Method for optimizing the design of multiple-source arrays used in marine seismic surveys

A method comprising:

• determining respective de-ghosting errors for a de-ghosting process associated with ones of a plurality of seismic source configurations of a marine seismic survey, wherein the de-ghosting process includes removing effects of surface-reflected, downwardly traveling acoustic waves;
• determining a particular seismic source configuration of the plurality of seismic source configurations that has a smallest associated error out of the determined respective de-ghosting errors, wherein the determined error is indicative of errors in the de-ghosting process caused by interference with waves detected resulting from transmissions from two or more sources, wherein the seismic source configuration includes at least two different source depths, and wherein the errors are determined without performing wave-field separation of wave-fields associated with the two or more sources;
• configuring marine seismic survey equipment according to the determined seismic source configuration;
• and
• performing a marine seismic survey with the configured marine seismic survey equipment, the marine seismic survey producing at least one data set.

A method comprising:

• performing a marine seismic survey using a first configuration of seismic sources and determining an associated first de-ghosting error for a de-ghosting process wherein the de-ghosting process includes removing effects of surface-reflected, downwardly traveling acoustic waves;
• performing the marine seismic survey using a second configuration of seismic sources and determining an associated second de-ghosting error for the de-ghosting process;
• determining which of the first and second de-ghosting errors is smaller, wherein the first and second de-ghosting errors are indicative of errors in the de-ghosting process caused by interference with waves detected resulting from concurrent transmissions from two or more sources in each configuration, wherein each of the first and second configurations includes at least two different source depths, and wherein the first and second de-ghosting errors are determined without performing wave-field separation of wave-fields associated with the first or second configuration of seismic sources;
• and
• performing additional marine seismic surveys using the configuration determined to have the smaller associated de-ghosting error, the additional marine seismic surveys producing at least one data set.

A non-transitory, computer readable medium storing instructions that, when executed by a computer system, cause the computer system to:

• determine an associated de-ghosting error c for each of a plurality of seismic source configurations of a marine seismic survey, wherein the de-ghosting errors are indicative of interference with waves detected resulting from transmissions from first and second sources, wherein each of the plurality of seismic source configurations includes at least two different source depths, and wherein the de-ghosting errors are determined without performing wave-field separation of wave-fields associated with the first and second sources;
• and
• selecting a seismic source configuration having the smallest associated de-ghosting error;
• wherein the selected seismic source configuration is usable to perform a marine seismic survey with marine seismic equipment to generate at least one data set;
• wherein the de-ghosting error c for a particular seismic source configuration is determined as:
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• wherein S1 and S2 are representative of the wave-fields emitted by the first and second sources, respectively, G1 and G2 are ghost functions associated with the first and second sources, respectively, S2G2S1G1 and S1G1S2 G2 represent the cross-correlation between the first and the second source wave-fields including the ghost functions, Δt1 and Δt2 are firing time delays of the first and second sources, respectively, and ω is the angular frequency.

A non-transitory, computer readable medium storing instructions that, when executed by a computer system, cause the computer system to perform operations comprising:

• determining an associated de-ghosting error for a de-ghosting process for each of a plurality of seismic source configurations of a marine seismic survey, wherein the determined de-ghosting errors are indicative of errors in the de-ghosting process caused by interference with waves detected resulting from transmissions from two or more sources, wherein each of the plurality of seismic source configurations includes at least two different source depths, and wherein the de-ghosting errors are determined based on:
• cross-correlation between source wavefields;
• and
• ghost functions for two or more sources and one or more time delays such that the de-ghosting errors are determined without performing wave-field separation of wave-fields associated with the sources;
• and
• selecting, for performance of a marine seismic survey to generate at least one data set with marine seismic equipment, a seismic source configuration based on the determined de-ghosting errors.