• Sri Niwas

Articles written in Journal of Earth System Science

• Electrical resistivity anomalies over hydrocarbon bearing structures

The present study is aimed at working out the possible resistivity anomalies associated with hydrocarbon bearing structures. The anomaly due to a typical two-dimensional anticlinal structure filled with hydrocarbon, and overlying a basement of infinite resistivity was computed using the conformal mapping technique. A more realistic and elaborate model, which could not be simplified by conformal mapping, was studied using the finite element method. This model consisted of a two-dimensional anticlinal structure filled with oil or gas-embedded midway in a homogeneous layer which itself overlies a half-space of infinite resistivity, the electrical resistivity of the hydrocarbon bearing structure being simulated as infinite.

• Fast automatic solution of the inverse resistivity problem

The paper presents a fast automatic approach to solve the inverse resistivity problem, assisted by optimization, which is a non-linear model-fitting technique. The selected inverse problems are ill-posed and the inverse solution is defined by ‘best fit’ in the sense of least-squares. Formulations are presented in a systematic manner for Newton’s method, least squares method and Marquardt’s modification (ridge regression) method based on local linearization of non-linear problem. The convergence of least-squares method and Marquardt’s method, to provide a robust solution, are first tested on a theoretical model and effectiveness of Marquardt’s method is demonstrated, and then two-field apparent resistivity curves from Banda district, India are interpreted and discussed.

• 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.

• Inversion of GDS data of northwest Himalaya using EM2INV

This paper reviews the validity of earlier models obtained after quantitative interpretation of GDS data and presents a fresh model using the inversion scheme EM2INV. The 2-D inversion of data is more objective than the earlier interpretation performed by using trial and error method. The inversion results indicate that the present model differs from the earlier ones. The reason could be that available GDS data are sufficient only for deriving the horizontal variation of subsurface resistivity. In order to study the vertical resistivity variation additional MT sounding data would be required. It would therefore be desirable to carry out MT survey in the specified area. A more comprehensive/appropriate model could be derived from joint inversion of GDS and MT data.

• EM2INV — A finite difference based algorithm for two-dimensional inversion of geoelectromagnetic data

The paper presents an efficient finite difference based 2D-inversion algorithm, EM2INV, for geoelectromagnetic data. The special features of the algorithm are

• optimal grid generation based on grid design thumb rules,

• finite domain boundary conditions,

• interpolation matrix that permits generation of response at observation points different from grid points,

• Gaussian elimination forward matrix solver, that enables reuse of already decomposed coefficient matrix,

• super-block notion that reduces the number of blocks with unknown resistivities and, in turn, the size of Jacobian matrix and

• bi-conjugate gradient matrix solver for inverse problem which circumvents the need of explicit Jacobian matrix computation.

The algorithm is tested rigorously by setting up exercises of diverse nature and of practical significance. The stability of the algorithm is established by inverting the synthetic response corrupted with Gaussian noise. The inversion experiments are aimed at studying

• relative performance of response functions,

• inversion quality of E- and B-polarization data,

• efficacy of single and multi-frequency data inversion,

• minimum number of frequencies and observation points needed for successful data inversion.

It has been observed that the Magneto-telluric data deciphers better the vertical position of the target and Geomagnetic Depth Sounding data deciphers the horizontal variations in a better way. The conductive and resistive bodies are better resolved by inversion of E- and B-polarization data respectively. The results of multi-frequency inversion imply that the increase in the number of frequencies does not necessarily enhance the inversion quality especially when the spread of observation points is sufficiently large to sense the target. The study of a minimum number of observation points highlights the importance of single point inversion that furnishes useful information about the inhomogeneity.

• 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.

• Fast computation of Hankel Transform using orthonormal exponential approximation of complex kernel function

The computation of electromagnetic (EM) fields, for 1-D layered earth model, requires evaluation of Hankel Transform (HT) of the EM kernel function. The digital filtering is the most widely used technique to evaluate HT integrals. However, it has some obvious shortcomings. We present an alternative scheme, based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals. This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature. This expansion reduces the integral to a simple algebraic sum. The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated. The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method. The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital filtering technique with Anderson filters. The field curves for four types (A-, K-, H-and Q-type) of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson sc heme. It is concluded that the present scheme is more accurate than the Anderson scheme

• Magnetotelluric investigations for imaging electrical structure of Garhwal Himalayan corridor, Uttarakhand, India

Magnetotelluric investigations have been carried out in the Garhwal Himalayan corridor to delineate the electrical structure of the crust along a proﬁle extending from Indo-Gangetic Plain to Higher Himalayan region in Uttarakhand,India.The proﬁle passing through major Himalayan thrusts:Himalayan Frontal Thrust (HFF),Main Boundary Thrust (MBT)and Main Central Thrust (MCT),is nearly perpendicular to the regional geological strike.Data processing and impedance analysis indicate that out of 44 stations MT data recorded,only 27 stations data show in general,the validity of 2D assumption.The average geoelectric strike, N70°W, was estimated for the proﬁle using tensor decomposition.2D smooth geoelectrical model has been presented,which provides the electrical image of the shallow and deeper crustal structure.The major features of the model are (i)a low resistivity (&gt; 50𝛺 m),shallow feature interpreted as sediments of Siwalik and Indo-Gangetic Plain,(ii)highly resistive (&lt; 1000 𝛺m)zone below the sediments at a depth of 6 km,interpreted as the top surface of the Indian plate,(iii)a low resistivity (&gt; 10𝛺 m) below the depth of 6 km near MCT zone coincides with the intense micro-seismic activity in the region. The zone is interpreted as the partial melting or ﬂuid phase at mid crustal depth.Sensitivity test indicates that the major features of the geoelectrical model are relevant and desired by the MT data.

• Efficient two-dimensional magnetotellurics modelling using implicitly restarted Lanczos method

This paper presents an efficient algorithm, FDA2DMT (Free Decay Analysis for 2D Magnetotellurics (MT)), based on eigenmode approach to solve the relevant partial differential equation, for forward computation of two-dimensional (2D) responses. The main advantage of this approach lies in the fact that only a small subset of eigenvalues and corresponding eigenvectors are required for satisfactory results. This small subset (pre-specified number) of eigenmodes are obtained using shift and invert implementation of Implicitly Restarted Lanczos Method (IRLM). It has been established by experimentation that only 15–20% smallest eigenvalue and corresponding eigenvectors are sufficient to secure the acceptable accuracy. Once the single frequency response is computed using eigenmode approach, the responses for subsequent frequencies can be obtained in negligible time. Experiment design results for validation of FDA2DMT are presented by considering two synthetic models from COMMEMI report, Brewitt-Taylor and Weaver (1976) model and a field data based model from Garhwal Himalaya.

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019