Abstract: Through analysis on an effective detection space of a gamma detector, a one-dimensional equivalent longitudinal contribution coefficient (varying with a distance between a formation and the detector) of a natural gamma-ray flux received by the gamma detector under the condition that the formation and a wellbore are orthogonal is obtained in the effective detection space, and then a corresponding function expression is given by fitting. An integral of a gamma-ray flux received by the detector under the condition of a deviated well is converted into a one-dimensional equivalent integral problem under the condition of a straight well, so as to achieve the fast forward of natural gamma-ray logging of the formation under the conditions of highly-deviated and horizontal wells. This simplified fast forward algorithm can replace a gamma forward method of spherical spatial-division integrals in parallel sedimentary formations, reduce a space-time complexity of algorithms, and improve a calculation efficiency.

Abstract: Through analysis on an effective detection space of a gamma detector, a one-dimensional equivalent longitudinal contribution coefficient (varying with a distance between a formation and the detector) of a natural gamma-ray flux received by the gamma detector under the condition that the formation and a wellbore are orthogonal is obtained in the effective detection space, and then a corresponding function expression is given by fitting. An integral of a gamma-ray flux received by the detector under the condition of a deviated well is converted into a one-dimensional equivalent integral problem under the condition of a straight well, so as to achieve the fast forward of natural gamma-ray logging of the formation under the conditions of highly-deviated and horizontal wells. This simplified fast forward algorithm can replace a gamma forward method of spherical spatial-division integrals in parallel sedimentary formations, reduce a space-time complexity of algorithms, and improve a calculation efficiency.

Abstract: A method for clipping a two-dimensional (2D) polygon against a rectangular view window, including inputting a vertex coordinate set A? of the 2D polygon and coordinates of the rectangular view window; creating a search circular linked list A and a vertex set B of an overlapping region; numbering vertices and edges of the 2D polygon and the rectangular view window; and storing vertices in the set A? into the list A; obtaining spatial relationship based on relative position between vertices of the 2D polygon and the rectangular view window; performing different operations according to the spatial relationship; adding the starting point A0 in the list A to the vertex set B; allowing a pointer to point to the starting point A0; determining whether a current vertex of the 2D polygon pointed by the pointer is within the rectangular view window; and clipping the 2D polygon.