Kirchhoff migration without phases

TL;DR

This paper introduces a frequency domain preprocessing step for Kirchhoff migration that enables imaging with only intensity measurements, bypassing the need for phase information, and achieves asymptotically equivalent images at high frequencies.

Contribution

A novel preprocessing method for Kirchhoff migration that reconstructs images using intensity-only data without phase information, effective at high frequencies.

Findings

Imaging quality asymptotically matches full waveform data at high frequencies.

Method works with intensity data and autocorrelations, no phase knowledge needed.

Simplifies data acquisition in wave imaging scenarios.

Abstract

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.