Imaging near‐surface inhomogeneities using weighted multipath summation

Imaging of shallow subsurface objects in 3D space can be performed by a spatial summation of seismic waves diffracted by these objects. The summation can be implemented using either a fixed velocity or, alternatively, a recently introduced multipath summation approach. The multipath summation does not require any explicit information on velocities since it is performed for all possible velocity values within a wide specified range. However, the spatial resolution of the images obtained by the multipath summation is usually inferior to those obtained using the fixed velocity approach.

In order to improve the image quality, we propose a new approach to the multipath summation performing the summation with image dependent weights. The ‘optimal’ weights can be obtained from asymptotics of the corresponding path integral (which is a continuous analogue of the multi‐path summation). Application of the weighted multipath summation to synthetic and real data demonstrates that the quality of the imaging can be greatly improved as compared to the unweighted summation and sometimes even to the fixed velocity approach. Moreover, the weighted multipath summation can produce reliable estimates of the summation parameter (velocity above the target object), which in some cases can be used to further improve the image quality.