Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Outward spherical solidification of a superheated melt with time dependent boundary flux

Short-time analytical solutions of solid and liquid temperatures and freezing front have been obtained for the outward radially symmetric spherical solidification of a superheated melt. Although results are presented here only for time dependent boundary flux, the method of solution can be used for other kinds of boundary conditions also. Later, the analytical solution has been compared with the numerical solution obtained with the help of a finite difference numerical scheme in which the grid points change with the freezing front position. An efficient method of execution of the numerical scheme has been discussed in details. Graphs have been drawn for the total solidification times and temperature distributions in the solid.

Analytical and numerical solutions of inward spherical solidification of a superheated melt with radiative-convective heat transfer and density jump at freezing front

Analytical and numerical solutions of a general problem related to the radially symmetric inward spherical solidification of a superheated melt have been studied in this paper. In the radiation-convection type boundary conditions, the heat transfer coefficient has been taken as time dependent which could be infinite, at time,t=0. This is necessary, for the initiation of instantaneous solidification of superheated melt, over its surface. The analytical solution consists of employing suitable fictitious initial temperatures and fictitious extensions of the original region occupied by the melt. The numerical solution consists of finite difference scheme in which the grid points move with the freezing front. The numerical scheme can handle with ease the density changes in the solid and liquid states and the shrinkage or expansions of volumes due to density changes. In the numerical results, obtained for the moving boundary and temperatures, the effects of several parameters such as latent heat, Boltzmann constant, density ratios, heat transfer coefficients, etc. have been shown. The correctness of numerical results has also been checked by satisfying the integral heat balance at every timestep.

Average lattices and aperiodic structures

Statistically averaged lattices provide a common basis to understand the diffraction properties of structures displaying deviations from regular crystal structures. An average lattice is defined and examples are given in one and two dimensions along with their diffraction patterns. The absence of periodicity in reciprocal space corresponding to aperiodic structures is shown to arise out of different projected spacings that are irrationally related, when the grid points are projected along the chosen coordinate axes. It is shown that the projected length scales are important factors which determine the existence or absence of observable periodicity in the diffraction pattern more than the sequence of arrangement.

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.

Evaluation of spatial variation of peak horizontal acceleration and spectral acceleration for south India: a probabilistic approach

In this work, an attempt has been made to evaluate the spatial variation of peak horizontal acceleration (PHA) and spectral acceleration (SA) values at rock level for south India based on the probabilistic seismic hazard analysis (PSHA). These values were estimated by considering the uncertainties involved in magnitude, hypocentral distance and attenuation of seismic waves. Different models were used for the hazard evaluation, and they were combined together using a logic tree approach. For evaluating the seismic hazard, the study area was divided into small grids of size 0.1A degrees A xA 0.1A degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources within a radius of 300 km. Rock level PHA values and SA at 1 s corresponding to 10% probability of exceedance in 50 years were evaluated for all the grid points. Maps showing the spatial variation of rock level PHA values and SA at 1 s for the entire south India are presented in this paper. To compare the seismic hazard for some of the important cities, the seismic hazard curves and the uniform hazard response spectrum (UHRS) at rock level with 10% probability of exceedance in 50 years are also presented in this work.

Seismic hazard map of Coimbatore using subsurface fault rupture

This study presents the future seismic hazard map of Coimbatore city, India, by considering rupture phenomenon. Seismotectonic map for Coimbatore has been generated using past earthquakes and seismic sources within 300 km radius around the city. The region experienced a largest earthquake of moment magnitude 6.3 in 1900. Available earthquakes are divided into two categories: one includes events having moment magnitude of 5.0 and above, i.e., damaging earthquakes in the region and the other includes the remaining, i.e., minor earthquakes. Subsurface rupture character of the region has been established by considering the damaging earthquakes and total length of seismic source. Magnitudes of each source are estimated by assuming the subsurface rupture length in terms of percentage of total length of sources and matched with reported earthquake. Estimated magnitudes match well with the reported earthquakes for a RLD of 5.2% of the total length of source. Zone of influence circles is also marked in the seismotectonic map by considering subsurface rupture length of fault associated with these earthquakes. As earthquakes relive strain energy that builds up on faults, it is assumed that all the earthquakes close to damaging earthquake have released the entire strain energy and it would take some time for the rebuilding of strain energy to cause a similar earthquake in the same location/fault. Area free from influence circles has potential for future earthquake, if there is seismogenic source and minor earthquake in the last 20 years. Based on this rupture phenomenon, eight probable locations have been identified and these locations might have the potential for the future earthquakes. Characteristic earthquake moment magnitude (M-w) of 6.4 is estimated for the seismic study area considering seismic sources close to probable zones and 15% increased regional rupture character. The city is divided into several grid points at spacing of 0.01 degrees and the peak ground acceleration (PGA) due to each probable earthquake is calculated at every grid point in city by using the regional attenuation model. The maximum of all these eight PGAs is taken for each grid point and the final PGA map is arrived. This map is compared to the PGA map developed based on the conventional deterministic seismic hazard analysis (DSHA) approach. The probable future rupture earthquakes gave less PGA than that of DSHA approach. The occurrence of any earthquake may be expected in near future in these eight zones, as these eight places have been experiencing minor earthquakes and are located in well-defined seismogenic sources.

Deterministic seismic hazard macrozonation of India

Earthquakes are known to have occurred in Indian subcontinent from ancient times. This paper presents the results of seismic hazard analysis of India (6 degrees-38 degrees N and 68 degrees-98 degrees E) based on the deterministic approach using latest seismicity data (up to 2010). The hazard analysis was done using two different source models (linear sources and point sources) and 12 well recognized attenuation relations considering varied tectonic provinces in the region. The earthquake data obtained from different sources were homogenized and declustered and a total of 27,146 earthquakes of moment magnitude 4 and above were listed in the study area. The sesismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones which are associated with earthquakes of magnitude 4 and above. A new program was developed in MATLAB for smoothing of the point sources. For assessing the seismic hazard, the study area was divided into small grids of size 0.1 degrees x 0.1 degrees (approximately 10 x 10 km), and the hazard parameters were calculated at the center of each of these grid cells by considering all the seismic sources within a radius of 300 to 400 km. Rock level peak horizontal acceleration (PHA) and spectral accelerations for periods 0.1 and 1 s have been calculated for all the grid points with a deterministic approach using a code written in MATLAB. Epistemic uncertainty in hazard definition has been tackled within a logic-tree framework considering two types of sources and three attenuation models for each grid point. The hazard evaluation without logic tree approach also has been done for comparison of the results. The contour maps showing the spatial variation of hazard values are presented in the paper.

Assessing future rainfall projections using multiple GCMs and a multi-site stochastic downscaling model

Impact of global warming on daily rainfall is examined using atmospheric variables from five General Circulation Models (GCMs) and a stochastic downscaling model. Daily rainfall at eleven raingauges over Malaprabha catchment of India and National Center for Environmental Prediction (NCEP) reanalysis data at grid points over the catchment for a continuous time period 1971-2000 (current climate) are used to calibrate the downscaling model. The downscaled rainfall simulations obtained using GCM atmospheric variables corresponding to the IPCC-SRES (Intergovernmental Panel for Climate Change - Special Report on Emission Scenarios) A2 emission scenario for the same period are used to validate the results. Following this, future downscaled rainfall projections are constructed and examined for two 20 year time slices viz. 2055 (i.e. 2046-2065) and 2090 (i.e. 2081-2100). The model results show reasonable skill in simulating the rainfall over the study region for the current climate. The downscaled rainfall projections indicate no significant changes in the rainfall regime in this catchment in the future. More specifically, 2% decrease by 2055 and 5% decrease by 2090 in monsoon (HAS) rainfall compared to the current climate (1971-2000) under global warming conditions are noticed. Also, pre-monsoon (JFMAM) and post-monsoon (OND) rainfall is projected to increase respectively, by 2% in 2055 and 6% in 2090 and, 2% in 2055 and 12% in 2090, over the region. On annual basis slight decreases of 1% and 2% are noted for 2055 and 2090, respectively.

Assessment of Seismically Induced Landslide Hazard for the State of Karnataka Using GIS Technique

Landslide hazards are a major natural disaster that affects most of the hilly regions around the world. In India, significant damages due to earthquake induced landslides have been reported in the Himalayan region and also in the Western Ghat region. Thus there is a requirement of a quantitative macro-level landslide hazard assessment within the Indian subcontinent in order to identify the regions with high hazard. In the present study, the seismic landslide hazard for the entire state of Karnataka, India was assessed using topographic slope map, derived from the Digital Elevation Model (DEM) data. The available ASTER DEM data, resampled to 50 m resolution, was used for deriving the slope map of the entire state. Considering linear source model, deterministic seismic hazard analysis was carried out to estimate peak horizontal acceleration (PHA) at bedrock, for each of the grid points having terrain angle 10A degrees and above. The surface level PHA was estimated using nonlinear site amplification technique, considering B-type NEHRP site class. Based on the surface level PHA and slope angle, the seismic landslide hazard for each grid point was estimated in terms of the static factor of safety required to resist landslide, using Newmark's analysis. The analysis was carried out at the district level and the landslide hazard map for all the districts in the Karnataka state was developed first. These were then merged together to obtain a quantitative seismic landslide hazard map of the entire state of Karnataka. Spatial variations in the landslide hazard for all districts as well as for the entire state Karnataka is presented in this paper. The present study shows that the Western Ghat region of the Karnataka state is found to have high landslide hazard where the static factor of safety required to resist landslide is very high.

Recent Seismicity in India and Adjoining Regions

In the present work, historical and instrumental seismicity data of India and its adjoining areas (within 300km from Indian political boundary) are compiled to form the earthquake catalog for the country covering the period from 1505 to 2009. The initial catalogue consisted of about 139563 earthquake events and after declustering,the total number of events obtained was 61315. Region specific earthquake magnitude scaling relations correlating different magnitude scales were achieved and a homogenous earthquake catalogue in moment magnitude (MW) scale was developed for the region. This paper also presents the results of the use of Geographic Information Systems (GIS) to prepare a digitized seismic source map of India. The latest earthquake data were superimposed on the digitized source map to get a final Seismotectonic map of India. The study area has been divided into 1225 grid points (approximately 110km×110km) and the seismicity analysis has been done to get the spatial variation of seismicity parameters ‘a’ and ‘b’ across the country. The homogenized earthquake catalogue with the event details is listed in the website http://civil.iisc.ernet.in/~sreevals/resource.htm

Spatial variation of seismicity parameters across India and adjoining areas

An attempt has been made to quantify the variability in the seismic activity rate across the whole of India and adjoining areas (0–45°N and 60–105°E) using earthquake database compiled from various sources. Both historical and instrumental data were compiled and the complete catalog of Indian earthquakes till 2010 has been prepared. Region-specific earthquake magnitude scaling relations correlating different magnitude scales were achieved to develop a homogenous earthquake catalog for the region in unified moment magnitude scale. The dependent events (75.3%) in the raw catalog have been removed and the effect of aftershocks on the variation of b value has been quantified. The study area was divided into 2,025 grid points (1°91°) and the spatial variation of the seismicity across the region have been analyzed considering all the events within 300 km radius from each grid point. A significant decrease in seismic b value was seen when declustered catalog was used which illustrates that a larger proportion of dependent events in the earthquake catalog are related to lower magnitude events. A list of 203,448 earth- quakes (including aftershocks and foreshocks) occurred in the region covering the period from 250 B.C. to 2010 A.D. with all available details is uploaded in the website http://www.civil.iisc.ernet.in/*sreevals/resource.htm.

Ranking of global climate models for India using multicriterion analysis

Eleven GCMs (BCCR-BCCM2.0, INGV-ECHAM4, GFDL2.0, GFDL2.1, GISS, IPSL-CM4, MIROC3, MRI-CGCM2, NCAR-PCMI, UKMO-HADCM3 and UKMO-HADGEM1) were evaluated for India (covering 73 grid points of 2.5 degrees x 2.5 degrees) for the climate variable `precipitation rate' using 5 performance indicators. Performance indicators used were the correlation coefficient, normalised root mean square error, absolute normalised mean bias error, average absolute relative error and skill score. We used a nested bias correction methodology to remove the systematic biases in GCM simulations. The Entropy method was employed to obtain weights of these 5 indicators. Ranks of the 11 GCMs were obtained through a multicriterion decision-making outranking method, PROMETHEE-2 (Preference Ranking Organisation Method of Enrichment Evaluation). An equal weight scenario (assigning 0.2 weight for each indicator) was also used to rank the GCMs. An effort was also made to rank GCMs for 4 river basins (Godavari, Krishna, Mahanadi and Cauvery) in peninsular India. The upper Malaprabha catchment in Karnataka, India, was chosen to demonstrate the Entropy and PROMETHEE-2 methods. The Spearman rank correlation coefficient was employed to assess the association between the ranking patterns. Our results suggest that the ensemble of GFDL2.0, MIROC3, BCCR-BCCM2.0, UKMO-HADCM3, MPIECHAM4 and UKMO-HADGEM1 is suitable for India. The methodology proposed can be extended to rank GCMs for any selected region.

Ranking general circulation models for India using TOPSIS

Eleven general circulation models/global climate models (GCMs) - BCCR-BCCM2.0, INGV-ECHAM4, GFDL2.0, GFDL2.1, GISS, IPSL-CM4, MIROC3, MRI-CGCM2, NCAR-PCMI, UKMO-HADCM3 and UKMO-HADGEM1 - are evaluated for Indian climate conditions using the performance indicator, skill score (SS). Two climate variables, temperature T (at three levels, i.e. 500, 700, 850 mb) and precipitation rate (Pr) are considered resulting in four SS-based evaluation criteria (T500, T700, T850, Pr). The multicriterion decision-making method, technique for order preference by similarity to an ideal solution, is applied to rank 11 GCMs. Efforts are made to rank GCMs for the Upper Malaprabha catchment and two river basins, namely, Krishna and Mahanadi (covered by 17 and 15 grids of size 2.5 degrees x 2.5 degrees, respectively). Similar efforts are also made for India (covered by 73 grid points of size 2.5 degrees x 2.5 degrees) for which an ensemble of GFDL2.0, INGV-ECHAM4, UKMO-HADCM3, MIROC3, BCCR-BCCM2.0 and GFDL2.1 is found to be suitable. It is concluded that the proposed methodology can be applied to similar situations with ease.

Efficient computation of volume fractions for multi-material cell complexes in a grid by slicing

The paper presents a novel slicing based method for computation of volume fractions in multi-material solids given as a B-rep whose faces are triangulated and shared by either one or two materials. Such objects occur naturally in geoscience applications and the said computation is necessary for property estimation problems and iterative forward modeling. Each facet in the model is cut by the planes delineating the given grid structure or grid cells. The method, instead of classifying the points or cells with respect to the solid, exploits the convexity of triangles and the simple axis-oriented disposition of the cutting surfaces to construct a novel intermediate space enumeration representation called slice-representation, from which both the cell containment test and the volume-fraction computation are done easily. Cartesian and cylindrical grids with uniform and non-uniform spacings have been dealt with in this paper. After slicing, each triangle contributes polygonal facets, with potential elliptical edges, to the grid cells through which it passes. The volume fractions of different materials in a grid cell that is in interaction with the material interfaces are obtained by accumulating the volume contributions computed from each facet in the grid cell. The method is fast, accurate, robust and memory efficient. Examples illustrating the method and performance are included in the paper.