a SciTechnol journal Research Article Chesnokov et al., J Phys Res Appl 2017, 1:1 Journal of Physics Research and Applications All articles published in Journal of Physics Research and Applications are the property of SciTechnol, and is protected by copyright laws. Copyright © 2017, SciTechnol, All Rights Reserved. International Publisher of Science, Technology and Medicine 3D Seismic Heterogeneity Characterization for Karst, Fault and Fold Imaging: Statistical Approach Chesnokov EM 1 *, Bayuk IO 2 and Tiwary DK 3 Abstract The effective elastic properties ) ( ∗ ijkl C of a random heterogeneous medium can be presented in terms of average value ) ( > < ijkl C and the fuctuation ) ( ' ijkl C . In such medium, the amplitude of spatial correlation function will have non-zero value because the inclusions and matrix will have different elastic properties of. The higher contrast between the inclusions and host rock, the higher will be the amplitude of the spatial correlation function, and vice- versa. The heterogeneities having smaller and larger slowness are characterized by positive and negative normalized fuctuation, respectively. Theoretical modeling results, based on normalized fuctuation of traveltime slowness, to detect seismic heterogeneities in 3D random media is shown. We have used the radius of the spatial correlation function to calculate the extension of the inclusion in X-, Y- and Z-direction to demarcate the shape of heterogeneity. Upscaling of the physical properties of the medium is performed to calibrate the result to the seismic frequency range by changing the averaging window size. The properties of the medium inside the averaging window are assumed statistically homogeneous. Results obtained from this method show that as the size of the sliding window decreases the resolution of the heterogeneity increases. Keywords Seismic heterogeneity; Intrinsic attenuation; Seismic amplitude *Corresponding author: Evgeni M Chesnokov, Earth and Atmospheric Science Department, University of Houston, USA, Tel: (713) 743-2579; E-mail: emchesno@central.uh.edu Received: September 25, 2017 Accepted: October 20, 2017 Published: October 25, 2017 similarity of the adjacent waveforms in inline and crossline direction. Tey used cross correlation technique on adjacent traces to compute coherence coefcient from the seismic amplitude, and any changes in the nature of the traces was attributed to the seismic heterogeneity or discontinuity. Tree traces cross correlation algorithm was modifed with the introduction of semblance and eigendecomposition based coherence estimate [2-4]. Another well-known seismic attributes to delineate seismic heterogeneity is spectral decomposition which uses short-window Fourier transform to compare seismic waveform to precomputed waveform [5,6]. Seismic attributes analysis is based upon the concept to fnd: why the nature of one seismic trace is diferent than others and fnding out geological and geophysical reasons which may have attributed to these diferences. Velocities and their attenuation are two fundamental properties of the wave propagation that provide information about the saturation and structure of in situ rocks [7]. In a random heterogeneous media where size of the heterogeneity exceeds the wavelength of the seismic wave, scattering attenuation becomes more pronounced [8]. Te seismic velocity changes are generally related to the physical properties of the reservoir rocks, such as lithology, diferential pressure, temperature, fuid saturation, fuid viscosity, frequency and fuid mobility [9-15]. Te infuence of frequency on the seismic wave propagation in elastic media and porous media is studied by Mukerji and Mavko [16] and Vikhorev et al. [17], respectively. We have used statistical approach to characterize heterogeneous reservoir using the concept of normalized fuctuation; and the radius and amplitude of the spatial correlation function, to delineate small and large scale heterogeneity. Te question arises how the velocity should be treated in order to determine the location and size of fault or karst. In this work we suggest some characteristics derived from 3D seismic data, which are helpful in solving the problem. Application of normalized fuctuation, and correlation function amplitude and radius to detect heterogeneity is rarely available in literature. Geological Signifcance Sedimentary rocks, with few exceptions, are characterized as heterogeneous media whose physical properties changes from one point to other in space. A geologic formation is not composed by a single material but consists of a collection of diferent materials. Such heterogeneous composition occurs in many geological media where depositional processes that act over diferent characteristic time scales induce spatial patterns with diferent characteristic spatial scales. Commonly, a region having properties diferent than its adjacent region is called a heterogeneous system (Figure 1a). In sedimentary rock, lateral heterogeneities are generally related to the depositional environment. But in some cases the lateral heterogeneities might occur due to vertical throw of the faulted block across the fault plane (Figure 1b) or fault plane (Figure 1c). Heterogeneity associated with porosity, permeability, pore fuid properties, and conditions of pore pressure, temperature, and stress are generally post depositional, whereas lateral heterogeneities are caused by variations in the lithology due to facies change are syn-depositional in nature. Some other large scale post depositional heterogeneity, such as fold, fault can develop due to regional tectonics whereas development of karst is the result of dissolution of carbonate rock such as limestone and dolomite. Introduction Intrinsic attenuation and scattering are the two main causes of the seismic attenuation. In an attenuating medium, scattering and intrinsic attenuation afect diferently depending upon the size of the heterogeneity and the wavelength of the propagating wave and therefore, a medium becomes frequency dependent. Te traveltime of seismic wave will be the refection of the medium through which the wave has traveled. In a heterogeneous medium, each seismic trace is supposedly unique because it travels through unique path and refects the characteristics of the medium through that path. Te information of the medium imbedded in the seismic traces can be deconvolved as seismic attributes which can be used for reservoir characterization. During the last fve decade, exploration geophysicists have come up with more than ffy seismic attributes which have been applied to reservoir characterization. Bahorich and Farmer [1] analyzed the