Premigration deghosting of seismic data with a bootstrap technique

A method, stored in a memory and executing on a processor, for generating a receiver-based ghost filter from recorded data, said method comprising:

• generating mirror data from said recorded data;
• transforming said recorded data and said mirror data from a time-space domain to a frequency-space domain;
• adding a phase coefficient to a mirror ghost filter so that the mirror ghost filter is time aligned with a ghost filter, wherein the transformed recorded data is expressed by multiplying initial primary receiver ghost-free data with the ghost filter and the transformed mirror data is expressed by multiplying the initial primary receiver ghost-free data with the mirror ghost filter;
• generating an initial ghost as a difference between the transformed recorded data and the initial primary receiver ghost-free data, wherein the initial primary receiver ghost-free data is calculated by jointly solving (i) a first equation that relates the transformed recorded data, the initial primary receiver ghost-free data and the ghost filter, and (ii) a second equation that relates the transformed mirror data, the initial primary receiver ghost-free data and the mirror ghost filter;
• generating said ghost filter by iterating through said transformed recorded data from which the initial primary receiver ghost-free data is subtracted and minimizing a sum of the initial primary receiver ghost-free data and the initial ghost multiplied by the phase coefficient to obtain a ghost delay time;
• calculating a final primary receiver ghost-free data associated with a current iteration based on the transformed recorded data and the ghost filter;
• and
• generating an image of a geophysical structure underground based on the final primary receiver ghost-free data.