Shallow lithosphere-asthenosphere boundary beneath Cambay Rift Zone of India: Inferred presence of carbonated partial melt

A vast area between Phalodi in Jodhpur and Pokaran in Jaisalmer district of western Rajasthan, is occupied distinctly by rocky, shallow gravelly surfaces and occasional hills. These surfaces exhibit quartz and quartzite pebbles, angular, sub-angular and few rounded sandstone gravels, have slightly convex outline and can be best described as desert pavements. Such land features assume significance because of their extent and variability under a dominantly dry aeolian environment. Morphology and distributional pattern of such formations indicate that sediments are either of in situ origin or may have been transported to a short distance. The present study is based on field level assessment of such surfaces in the above two desert districts. Over much of the area, the profile shows a surficial concentration of gravels followed by thick sand and silt mixed with gravels and then the parent material. There are also occasional rock outcrops of very low relief exhibiting vertical, horizontal and conchoidal pattern of fractures over these surfaces near Pokaran and north of Jaisalmer which indicate disintegration of rocks under extreme diurnal fluctuation of temperature. Such manifestations in the morphology indicate impact of both thermal as well as aeolian processes. In the east of Jaisalmer town near Basanpir and Bhojka, the pavement surfaces are found covered with abundant sub-rounded to rounded pebbles and cobbles. This type of condition would indicate a profound action by fluvial activities followed by wind sorting. Our study found significant spatial variability in the distribution of pavement surfaces, which carried imprints of climatic fluctuations and environment of deposition during Holocene.     

Hybrid Gaussian-cubic radial basis functions for scattered data interpolation

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent; however, for the datasets having insufficient observations, RBFs have the advantage over geostatistical methods as the latter requires variogram study and statistical expertise. Moreover, RBFs can be used for scattered data interpolation with very good convergence, which makes them desirable for shape function interpolation in meshless methods for numerical solution of partial differential equations. For interpolation of large datasets, however, RBFs in their usual form, lead to solving an ill-conditioned system of equations, for which, a small error in the data can cause a significantly large error in the interpolated solution. In order to reduce this limitation, we propose a hybrid kernel by using the conventional Gaussian and a shape parameter independent cubic kernel. Global particle swarm optimization method has been used to analyze the optimal values of the shape parameter as well as the weight coefficients controlling the Gaussian and the cubic part in the hybridization. Through a series of numerical tests, we demonstrate that such hybridization stabilizes the interpolation scheme by yielding a far superior implementation compared to those obtained by using only the Gaussian or cubic kernels. The proposed kernel maintains the accuracy and stability at small shape parameter as well as relatively large degrees of freedom, which exhibit its potential for scattered data interpolation and intrigues its application in global as well as local meshless methods for numerical solution of PDEs.     

Enforcing smoothness and assessing uncertainty in non-linear one-dimensional prestack seismic inversion

Estimation of elastic properties of rock formations from surface seismic amplitude measurements remains a subject of interest for the exploration and development of hydrocarbon reservoirs. This paper develops a global inversion technique to estimate and appraise 1D distributions of compressional‐wave velocity, shear‐wave velocity and bulk density, from normal‐moveout‐corrected PP prestack surface seismic amplitude measurements. Specific objectives are: (a) to evaluate the efficiency of the minimization algorithm (b) to appraise the impact of various data misfit functions, and (c) to assess the effect of the degree and type of smoothness criterion enforced by the inversion. Numerical experiments show that very fast simulated annealing is the most efficient minimization technique among alternative approaches considered for global inversion. It is also found that an adequate choice of data misfit function is necessary for a reliable and efficient match of noisy and sparse seismic amplitude measurements. Several procedures are considered to enforce smoothness of the estimated 1D distributions of elastic parameters, including predefined quadratic measures of length, flatness and roughness. Based on the general analysis of global inversion techniques, we introduce a new stochastic inversion algorithm that initializes the search for the minimum with constrained random distributions of elastic parameters and enforces predefined autocorrelation functions (semivariograms). This strategy readily lends itself to the assessment of model uncertainty. The new global inversion algorithm is successfully tested on noisy synthetic amplitude data. Moreover, we present a feasibility analysis of the resolution and uncertainty of prestack seismic amplitude data to infer 1D distributions of elastic parameters measured with wireline logs in the deepwater Gulf of Mexico. The new global inversion algorithm is computationally more efficient than the alternative global inversion procedures considered here.     

On propagation of love-type waves on a spherical model with rigidity and density both varying exponentially with the radial distance

Summary The propagation of Love type waves on a spherical model' in the mantle of which the rigidity and density vary exponentially with the radial distance while in the core they remain constant — has been investigated. The frequency equation that has been worked out has been examined in detail for the existence of root in the particular cases when they involve Bessel Functions of smallest and largest orders.     

Uncertainty propagation in orbital mechanics via tensor decomposition

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.     

Lithospheric structure below transantarctic mountain using receiver function analysis of TAMSEIS data

The lithospheric structure of Antarctica has been investigated from P- (PRF) and S- receiver functions (SRF) using the seismological data from Trans-Antarctic Mountain Seismic Experiment (TAMSEIS). For the stations deployed on the thick ice sheet, estimation of crustal parameters from PRF may be erroneous as the Moho conversions may interfere with the reverberations within the thick ice sheet. However, the free surface multiples are well observed in PRF. On the other hand, in SRFs, the primary conversions of interest and multiples are separated by the mother S-phase. Therefore, it is advantageous to interpret PRF and SRF jointly for the regions where we have thick low velocity layer at the top such as ice or sediments. The crustal structure and corresponding parameters have already been estimated by various workers, but here we interpret the PRF and SRF jointly to minimize the ambiguity and map the lithospheric architecture below TAM. Our analysis reveals that the average crustal thickness beneath the east Antarctica craton is ～44 km with Vp/Vs ranging between ～1.7 and 1.9. Below Trans-Antarctic Mountain (TAM), the average crustal thickness is ～36 km with higher Vp/Vs of ～1.8–2.0. The rift and the volcanic affected coastal region show erratic depths and Vp/Vs, primarily due to the absence of either primary conversion or multiples in the receiver functions. A small number of stations far from the volcano show that the crust is thinnest (～26 to 34 km thick) in the coastal part. The contribution of this study is the mapping of the lithospheric configuration, not done so far using SRF. The SRF section along a profile spanning E-, W- Antarctica and TAM reveals that the lithospheric thickness in the coast is ～80 km and below TAM it is ～120 km. In the central thick ice cover region, the lithosphere thickens upto ～150 km towards Vostok highlands. The most intriguing feature in our SRF section is that the crust and lithosphere are shallow below TAM compared to the E- Antarctica. Further, we observe a mid-lithospheric low velocity layer confined mostly below TAM, suggesting that the thermal buoyancy could be the prime cause for the upliftment of TAM.     

A Comparative study between two models of propagation of spherical and cylindrical shock waves with varying energy in self-gravitating, magneto-radiative non-uniform atmosphere

Two theoretical models, spherical and cylindrical, of propagation of shockwaves with varying energy in a rotating, magneto-radiative,self-gravitating non-uniform atmosphere have been developed. Subsequently,a comparison between the two models has been drawn with the aid ofvariation of flow variables with distance graphically. Significant is thedifference between two models, when one observes the variations of radialvelocity, pressure, mass, radiation flux, magnetic field and energy withdistance. Also, the respective influences of radiation flux, magneticfield and rotational velocity on the variations of the flow variables havebeen studied.     

Time‐lapse pre‐stack seismic data registration and inversion for CO2 sequestration study at Cranfield

Pre‐stack seismic data are indicative of subsurface elastic properties within the amplitude versus offset characteristic and can be used to detect elastic rock property changes caused by injection. We perform time‐lapse pre‐stack 3‐D seismic data analysis for monitoring sequestration at Cranfield. The time‐lapse amplitude differences of Cranfield datasets are found entangled with time‐shifts. To disentangle these two characters, we apply a local‐correlation‐based warping method to register the time‐lapse pre‐stack datasets, which can effectively separate the time‐shift from the time‐lapse seismic amplitude difference without changing the original amplitudes. We demonstrate the effectiveness of our registration method by evaluating the inverted elastic properties. These inverted time‐lapse elastic properties can be reliably used for monitoring plumes.     

Suppressing non‐Gaussian noises with scaled receiver wavefield for reverse‐time migration: comparison of different approaches

Numerical implementation of the gradient of the cost function in a gradient‐based full‐ waveform inversion (FWI) is essentially a migration operator used in wave equation migration. In FWI, minimizing different data residual norms results in different weighting strategies of data residuals at receiver locations prior to back‐propagation into the medium. In this paper, we propose different scaling methods to the receiver wavefield and compare their performances. Using time‐domain reverse‐time migration (RTM), we show that compared to conventional algorithms, this type of scaling is able to significantly suppress non‐Gaussian noise, i.e., outliers. Our tests also show that scaling by its absolute norm produces better results than other approaches.