Efficient wave-equation-based diffraction imaging

Abstract

We have developed an efficient and practical wave-equation-based technique to image subsurface geologic features such as isolated scatterers, reflector edges, fault, fracture zones, and erosion whose information is mainly contained in diffracted waves. This technique has the ability to directly reveal and differentiate important geologic features compared with results obtained using reflected seismic waves. This new technique comprises three steps. First, the source and receiver wavefields are decomposed into left- and right-downgoing propagating waves, respectively. Second, applying the imaging condition to the right-downgoing source and receiver wavefields to generate the so-called right-right image. Similarly, a left-left image is generated. Third, the left-left and right-right images are multiplied sample-by-sample to form the final diffraction-based image. The key idea of this method is based on the fact that any dipping reflector exhibits a particular dip direction, so its subsurface image can exist either in the left-left or the right-right image, but not in both. As a result, the sample-by-sample multiplication of the two images eliminates the reflector images. Alternatively, because diffractions are generated by subsurface geologic features, which act as secondary sources and radiate in all directions, ranging from [Formula: see text] to 90°, their energy can exist in both images. After multiplication of both images, only the diffractors remain, whereas the reflectors are suppressed. Our method is applicable only for diffracting objects that radiate in all directions. An exception occurs when reflectors exhibit zero dip. In such a case, zero-dip reflectors could be present in both images and leak into the final diffractor image. We mitigate this problem in several ways, such as omitting near zero-offset input data, muting vertical-propagation components, or applying an [Formula: see text]-[Formula: see text] filter on the final diffraction image.