In recent years, the encoded simultaneous-source full-waveform inversion (ESSFWI) algorithm, which can reduce the computational cost of the individual-source full-waveform inversion (FWI), has been studied by many researchers. Although the ESSFWI technique can be successfully applied to fixed-spread acquisition data, the application of this technique to marine-streamer data is difficult because of the acquisition geometry. The difference in the acquisition geometry between the observed and modeled data produces missing trace parts in a stacked seismogram and unwanted events in the residual seismogram. To avoid these unwanted residuals, the correlation-based ESSFWI technique has been suggested by several researchers. However, the correlation-based approach unpredictably modifies the residual seismograms, which may result in distortion of the inverted velocity model. We developed an alternative approach to properly cope with the acquisition geometry problem. Our algorithm modified the offset-limited observed data to full-offset data by combining the original observed data with the modeled data. This modification led to an undistorted residual seismogram for the simultaneous multiple shot data. However, if we applied this modification process at every iteration of the inversion, the computational cost increased. To accelerate our ESSFWI algorithm, we proposed a strategy that modified the observed data at the iterations corresponding to the square numbers. Through the numerical examples, we discovered that our ESSFWI strategy better described the velocity structure of Marmousi-2 model than the correlation-based approach. Based on the comparison of computational speed-up for several strategies, we also confirmed that our ESSFWI algorithm using square numbers was a reasonable strategy. An example using real data found that our algorithm is slightly sensitive to noise, but we could minimize this sensitivity to noise by using a reasonable strategy to reduce the problem of missing traces. As a result, we could perform an effective ESSFWI even for marine-streamer acquisitions.

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