Harmonic encoding for FWI

A computer-implemented iterative method for inversion of seismic data to update a model of subsurface velocity or other physical property, wherein a plurality of encoded source gathers of data are inverted simultaneously, said method comprising:

• (a) with a computer, selecting a plurality of individual source gathers of the seismic data;
• (b) in a first iteration, encoding the selected gathers with weights using the computer, said weights forming components of a weight vector, and summing the encoded gathers to form a composite gather;
• (c) generating, with the computer, at least one realization of predicted data for the entire composite gather, wherein the predicted data are computer-simulated, using a current model, in a single forward-modeling operation, a different realization being characterized by a different weight vector;
• (d) updating, with the computer, the current model using the composite gather and the simulated composite gather from each of the at least one realization;
• (e) in a second iteration, repeating (b)-(d), using the updated model from the first iteration as the current model for the second iteration, resulting in a further updated model;
• and
• (f) using the further updated model in prospecting for hydrocarbons;
• wherein, (i) each iteration has a plurality of realizations, and the weight vectors for each realization are orthogonal to one another;
• or (ii) the weight vector or weight vectors for the first iteration are orthogonal to the weight vector or weight vectors for the second iteration;
• or both (i) and (ii);
• and
• wherein the orthogonal weight vectors are generated by selecting a set of random, linearly independent vectors and applying a Gram-Schmidt orthogonalization algorithm to them to produce an orthonormal set of vectors.