Flatten_Surface : a computer program to restore a folded and faulted gridded surface

A computer program called Flatten Surface has been written which uses a method of best fitting of finite elements to restore a folded and faulted gridded surface to its predeformational state. The program calculates the intersection of the surface with fault surfaces so that the finite elements can be fit across faults. The method treats the regular grid of a surface as a series of columns of quadrilateral finite elements. The columns of the grid should be generally perpendicular to the fold axis and generally parallel to the faults. For each element that intersects a fault surface, two of its corner points are reassigned to be the element's calculated intersection points with the fault. Through a series of 3- D rotations each element is flattened by rotating the triangular halves of each element to horizontal. Each element is fit to its two previously fit neighbors, one to the side and the other below/above. The corner of the element that is coincident with the meeting point of the two neighboring elements is fit directly to the vector mean of the meeting point. The element is then rotated about this point using a simple iterative 2-D rotation procedure that balances area of overlap/underlap or distance between two adjacent previously fit finite elements. After the entire surface has been fit, a vector mean of all coincident corner points can be used when repeating the fitting process. When an element or a surrounding element is faulted, great care is taken in the selection of the coincident points to be averaged to ensure that the points are truly coincident. The fitting process can be repeated as many times as the user determines is necessary to achieve a satisfactory fit. The user determines best fit with statistics on the area of overlap/underlap and an experienced judgment call on a visual estimation of the distribution of overlap/underlap. The vector mean of all coincident corner points is used to create the output grid of the surface. The program is written in the c language and runs under UNIX and the SunView windowing system. Accuracy of the program was tested for the restoration of six data sets: (1, 2) two 4 x 4 hand created perfect grids, one unfaulted and one faulted; (3) a 100 x 100 faulted sine curve; (4) a 119 x 153 grid of a contour map of an experimentally folded sheet of paper (Gratier and others (1991); (5, 6) two 76 x 115 grids of contoured horizons from an oil field with faults. Results for the 4 x 4 grids and the faulted sine curve were perfect after the first fitting iteration. For the folded sheet of paper the total area of overlap/underlap was 0.000062% of the total area of the surface, after 96 fittings. For the oil-field data convergence was achieved rapidly and the degree of fit was good; after 94 fittings the total area of overlap/underlap was 0.000963% of the total area. Although a successful restoration does not guarantee a correct final interpretation, it helps check for local anomalies or errors in construction of the surface.