An Improved Complex Image Theory for Fast Resistivity Modeling and Its Application to Geosteering

Summary azimuthal resistivity logging-while-drilling (LWD) tools with tilted antennas (Bittar 2002; Li et al. 2005) are widely used in geosteering because of their azimuthal sensitivity and the relatively large depth of investigation compared with other LWD tools such as nuclear, acoustic, or gamma ray measurements. Compared with conventional resistivity tools, azimuthal-resistivity LWD measurements can provide additional information including distance-to-boundary, relative dip angle, and resistivity anisotropy (Li et al. 2014). Because of the computing efficiency requirement, modeling and inversion of azimuthal-resistivity LWD measurements are usually based on a 1D parallel-layer model in practice (Zhong et al. 2008). Clearly, this 1D model assumption is not applicable to some realistic situations such as when the tool is navigating in unparallel-layer formation, or approaching a fault. The 3D full-wave simulations such as finite-difference or finite-element methods can handle the complex cases, but they are generally too slow for real jobs, not to mention the inversion that is based on iterative calls of forward modeling. An approximation method called complex image theory was proposed for geophysical prospecting (Wait 1969; Bannister 1986), and recently was introduced to well logging (Dong and Wang 2011; Wang and Liu 2014). This theory approximates electromagnetic-wave reflection by an interface between local and adjacent beds as signal radiated from a virtual source with a complex distance from the observation point. The complex image theory can be several orders of magnitude more efficient than 3D simulations. However, it also has several limitations: This method only works in resistive beds with conductive shoulders, and the measurement cannot be too close to bed interfaces. Those shortcomings greatly limit this method to more extensive applications. An improved complex image theory is proposed here to tackle the aforementioned difficulties. This improved theory can handle a very short distance from the tool to a bed interface as well as the scenarios in which the source is in a conductive bed instead of a resistive one. One can implement robust inversion schemes on the basis of this method. The effectiveness and efficiency of this method are verified by several numerical examples as well as laboratory tests and field jobs.

Download Full-text

Multichannel processing for airborne gamma‐ray spectrometry

Geophysics ◽

10.1190/1.1444491 ◽

1998 ◽

Vol 63 (6) ◽

pp. 1971-1985 ◽

Cited By ~ 10

Author(s):

Brian R. S. Minty ◽

Phil McFadden ◽

Brian L. N. Kennett

Keyword(s):

Gamma Ray ◽

Principal Component ◽

Observation Point ◽

Gamma Ray Spectrometry ◽

Spectrometric Data ◽

Additional Information ◽

Relative Contribution ◽

Multichannel Processing ◽

Best Fit ◽

Broad Energy

The conventional approach to the processing of airborne gamma‐ray spectrometric data is to first sum the observed spectra over three relatively broad energy windows. These three window count rates are then processed to obtain estimates of the potassium (K), uranium (U), and thorium (Th) elemental abundances. However, multichannel spectra contain additional information on the concentrations of K, U, and Th in the source, on the distance between the source and the detector, and on the relative contribution of atmospheric radon to the observed spectrum. This information can be extracted using multichannel processing procedures. The observed spectrum is considered as the sum of three terrestrial and three background component spectra, which are determined through suitable airborne and ground calibrations. The background components can be calculated independently and removed from the observed spectra. A parametric model based on a principal component analysis of the terrestrial components as functions of simulated detector height is then used to find the effective heights at which the K, U, and Th terrestrial components best fit the background‐corrected airborne data. The component spectra for these heights are then fitted to the background‐corrected observed spectra to obtain elemental count rates. The multichannel processing results in significant reductions in the fractional errors associated with the estimated elemental count rates. For three surveys processed using the new methodology, the average deviations of the K, U, and Th elemental count rates from the estimated mean elemental count rates at each observation point are reduced by 12.4%, 26.5 %, and 20.3 %, respectively, when compared with the conventional three‐channel method. This results in a better structural resolution of small anomalies in enhanced images of the processed data.

Download Full-text

LEARNINGS FROM SPECTRAL GR MEASUREMENTS FROM LWD AND FROM CUTTINGS IN HIGH AND LOW ANGLE WELLS

10.30632/spwla-2021-0062 ◽

2021 ◽

Author(s):

Mohamed Azizi Ibrahim ◽

◽

Faisal Al-Enezi ◽

Marie Van Steene ◽

Alan Fernandes ◽

...

Keyword(s):

Gamma Ray ◽

Potassium Feldspar ◽

Heavy Minerals ◽

High Angle ◽

Volume Calculation ◽

X Ray ◽

Additional Information ◽

Elemental Concentrations ◽

Depth Control ◽

Good Agreement

Spectral gamma-ray (SGR) data were acquired from a new slim logging-while-drilling (LWD) tool and from surface cuttings in a near vertical well and in a horizontal well across clastic deposits. Comparison of the data from both measurements indicates that there are advantages from both methods. X-ray diffraction (XRD) and X-ray fluorescence (XRF) data from cuttings also support the findings. The formation evaluation objective is to quantify the volumes of each mineral and fluid present in the formation. SGR data brings the required additional information to reduce the mineral volume uncertainty, especially for the clays in the formation with complex mineral assemblages. In the studied clastic deposits, several clay types are present (with the dominant contribution from illite and kaolinite) together with feldspars and trace elements like zircon and other heavy minerals. The presence of gas introduces another unknown, since it affects the porosity measurements and fluid volume calculation through bulk density and neutron porosity. The comparison of SGR data from LWD logs and from cuttings brings robustness to our conclusions. Comparison of the thorium, potassium, and uranium concentrations from LWD logs and from cuttings shows good agreement in the measurements for the low-angle well. The high-angle well data also shows good agreement between the two measurements except for the cleaner sand section. The results from the cuttings are affected by the accuracy of sample depth control due to the poor borehole conditions and inefficiency in evacuating cuttings in high-angle wells compared to low-angle wells. The trend of the SGR is maintained. The LWD SGR elemental concentrations are then used to solve the formation mineral fractions, which are compared with the same fractions from the XRD on cuttings. Similar conclusions are drawn for the elemental concentrations. The potassium concentration enables the quantification of illite and potassium feldspar. Uranium brings a significant contribution to the total GR measurement, which could lead to a clay volume overestimation if the uranium contributions weren’t excluded. In conclusion, LWD provides superior quality SGR data compared with SGR from cuttings because of the better depth control and vertical resolution. SGR on cuttings can be an alternative when combined with other LWD measurements and accepting a higher uncertainty, in case LWD SGR cannot be run due to certain borehole conditions. This paper compares the results of a slim tool LWD and cuttings SGR data for the first time and concludes on the applicability of each technique.

Download Full-text

Applications of complex image theory

Radio Science ◽

10.1029/rs021i004p00605 ◽

1986 ◽

Vol 21 (4) ◽

pp. 605-616 ◽

Cited By ~ 44

Author(s):

Peter R. Bannister

Keyword(s):

Image Theory ◽

Complex Image

Download Full-text

Electromagnetic field radiated from a horizontal magnetic dipole immersed in seawater based on complex image theory

OCEANS 2017 - Aberdeen ◽

10.1109/oceanse.2017.8084851 ◽

2017 ◽

Author(s):

Aiping Huang ◽

Linwei Tao

Keyword(s):

Electromagnetic Field ◽

Magnetic Dipole ◽

Image Theory ◽

Complex Image

Download Full-text

Interpretation of total gamma logs in thin and dipping beds

Geophysics ◽

10.1190/1.1441069 ◽

1980 ◽

Vol 45 (12) ◽

pp. 1847-1856

Author(s):

Donald C. Moore

Keyword(s):

Gamma Ray ◽

Mass Attenuation Coefficient ◽

Integral Function ◽

Calibration Model ◽

Linear Absorption Coefficient ◽

Linear Absorption ◽

K Factor ◽

Proportional Relationship ◽

Dip Angle ◽

Gamma Ray Log

The proportional relationship between the grade‐thickness product and the area under a gross gamma‐ray log is well known and generally accepted as correct. A set of conditions for its correctness is derived. It is shown that the proportionality factor (K factor) is independent of the dip angle of the bed, because both the thickness of the bed (measured along the borehole) and the area under the gross gamma‐ray log increase in the ratio of the secant of the dip angle. Experimental data supporting this conclusion are presented. It is also shown that the dip angle of a relatively thick bed can be estimated by deconvolving the log near the edge of the bed. Finally, the comparison parameters between a formation and a calibration model are shown to be grade, gamma‐ray mass attenuation coefficient, moisture content, and an integral function of the build‐up factor and the gamma‐ray linear absorption coefficient.

Download Full-text