Source-receiver position estimation using direct arrival modeling and inversion

A computing device for correcting observed positions of seismic sensors and/or seismic sources for a seismic data acquisition system, the computing device comprising:

• an interface configured to receive a position of each source element within the source array and a position of each individual seismic sensor within a composite receiver;
• and
• a processor connected to the interface and configured
• to estimate a source element energy generated by each source element, which belongs to the source array,
• to estimate a model of direct arrival waves that propagate straight from the source elements to the seismic sensors, respectively, the model being based on source modelling, propagation modelling and characteristics of the seismic data acquisition system related to each of individual seismic sensors of a composite receiver,
• for at least two sets of positions among which at least one set of positions is obtained by perturbing at least a position of one of the seismic sensors and/or of the source elements from another of the at least two sets of positions,
• to calculate direct arrival energies expected to be recorded by each individual seismic sensor and due to each of the source elements of the source array, respectively, a direct arrival energy being calculated using
• the model,
• the estimated source element energy of a respective source element, and
• positions of the respective source element within the source array and of a respective individual seismic sensor within the composite receiver according to one of the at least two sets of positions, and
• to sum, for each individual seismic sensor, the direct arrival energies from the source elements,
• to calculate values of an objective function for the at least two sets of positions, respectively, each of the values indicating a mismatch between
• the direct arrival waves computed using the model of direct arrival waves for a set of positions among the at least two sets of positions, and
• direct arrival waves according to observed seismic data,
• to select a best set of positions among the at least two sets of positions based on the values of the objective function, the best set of positions corresponding to a lowest value of the objective function, and
• to correct one or more of the observed positions of the individual seismic sensors and/or of the source elements according to the best set of positions.

A method for correcting observed positions of seismic sensors and/or seismic sources for a seismic data acquisition system, the method comprising:

• estimating a source element energy generated by each source element, which belongs to a source array;
• estimating a model of direct arrival waves that propagate straight from the source elements to the individual seismic sensors, respectively, the model being based on source modeling, propagation modeling and characteristics of the seismic data acquisition system related to each of individual seismic sensors of a composite receiver;
• calculating direct arrival energies of the direct arrival waves expected to be recorded by each individual seismic sensor and due to each source element of the source array, using the model, the estimated source element energy of a source element, an observed position of the source element within the source array and an observed position of a respective individual seismic sensor within the composite receiver;
• summing, for each individual seismic sensor, the direct arrival energies from the source elements;
• extracting a parameter representing mismatches between the direct arrival waves according to the model and direct arrival waves observed in seismic data recorded by the individual seismic sensors;
• applying an inversion process to the parameter for determining one or more positioning residuals for one or more of the individual seismic sensors;
• and
• correcting one or more of the observed positions of the individual seismic sensors with the corresponding one or more positioning residuals.

A computing device for correcting observed positions of seismic sensors and/or seismic sources for a seismic data acquisition system, the computing device comprising:

• an interface configured to receive an observed position of each source element within a source array and an observed position of each individual seismic sensor within a composite receiver;
• and
• a processor connected to the interface and configured
• to estimate a source element energy generated by each source element, which belongs to the source array,
• to estimate a model of direct arrival waves that propagate straight from the source elements to the seismic sensors, the model being based on source modelling, propagation modelling and characteristics of the seismic data acquisition system related to each individual sensor of a composite receiver
• to calculate direct arrival energies of the direct arrival waves expected to be recorded by each individual seismic sensor and due to each source element of the source array, using the model, the estimated source element energy, the observed position of the each source element within the source array, the observed position of the each individual seismic sensor within the composite receiver and characteristics of the seismic data acquisition for the each respective individual seismic sensor,
• to sum, for each seismic sensor, the direct arrival energies from the source elements,
• to extract a parameter representing mismatches between the direct arrival waves according to the model and direct arrival waves observed in seismic data recorded by the individual seismic sensors,
• to apply an inversion process to the parameter for determining one or more positioning residuals for one or more of the individual seismic sensors, and
• to correct one or more of the observed positions of the individual seismic sensors with corresponding one or more positioning residuals.