Kirchhoff migration without phases
It addresses the problem of imaging with phase-less data, which is relevant for applications where phase information is unavailable or difficult to obtain.
This paper introduces a preprocessing step for Kirchhoff migration that enables imaging of scatterers using only intensity measurements, without phase information. The method recovers a projection of the scattered field via a simple least-squares problem, achieving Kirchhoff images asymptotically identical to those from full waveform data at high frequencies.
We present a simple, frequency domain, preprocessing step to Kirchhoff migration that allows the method to image scatterers when the wave field phase information is lost at the receivers, and only intensities are measured. The resulting imaging method does not require knowing the phases of the probing field or manipulating the phase of the wave field at the receivers. In a regime where the scattered field is small compared to the probing field, the problem of recovering the full-waveform scattered field from intensity data can be formulated as an embarrassingly simple least-squares problem. Although this only recovers the projection (on a known subspace) of the full-waveform scattered field, we show that, for high frequencies, this projection gives Kirchhoff images asymptotically identical to the images obtained with full waveform data. Our method can also be used when the source is modulated by a Gaussian process and autocorrelations are measured at an array of receivers.