Thin Bed Information Resolution Of Well-logs And Its Applications

We develop the theoretical potential of well logs for distinguishing thin beds, and introduce a new vertical resolution concept for logs, thin bed information resolution (TBIR). This is developed by combining Walsh function theory, linear systems theory, and logging instrument response functions. The relationship between minimum bed thickness and Walsh functions is established. Two definitions and three theorems are introduced to support the relationship. TBIR is defined and explained using two examples, and is then applied to enhance the vertical resolution of a sonic interval transit time log and an induction conductivity log. The results show that both logs have information resolution of 0.25m when the sampling interval in depth is 0.125m. TBIR is higher than the vertical resolution as usually defined. Moreover, TBIR can also be helpful in the development of new logging instruments that are desired to possess both deep radial investigation and high vertical resolution.