave height distribution by the method of characteristic function. An empirical support of 100.00% is established by Χ²-test at 0.05 level of significance for 3 sets of data at 0900, 1200 and 1500 hrs at Valiathura, Kerala coast. Parametric relations have been derived for the redefined significant wave height parameters such as mean, maximum one-third average, extreme wave heights, return periods of an extreme wave height and the probability of realising an extreme wave height in a time less than the designated return period.     

On vertical velocity fluctuations and internal tides in an upwelling region off the west coast of India

Hourly fluctuations of vertical velocity in relation to components of flow and wind and temperature oscillations at a morring site in the shelf waters off the west coast of India are discussed. The vertical velocities were computed from a time series of vertical temperature profiles assuming that horizontal advection of temperature is negligible. The computed values at a depth of 40 m during the 72-h period of observation were of the order of 10⁻¹ to 10⁻²cm s⁻¹, with a mean value of −2·77 × 10⁻² cm s⁻¹ indicating a net upward movement of water. The computed vertical velocity showed fluctuations of about 2–3 h, in addition to weaker signals of about 12 h. Based on the spectral estimates, we speculate that these fluctuations of 2–3 h in the vertical velocity may be caused by the fluctuations in the along-shore wind. The oscillations of isotherms found in the temperaturedepth time series and the spectral estimates of temperature and cross-shore flow component showed a periodicity of about 12 h, which indicated the presence of semi-diurnal internal waves. The fact that these internal wave troughs were associated with the measured onshore flow suggested that the waves were propagating offshore. The computed stability parameters showed little evidence of instability or mixing. It was found that the isotherm troughs in the temperaturedepth time series at about 12-h period coincided with high vertical shear in the cross-shore direction and low values of Brunt Vaisälä frequency.     

Seasonal variation of the diurnal cycle of rainfall in the eastern equatorial Indian Ocean

Summary The diurnal cycle of rainfall over the eastern equatorial Indian Ocean was studied for the period 23^rd October 2001 to 31^st October 2003 using hourly data from the Triton buoy positioned at 1.5° S and 90° E. An analysis of the active and weak spells of rainfall for different seasons revealed peaks in the late evening hours in Winter, Summer and Fall and in early morning hours (in Spring) in 2002. The active spell of rainfall peaked in the afternoon hours, during Winter, Spring and Summer in 2003, which agrees with the previous results of Janowiak et al. (1994). An analysis of rainfall events showed that Fall 2002 had a maximum number of rainfall events (90) and minimum (60) were observed in Spring 2003. Further it was found that the majority of rain events (>60%) were less than 3 hours in duration throughout the study period. The longer duration rainfall events (i.e. rain events greater than 6 hour duration) contributed significantly to Spring 2002 (20% of the total rainfall) and Winter 2003 (21% of the total rainfall). Harmonic analysis of the hourly rainfall data for different seasons revealed that diurnal harmonic explains more than 80% of the variance for all seasons. Furthermore, the diurnal harmonic has a maximum amplitude for all seasons except summer, where the semidiurnal and six hourly harmonics are significant.     

Development of fragility curves using high‐dimensional model representation

Fragility curves represent the conditional probability that a structure's response may exceed the performance limit for a given ground motion intensity. Conventional methods for computing building fragilities are either based on statistical extrapolation of detailed analyses on one or two specific buildings or make use of Monte Carlo simulation with these models. However, the Monte Carlo technique usually requires a relatively large number of simulations to obtain a sufficiently reliable estimate of the fragilities, and it is computationally expensive and time consuming to simulate the required thousands of time history analyses. In this paper, high‐dimensional model representation based response surface method together with the Monte Carlo simulation is used to develop the fragility curve, which is then compared with that obtained by using Latin hypercube sampling. It is used to replace the algorithmic performance‐function with an explicit functional relationship, fitting a functional approximation, thereby reducing the number of expensive numerical analyses. After the functional approximation has been made, Monte Carlo simulation is used to obtain the fragility curve of the system. Copyright © 2012 John Wiley & Sons, Ltd.     

Characteristics of Tides in the Bay of Bengal

A vertically integrated 2D numerical model was developed for the simulation of major tidal constituents (M₂, S₂, N₂, K₁ and O₁) in the Bay of Bengal. The bathymetry for the model domain was derived from an improved ETOPO5 dataset prepared in our earlier work. The simulated tidal elevations showed good agreement with the hourly tide gauge observations at Paradip, Visakhapatnam, and Chennai. The amplitudes and phases of M₂, S₂, K₁, and O₁ at the coastal stations, obtained from harmonic analysis of simulated tides, were found to agree well with those obtained from Admiralty Tide Tables with the RMS misfit 9.2, 5.6, 2.9 and 3.1 cm, respectively. In the Bay of Bengal, semi-diurnal tides (M₂, S₂, and N₂) attain highest amplitudes (180, 80, 30 cm, respectively) in the Gulf of Martaban while amplitudes of diurnal tides (K₁, O₁) reaches maximum (20, 12 cm, respectively) in the Malacca Strait. The continental shelf in the head bay and along the southern coast of Myanmar is about 200 km wide and the amplitudes of semi-diurnal tides are doubled in these regions while the diurnal tides amplify only marginally, which is consistent with Clarke and Battisti theory. In the north eastern end of the head bay and the Gulf of Martaban, the geometrical configuration of the coastline, in addition to the wide continental shelf, could contribute to the amplification of both semi-diurnal and diurnal constituents. In the Malacca Strait, the amplitudes of both semi-diurnal and diurnal tides are found to increase gradually from the northern end to the 2.5°N and decreases towards southern boundary. The co-tidal and co-range charts of M₂ and S₂ tidal constituents also show the presence of two degenerate amphidromic points in the head bay. A virtual amphidromic point for M₂ is identified in the Malacca Strait.