A Continuous Parameter Homogeneous Semi-Markov Model for Stratigraphic Analyses from Borehole Data
Alaa Ibrahim Ali and Upmanu Lall: Department of Civil and Environmental Engineering and Utah Water Research Laboratory, Utah State University

Abstract: Markov chain models are often used to represent subsurface stratigraphy and to simulate likely representations of the subsurface. The data used are cores or boreholes. Rock types are classified into a finite set of states, and a state transition probability matrix is estimated for some vertical sampling interval, Dz. The estimated transition probability matrix is sensitive to the Dz used. No objective methods for selecting a Dz are available. The underlying deposition process is continuous rather than discrete. Hence, information is lost by discretizing the sampling domain, irrespective of the Dz used.
The thrust of this article is to develop a Markov chain model of subsurface stratigraphy that explicitly considers layer thickness statistics, recognizes the continuous nature of the underlying deposition process, and does not suffer from the problems associated with sample discretization. A finite set of rock types is considered, and a state transition intensity matrix is estimated from interpreted borehole stratigraphic sequences. A simulation strategy is developed by using the transition intensity matrix to determine the state-by-state transitions and by bootstrapping (sampling with replacement from the empirical distribution function) a layer thickness corresponding to the new state from the borehole data. Example applications are provided to demonstrate the utility of the method.

Utilization of Interwell Seismic Logging for Formation Continuity at the Gypsy Test Site, Oklahoma
Jorge O. Parra and Brian J. Zook: Southwest Research Institute, San Antonio, Texas Hughbert A. Collier: Tarleton State University, Stephenville, Texas

Abstract: In-seam seismic or continuity logging consists of locating a seismic source in one borehole near or in a low-velocity layer and deploying a detector array in a second borehole. Detection of guided waves transmitted between the two wells indicates bed continuity. The guided wave signatures are either leaky modes or normal modes (or both).
In-seam seismic logging has been utilized in coal geophysics to determine discontinuities in coal seams. However, the technique has numerous applications in various types of heterogeneous geological environments. It can be used to determine the continuity of beds between wells, estimate and locate variations in the thickness of beds, and estimate the average rock physical properties of the beds. In this article we explain the technique of interwell seismic logging and analyze the propagation of guided waves in a fluvial sandstone formation at the Gypsy test site in Oklahoma. The study consists of an integration of the well logs, lithology, and interwell seismic data to determine the origin of the waveforms associated with specific geologic units. Selected full waveforms are correlated with the geologic units of interest, processed, and interpreted to identify trapped wave trains that may be associated with the presence of guided waves. Seismic events are extracted from the interwell seismic data using time-frequency representation techniques to analyze their propagation characteristics, which can be used to identify continuity of beds.
Analysis of the data suggests the presence of a continuous low-velocity clean sandstone in the Gypsy interval. The correlation of sandstone and shale units from well logs and guided waves is consistent with pressure-pulse test data. The pressure tests indicate the sands are in pressure communication between wells and that there is an impermeable barrier between the top and the bottom of the sand units in the Gypsy sandstone interval.

Borehole Geophysical Signatures of Kimberlites in Canada
C.J. Mwenifumbo, P.G. Killeen, and B.E. Elliott: Geological Survey of Canada, Ottawa, Canada

Abstract: Multiparameter borehole geophysical measurements were conducted at one kimberlite pipe in Saskatchewan and at four pipes in the Kirkland Lake area in Ontario to obtain in-situ physical rock property data in kimberlites and their host rocks. The measurements included natural gamma ray spectrometry, magnetic susceptibility, resistivity/conductivity, induced polarization, spectral gamma gamma (density and heavy element indicator), temperature, borehole three-component magnetometer, and seismic P-wave velocity. Most of the geophysical measurements show anomalous values within the kimberlite pipes compared to those in the host rocks. These geophysical parameters, however, vary considerably within individual kimberlite pipes and between the different pipes, primarily because of the different facies and source material of kimberlite intrusions. Density, magnetic susceptibility, and P-wave velocity logs indicate higher values in kimberlite compared to the overlying sediments at the Fort á la Corne kimberlite pipe in Saskatchewan. Crossplots for measurements of conductivity, magnetic susceptibility, gamma ray activity, and spectral gamma gamma ratio (SGGR) in the kimberlites indicate several distinctly different subpopulations of kimberlitic material that represent different eruptive phases of kimberlite in the Fort á la Corne pipe. There are no relationships between the various geophysical parameters except for the magnetic susceptibility and conductivity that are positively correlated. The geophysical signature of the C14 kimberlite pipe in the Kirkland Lake area of Ontario is different from that of the Fort á la Corne pipe that comprises kimberlite with crater facies pyroclastics. Most of the geophysical variables from the C14 pipe are moderately to highly correlated. The C14 pipe consists of diatreme and hypabyssal facies kimberlites that have distinct geophysical signatures. The diatreme facies kimberlites are characterized by lower density, resistivity, gamma ray activity, and magnetic susceptibility than the hypabyssal facies kimberlites. Crossplots and two-dimensional kernel density distribution analysis reveal several clusters that correspond to the different kimberlite units. hg