• V K Gaur

Articles written in Journal of Earth System Science

• Finite element modelling for evaluation of apparent resistivity over complex structures

The paper presents a computational algorithm designed for efficient modelling of apparent resistivity over complex geological structures, using finite element method. The algorithm can be used to study variations of apparent resistivities using any electrode configuration at any point on the earth’s surface, not necessarily regular. A Schlumberger apparent resistivity sounding curve over a buried anticline, is presented here as an example and compared with the corresponding analytical curve, to demonstrate the correctness of the FEM algorithm.

The various potential derivatives required for the computation of apparent resistivities evaluated through different electrode configurations have been obtained by calculating the ‘influence coefficients’ using reciprocal theorems, an approach successfully applied in structural engineering. In essence, a set of self balancing nodal currents, obtained from the appropriate derivative(s) of the shape functions of the elements contributing to the point of observation, is applied as the load vector.

The resulting quantities corresponding to the potential distribution in traditional finite element method, then, turn out to be the potential derivatives at the point of observation for different positions of the current electrodes. These are known as influence coefficients.

The continuum nature of the domain beyond the region of interest has been modelled by using ‘infinite elements’ across which the potential is assumed to decay exponentially.

• Estimation of the waiting time distributions of earthquakes

Whether the earthquake occurrences follow a Poisson process model is a widely debated issue. The Poisson process model has great conceptual appeal and those who rejected it under pressure of empirical evidence have tried to restore it by trying to identify main events and suppressing foreshocks and aftershocks. The approach here is to estimate the density functions for the waiting times of the future earthquakes. For this purpose, the notion of Gram-Charlier series which is a standard method for the estimation of density functions has been extended based on the orthogonality properties of certain polynomials such as Laguerre and Legendre. It is argued that it is best to estimate density functions in the context of a particular null hypothesis. Using the results of estimation a simple test has been designed to establish that earthquakes do not occur as independent events, thus violating one of the postulates of a Poisson process model. Both methodological and utilitarian aspects are dealt with.

• Hypotheses for earthquake occurrences

Very little work has been done in generating alternatives to the Poisson process model. The work reported here deals with alternatives to the Poisson process model for the earthquakes and checks them using empirical data and the statistical hypothesis testing apparatus. The strategy used here for generating hypotheses is to compound the Poisson process. The parameter of the Poisson process is replaced by a random variable having prescribed density function. The density functions used are gamma, chi and extended (gamma/chi). The original distribution is then averaged out with respect to these density functions. For the compound Poisson processes the waiting time distributions for the future events are derived. As the parameters for the various statistical models for earthquake occurrences are not known, the problem is basically of composite hypothesis testing. One way of designing a test is to estimate these parameters and use them as true values. Momentmatching is used here to estimate the parameters. The results of hypothesis testing using data from Hindukush and North East India are presented.

• Estimation of hypocentral parameters of local earthquakes when crustal layers have constantP-velocities and dipping interfaces

The paper describes an algorithm for estimating the hypocentral coordinates and origin time of local earthquakes when the wave speed model to be employed is a layered one with dipping interfaces. A constrained least-squared error problem has been solved using the penalty function approach, in conjunction with the sequential unconstrained optimization technique of Fiacco and McCormick. Joint confidence intervals for the computed parameters are estimated using the approach of Bard for nonlinear problems. These results show that when a hypocentre lies outside the array of recording stations and head waves from a dipping interface are involved, then its inclination must be taken into account for dip angles exceeding 5°.

• On self-similarity of premonitory patterns in the regions of natural and induced seismicity

Anticipating the scale invariance of rock fracturing processes, we applied Keilis-Borok’s algorithm M8, originally designed for identifying times of increased probability (TIPS) of occurrence of strong earthquakes (M &lt; 8.0), retrospectively to Koyna earthquakes which occurred in the region after the impoundment of the Shivaji Sagar reservoir in 1962. The algorithm which enables diagnosis of TIPS from the 7th year onwards after the commencement of the earliest available data set showed that the 5.3 magnitude earthquake of 20 September 1980 indeed occurred within a time of increased probability. This result, apart from its potential application to recognizing future TIPS in the region, points to selfsimilarity between the premonitory patterns of natural and induced earthquakes and to scale-invariant nature of their processes. Further, a typical precursory rise in seismicity followed by a relative quiescence was also found to precede all the three larger earthquakes of the sequence.

• Sensitivity of launch systems to gravity field

This paper considers the question of how sensitive inertially guided systems are to variations in the gravity field. There are systems which use other kinds of information for guidance, such as terrain. But, they will not be considered here.

• Preliminary results from very long period data collected by a broad band digital seismic station

Preliminary analysis of seismograms recorded by a wide band high dynamic range digital seismograph installed under a collaborative research programme between IPG, Paris and NGRI, Hyderabad, indicates that the crust and upper mantle structure below the Indian continent are characterized by high velocity up to a depth of 500 km. Both the group and phase velocities in the period range of 100–350s are found to be faster by 3–4% and 1–3% respectively compared with global models such as the preliminary reference earth model.

• Minimum norm inversion of observed ground elevation changes for slips on the causative fault during the 1905 Kangra earthquake

We estimate the distribution of slip in the dip section of the causative fault for the 1905 Kangra earthquake by applying the minimum norm inversion technique to differences in pre- and post-earthquake levelling data collected along the Saharanpur-Dehradun-Mussoorie highway. For this purpose it is assumed that the causative fault of the 1905 Kangra earthquake was planar with a dip of 5° in the northeast direction and that it had a depth of 6 km at the southern limit of the Outer Himalaya in Dehradun region. The reliably estimated maximum slip on the fault is 7.5 m under the local northern limit of the Outer Himalaya. Using the inverted slip distribution we estimate that the maximum permanent horizontal and vertical displacements at the surface due to the Kangra earthquake were about 4 m and 1.5m respectively. The maximum transient displacements at the surface should have exceeded these permanent displacements. These estimates of maximum slip on the causative fault and the resultant maximum permanent and transient displacements at the surface during the Kangra earthquake may be taken tentatively as being representative of the great Himalayan earthquakes.

• Microstrain stability of Peninsular India 1864–1994

We report the results of the South Indian Strain Measuring Experiment (SISME) designed to determine whether strain related to microseismicity in the past century may have deformed the networks of the 19th century Great Trigonometrical Survey of India (GTS). More than a dozen GTS points were measured between Mangalore, Madras, and Kanyakumari in southernmost India using GPS geodesy to determine regional deformation. Detailed measurements were made near two of the original baselines of the survey to determine the reliability of dilatational strain data for the network. The regional measurements revealed negligible regional dilatational (+ 11.2 + 10 microstrain) and shear strain changes (0.66± 1.2μradians) in the southernmost 530 km of India. In addition to these measurements, we determined the rate of northward and eastward motion of a point in Bangalore (1991–1994) in the ITRF92 reference frame to be 39 ± 3.5 mm/year, and 51 ± 11 mm/year respectively. This is consistent with NUVEL-1A plate motion estimate for India. Simultaneous measurements to a point near Kathmandu reveal that the Indian plate and the Southern Himalaya are moving approximately in unison, placing an upper limit on the rate of creep processes beneath the lesser Himalaya of ≈6 mm/year, and suggesting relatively rigid behavior of the Indian plate north of Bangalore. The stability of the Indian plate is confirmed by the absence of significant changes in the lengths of the two baselines at Bangalore and Cape Comorin, which, within the limits of experimental error have not changed since 1869. The measurements place an upper limit for recent deformation in the southern peninsula, and hence a lower limit for the renewal time for intraplate earthquakes in the region of approximately 10,000 years, assuming shear failure strain of approximately 100 μradians. This, in turn, implies that recurrence intervals for Peninsular Earthquakes far exceed the length of the written historic record, suggesting that the characterisation of seismic recurrence intervals from historical studies is likely to be fruitless. In contrast, the SISME experiment demonstrates that the noise level of geodetic studies based on 19th century GTS data is less than 0.02 μstrain/year, providing considerable scope for delineating regions of anomalously high seismogenic strain, by GPS measurements at all available trig points of the 19th century GTS survey.

• Straightforward inversion scheme (SIS) for one-dimensional magnetotelluric data

This paper presents a Straightforward Inversion Scheme (SIS) for interpreting one-dimensional magnetotelluric sounding data. The basic steps of SIS are (i) parameterization of the layered model such that the layer thickness, expressed in units of its skin depth, is a constant (α); (ii) expansion of the reflection function at each interface as a power series in parameter u = exp(-2(1 +j)α√f);(iii) development of a recurrence relation between the coefficients of the same powers ofu in the power series of reflection functions of any two successive layers; (iv) estimation of the impedance power series coefficients using regressed minimum norm estimator; and (v) evaluation of layer resistivities and thicknesses using the inverse recurrence relation. The power of SIS is established by inverting four synthetic data sets and two field data sets. The effect of noise is extensively studied on a synthetic data set, deliberately corrupted with increasing levels of Gaussian random noise up to 25%. It is found that the scheme can retrieve broad features of the true model even with noise levels as high as 25%. On the basis of findings of different experiments conducted on SIS, it is concluded that SIS is an efficient, robust algorithm with high resolving power. Further, being linear, it is non-iterative and it dispenses with the requirement of having to choose an initial guess model.

• Editorial

• Editorial

• Editorial

• Pre-seismic, co-seismic and post-seismic displacements associated with the Bhuj 2001 earthquake derived from recent and historic geodetic data

The 26th January 2001 Bhuj earthquake occurred in the Kachchh Rift Basin which has a long history of major earthquakes. Great Triangulation Survey points (GTS) were first installed in the area in 1856–60 and some of these were measured using Global Positioning System (GPS) in the months of February and July 2001. Despite uncertainties associated with repairs and possible reconstruction of points in the past century, the re-measurements reveal pre-seismic, co-seismic and post-seismic deformation related to Bhuj earthquake. More than 25 Μ-strain contraction north of the epicenter appears to have occurred in the past 140 years corresponding to a linear convergence rate of approximately 10 mm/yr across the Rann of Kachchh. Motion of a single point at Jamnagar 150 km south of the epicenter in the 4 years prior to the earthquake, and GTS-GPS displacements in Kathiawar suggests that pre-seismic strain south of the epicenter was small and differs insignificantly from that measured elsewhere in India. Of the 20 points measured within 150 km of the epicenter, 12 were made at existing GTS points which revealed epicentral displacements of up to 1 m, and strain changes exceeding 30 Μ-strain. Observed displacements are consistent with reverse co-seismic slip. Re-measurements in July 2001 of one GTS point (Hathria) and eight new points established in February reveal post-seismic deformation consistent with continued slip on the Bhuj rupture zone.

• Normalized impedance function and the straightforward inversion scheme for magnetotelluric data

This paper investigates the performance of normalized response function obtained by normalizing the Cagniard impedance function by a suitable factor and then rotating the phase by 45‡ to make it purely real for homogeneous half-space and equal to the square root of the half-space resistivity. Two apparent resistivity functions based on respectively the real and imaginary parts of this response function are proposed. The apparent resistivity function using the real part contains almost the same information as that yielded by the Cagniard expression while the one using the imaginary part qualitatively works as an indicator of the number of interfaces in the earth model. The linear straightforward inversion scheme (SIS), developed by the authors employing the concept of equal penetration layers, has been used to validate the proposed apparent resistivity functions. For this purpose, several synthetic and field models have been examined. Five synthetic models are studied to establish the veracity of the new functions and two well-studied published field data sets are inverted through SIS for comparison. We noticed that the new function and SIS compliment each other and lead to better understanding of the data information and model resolution.

• # Journal of Earth System Science

Volume 131, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019