The high cost of simulating densely sampled seismic forward modeling data arises from activating sources one at a time in sequence. To increase efficiency, one could leverage recent innovations in seismic field-data acquisition and activate several (e.g., 2–6) sources simultaneously during modeling. However, such approaches would suffer from degraded data quality because of the interference between the model's responses to the simultaneous sources. Two new efficient simultaneous-source modeling approaches are proposed that rely on the novel tandem use of randomness and sparsity to construct almost noise-free model response to individual sources. In each approach, the first step is to measure the model's cumulative response with all sources activated simultaneously using randomly scaled band-limited impulses or continuous band-limited random-noise waveforms. In the second step, the model response to each individual sourceis estimated from the cumulative receiver measurement by exploiting knowledge of the random source waveforms and the sparsity of the model response to individual sources in a known transform domain (e.g., curvelet domain). The efficiency achievable by the approaches is primarily governed by the sparsity of the model response. By invoking results from the field of compressive sensing, theoretical bounds are provided that assert that the approaches would need less modeling time for sparser (i.e., simpler or more structured) model responses. A simulated modeling example is illustrated that shows that data collected with as many as 8192 sources activated simultaneously can be separated into the 8192 individual source gathers with data quality comparable to that obtained when the sources were activated sequentially. The proposed approaches could also dramatically improve seismic field-data acquisition efficiency if the source signatures actually probing the earth can be measured accurately.

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