The examination of method to describe mathematically geological information observed at an outcrop is necessary to construct outcrops database. I have shown in the previous studies that the outcrop structure and the stratigraphy at an outcrop composed of unturned layers, intrusive rocks and faults are mathematically expressed in the form of a structure graph G and a stratigraphic graph S, respectively. The present study extends the idea to describe the outcrop including lens-formed layers and interfingering layers. The contact relation between geological bodies x and y is expressed in terms of binary relation xR^#y on a set of geological bodies V, where R^# = R∨I∨F∨L∨D, xRy indicates that geological units x and y contact each other and x is overlain by y, xIy indicates that x is intruded by an igneous rock y, xFy indicates that x is cut by a fault y, xLy indicates that x includes lens-formed layer y, and xDy indicates that x interfingers with y. Then we can express the outcrop structure in the form of structure graph G = (V, R^#, φ_V, φ_A), where R^# = {(x, y)|xR^# y, x, y∈V }, φ_V is a function which assigns the name of geolgic body to each vertex x and φ_A is a function which assigns the contact relation such as conformity, unconformity, intrusion and fault to each arc (x, y). If a geological body x includes a lens-formed layer y or interfingers with other layer y, it is considered that x and y were formed in the same period, denoted by xE^*y. The relation E^* is an equivalence relation on a set V, and so elements of V are classified into a set of equivalence classes or a quatient set V/E^*. The chronological order U^* on V/E^* can be derived from the contact relation: [x]R[y] implies [xU^*[y], and [x]I[y] or [x]F[y] implies [x]U^*[y]. Then we can express the stratigraphic sequence in the form of a stratigraphic graph S = (V/E^*, U^*, φ_V, φ_A) where U^* = {(x, y)|xU^*y, x, y∈V }, φ_V is a function which assigns the name of geolgic body to each vertex [x] and φ_A is a function which assigns the contact relation to each arc ([x], [y]). As the relation U^* on V/E^* is a partial ordering, elements of V/E^* are arranged in a linear sequence C₁, C₂, ..., C_m such that C_iU^*C_j implies i ≤ j. If U^* is a total ordering, the sequence represents the formation order. Finally, stratigraphy is expressed by P’= (C₁, φ_A (C₁, C₂), C₂, ..., C_m-1, φ_A (C_m-1, C_m), C_m).

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