V. P. Dimri

Scaling properties of potential fields due to scaling sources

The theoretical power spectrum of the 3-dimensional potential field caused by an arbitrary 3-dimensional source distribution is derived for gravity and magnetic data. A function with scale-invariant features has a power spectrum, which is proportional to the frequency raised to minus the scaling exponent. For scaling source distributions, the power spectrum of the gravity and magnetic field is anisotropic and a specific scaling exponent exists only for lower-dimensional cross sections of the field. We suggest an approach which allows, under certain conditions, to derive the power spectrum of a lower-dimensional subset from the power spectrum of a 3-dimensional function. For the special case where the 3-dimensional function has an isotropic scaling exponent β3D, we confirm a known property, namely that a (3-k)-dimensional subset of the function has a scaling exponent of approximately k less than β3D. This property is not applicable to the anisotropic 3-dimensional fields, but it can be applied to source distributions with isotropic scaling exponent. Summarizing our results, the scaling exponents of the density distribution and the gravity field are related by whereas the relationship between the scaling exponents of the susceptibility distribution and the magnetic field reduced to the pole can be stated as follows:

Potential field power spectrum inversion for scaling geology

We propose a method for inverting the power spectrum of gravity and magnetic data. The method is demonstrated on aeromagnetic and bore-well data from the German Continental Deep Drilling Project (KTB). Density and susceptibility distributions in the Earths crust exhibit scaling behavior with power spectra proportional to f -β , where f is the wavenumber and β is the scaling exponent of the source distribution. We model the sources of the potential field by a random function with scaling properties, defined on a half-space with its top at a specified depth beneath the observation plane. Comparing the theoretical power spectrum for this model with the power spectrum of the measured data, we obtain the best values for the depth to source and the scaling exponent as a global minimum of the misfit function. Despite the simplicity of the model, it offers a new understanding of the factors influencing the shape of the potential field power spectrum. In particular, the low wavenumber part of the power spectrum can be dominated by the scaling properties of the source distribution and not by the depth to some kind of basement. The scaling exponent of the field varies with the type of surface geology. The question of whether the scaling exponent can actually be used to identify different types of geology gives an interesting new aspect to power spectrum inversion.

Wavelet and rescaled range approach for the Hurst coefficient for short and long time series

The calculation of Hurst coefficient (H) by different techniques is sensitive to the length of the profile and noise. Synthetic fractional Brownian motions with different values of H have been generated and the effectiveness of the techniques has been tested on these time series. H values are calculated by wavelet transform (WT), power spectrum (PS), roughness length (RL), semi-variogram (SV), and rescaled range (R/S) methods. On the basis of the error estimates two methods: R/S analysis and WT are suggested for calculation of H for short/long datasets. Further, WT method is applied to geophysical data of the Bay of Bengal. The gravity, magnetic and bathymetry data indicate the self-affine nature with H=0.8, 0.8 and 0.9, respectively.

Depth Estimation from the Scaling Power Spectral Density of Nonstationary Gravity Profile

Abstract— A technique to estimate the depth to anomalous sources from the scaling power spectra of long nonstationary gravity profiles is presented. The nonstationary profile is divided into piecewise stationary segments based on the criterion of optimum gate length in which the time-varying and time-invariant autocorrelation functions are similar. The division of a nonstationary into piecewise stationary allows identification of the portion of the crust with different geological histories, and using the stationary portion of the gravity profiles, more consistent depths to the anomalous sources have been obtained. The technique is tested with the synthetic gravity profile and applied along the Jaipur-Raipur geotransect in western and central India. The geotransect has been divided into four stationary parts: Vindhyan low, Bundelkhand low, Narmada rift and Chhattisgarh basin; each section corresponding to a different geological formation. Forward modeling of gravity data using results of each stationary section is carried out to propose the subsurface structure along the Jaipur-Raipur transect.

Fractal geometry of faults and seismicity of Koyna-Warna region west India using LANDSAT images

Abstract—The Koyna-Warna region has been shaken by several earthquakes greater than magnitude 4 in the last 35 years. Four of them in 1967, 1973, 1980 and 1993, were potentially very destructive with magnitudes exceeding 5.0. The majority of seismic events recorded to date has been induced from Koyna-Warna reservoir areas. This paper discusses the fractal analysis of a fault map from LANDSAT images with the increasing seismic activity in the region. The region is divided into six blocks and the fractal dimension of each block is calculated using a box-counting technique. A plot of a three-dimensional map of the fractal dimension is prepared. It shows that the value of the fractal dimension is gently dipping from NE to SW. The fractal dimension is used to estimate the b-value in the frequency-magnitude relation of earthquakes in the region which is in agreement with earlier studies.

Gravity evidence for mid crustal domal structure below Delhi fold belt and Bhilwara super group of western India

A scheme to interpret nonstationary gravity profile is proposed in two steps (1) divide the entire nonstationary gravity profile into piecewise stationary sub-profiles, and (2) apply the scaling power spectral analysis to each sub-profile. The scheme is applied to gravity data along a well studied Nagaur- Jhalawar transect in western India. The profile has been subdivided into three sub-profiles; each sub-profile corresponds to a geological unit. Gravity data delineated a 2-D mid crustal domal structure below the Delhi fold belt and Bhilwara super group. Further, forward gravity modelling is carried out to model the subsurface along the entire profile.

Modelling of magnetic data for scaling geology

Interpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak−β , where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi-taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.

Spatial and Temporal Variations of b-Value and Fractal Analysis for the Makran Region

During the last three decades, the eastern segment of the Makran subduction zone has been more active than the western segment. We analyze Makran seismicity using the NEIC catalog from 1973 to 2008. A temporal decrease of b-value in eastern Makran indicates that stress is increasing, which may signal a future sizable earthquake. Also, the spatial variation of b suggests that the western segment is less stressed compared to the eastern segment. It has been observed that the fractal dimension is approximately twice the b value. The seismicity pattern analyzed does hold a key to understanding the seismotectonics of the region.

Study of CO2 EOR in a Sector Model from Mature Oil Field, Cambay Basin, India

Among various Enhanced Oil Recovery (EOR) methods, gas injection has been proven to be one of the effective ways of enhancing oil recovery from mature fields. The field under study has approached the economic limit of production under conventional recovery methods (primary and secondary recovery). Since start of production in sixties, the field has produced 48.5 % of the initial oil in place and the water cut has increased to 89 % in April 2011. Responding to the industry needs, initially a comprehensive study was performed to evaluate the potential of immiscible CO2 injection for the recovery of residual oil after water flooding in this mature field. This paper presents the preliminary results of immiscible CO2 injection on the basis of laboratory studies and detailed compositional simulations carried out on a sector model of the field. Based on the results obtained from laboratory studies it was found that CO2 injection yields significant incremental recovery. Simulation results show significant increase in field oil production, essentially from 200 to 1100 m3/day and considerable decrease in water cut were observed. In addition, detailed PVT simulations were carried out to obtain an equation of state (EOS) that would better describe the phase changes in the reservoir. These results would form the basis for carrying out CO2 EOR simulations on a field scale.

Tsunami Propagation and Inundation Due to Tsunamigenic Earthquakes in the Sumatra-Andaman Subduction Zone: Impact at Visakhapatnam

The Sumatra-Andaman arc is an active subduction zone that has generated several destructive tsunamis. The December 26, 2004, Sumatra-Andaman earthquake of magnitude Mw∼9.3 generated the most destructive tsunami known to man. The sustained high water level in several regions on the east coast of India due to tsunamis in the Bay of Bengal can be attributed to the reflection of direct tsunami waves and trapping of wave energy. In this paper we have simulated two scenarios of tsunamigenic earthquakes, the 2004 Sumatra earthquake and a possible great earthquake in the Andaman region. Tsunami wave propagation and inundation at Visakhapatnam due to these two earthquakes have been modeled. We find that the tsunami run-up heights for the 2004 Sumatra earthquake were about 1.5 m. For the other possible scenario, we observed that the run-up is about 3–4.6 m. The inundated distances have been estimated and are 1–2 km.