Limited vertical resolution of logging tools causes shoulder-bed effects on borehole measurements, therefore biases in the assessment of porosity and hydrocarbon saturation across thinly-bedded rock formations. Previously, a combined inversion procedure was developed for induction resistivity and density logs to improve the petrophysical assessment of multi-layer reservoirs. In this paper, we include the inversion of gamma-ray (GR) logs in the interpretation method and evaluate three field cases that comprise hydrocarbon-saturated Tertiary turbidite sequences. On average, inversion results yield 19% better agreement to core measurements and lead to 28% increase in hydrocarbon reserves when compared to standard well-log interpretation procedures. The most critical step for reliable and accurate inversion results is the detection/selection of bed boundaries. Inversion of field data also indicates that the minimum bed thickness resolvable with combined inversion is approximately 0.7ft (0.21m), and that inflection points of density logs are the best option for bed-boundary detection. Combined inversion also allows the detection of noisy, inconsistent, and inadequate measurements, including cases of abnormal measurement-correction biases otherwise difficult to diagnose on processed logs.
Superposition of individual-bed responses near layer boundaries causes shoulder-bed effects on borehole measurements. The corresponding effect on petrophysical interpretation depends on both the physical property being measured and the difference between vertical resolution of the measurement and bed thickness. Deterministic inversion is commonly used to reduce shoulder-bed effects on borehole measurements. In so doing, bed boundaries are first detected and continuous logs are transformed into piecewise-constant vertical distributions of properties, i.e. continuous logs are transformed into blocky-log representations for subsequent petrophysical analysis. Although the resolution of logging tools depends on the source-sensor arrangement, logging speed, sensor resolution, source strength, volume of investigation, borehole conditions, etc., there are typical values specified in the literature (Dewan, 1983; Passey et al., 2006). On the other hand, layers are generally designated as thick or thin depending on whether their thickness is above or below, respectively, of the vertical resolution of conventional logs. In this paper, we designate layers following Campbell's (1967) thickness-based classification and the methods that are commonly used to interpret their log responses. Figure 1 shows the classification of layers that we have adopted in our study, as well as typical values of vertical resolution assumed for various logging tools. Shoulder-bed effects in very thick layers are regarded negligible because in those cases the vertical resolution of the measurements is shorter than the thickness of the layers; i.e. well logs have the resolution necessary to resolve true layer petrophysical properties. The thickness of thick and medium beds is comparable to the vertical resolution of most conventional well logs, whereby logs can be adversely affected by shoulder beds to the point of rendering standard log analysis unreliable. Deterministic inversion can be used to reduce shoulder-bed effects and improve the estimation of true physical and petrophysical properties of multi-layer sequences. Conventional well logs cannot resolve thin beds, very thin beds, or laminations because bed thickness is too small when compared to the vertical resolution of logs.