1. A method for identifying geological features of a subsurface region from geophysical data gathered from the region, said method comprising: (a) selecting a transform from a group consisting of curvelet transforms, contourlet transforms, and surfacelet transforms, and selecting a corresponding basis set of elementary functions, called curvelet functions; (b) transforming the geophysical data into a curvelet representation of the data using the selected basis set and transform, wherein the geophysical data are represented as a series expansion of curvelet functions each multiplied by a corresponding expansion coefficient, wherein the expansion coefficients constitute weights in the curvelet expansion; (c) computing the geophysical attributes dip, frequency and location of each curvelet function used in the curvelet representation of the geophysical data; and (d) identifying geologic features directly from the weights and computed geophysical attributes of the curvelet functions; wherein at least one of (b) and (c) is performed using a computer.