3D pre-stack full waveform inversion

A program storage medium encoded with instructions that, when executed by a computing device, perform a method comprising:

• generating a macro P-wave velocity model, including resolution of residual moveout errors, using reflection tomography from a seismic data set;
• generating a diffraction response from the macro P-wave velocity model for a given common image gather location therein assuming a locally laterally invariant model;
• converting the generated diffraction response for the given common image gather location to a migrated reflection response to yield a modeled data set;
• comparing the modeled data set to the given common image point from the seismic data set;
• updating the macro P-wave velocity model based on the result of the comparison;
• and
• iterating the diffraction response generation, the diffraction response conversion, comparison, and update until the modeled data set converges to the common image gathers.

A computing apparatus, comprising:

• a computing device;
• a bus system;
• a storage communicating with the computing device over the bus system;
• an application residing on the storage that, when executed by the computing device, performs a method including:
• generating a macro P-wave velocity model, including resolution of residual moveout errors, using reflection tomography from a seismic data set;
• generating a diffraction response from the macro P-wave velocity model for a given common image gather location therein assuming a locally laterally invariant model;
• converting the generated diffraction response for the given common image gather location to a migrated reflection response to yield a modeled data set;
• comparing the modeled data set to the given common image point from the seismic data set;
• updating the macro P-wave velocity model based on the result of the comparison;
• and
• iterating the diffraction response generation, the diffraction response conversion, comparison, and update until the modeled data set converges to the common image gathers.

A method, comprising:

• (i) generate macro P-wave velocity model, and resolve all RMO errors, using reflection tomography;
• (ii) using the macro model generated in step (i), for each common image gather location, generate a diffraction response for each depth sample, or common image point for a locally laterally invariant model;
• (iii) for each common image gather location, convert the diffraction response to a migrated reflection response, for each image point, by back projecting rays from the given image point to the surface to find the source-receiver position for each offset (or angle), and time, using the local dip at that image point, and using the reflectivity computed from the source-receiver incident angle at the image point;
• (iv) for each common image gather location, compare the modeled data generated the previous two steps, to the real data, and compute a residual velocity which minimizes the difference between the model and real data, the real data being the common image gather;
• and
• (v) iterate (ii)-(iv) until the model converges to the real data within some suitable threshold.

A program storage medium encoded with instructions that, when executed by a computing device, perform a method comprising:

• (i) generate macro P-wave velocity model, and resolve all RMO errors, using reflection tomography;
• (ii) using the macro model generated in step (i), for each common image gather location, generate a diffraction response for each depth sample, or common image point for a locally laterally invariant model;
• (iii) for each common image gather location, convert the diffraction response to a migrated reflection response, for each image point, by back projecting rays from the given image point to the surface to find the source-receiver position for each offset (or angle), and time, using the local dip at that image point, and using the reflectivity computed from the source-receiver incident angle at the image point;
• (iv) for each common image gather location, compare the modeled data generated the previous two steps, to the real data, and compute a residual velocity which minimizes the difference between the model and real data, the real data being the common image gather;
• and
• (v) iterate (ii)-(iv) until the model converges to the real data within some suitable threshold.

A program storage medium encoded with instructions that, when executed by a computing device, perform a method comprising:

• a computing device;
• a bus system;
• a storage communicating with the computing device over the bus system;
• an application residing on the storage that, when executed by the computing device, performs a method including:
• (i) generate macro P-wave velocity model, and resolve all RMO errors, using reflection tomography;
• (ii) using the macro model generated in step (i), for each common image gather location, generate a diffraction response for each depth sample, or common image point for a locally laterally invariant model;
• (iii) for each common image gather location, convert the diffraction response to a migrated reflection response, for each image point, by back projecting rays from the given image point to the surface to find the source-receiver position for each offset (or angle), and time, using the local dip at that image point, and using the reflectivity computed from the source-receiver incident angle at the image point;
• (iv) for each common image gather location, compare the modeled data generated the previous two steps, to the real data, and compute a residual velocity which minimizes the difference between the model and real data, the real data being the common image gather;
• and
• (v) iterate (ii)-(iv) until the model converges to the real data within some suitable threshold.