Laplace-fourier 1.5d forward modeling using an adaptive sampling technique

One or more non-transitory machine-readable storage media storing instructions for producing a seismic wave velocity model of a subsurface area, the instructions being executable by one or more processing devices to perform operations comprising:

• receiving, from a seismic receiver, seismic data input comprising a recorded seismic wave field;
• receiving, an initial 1D velocity model of the subsurface area;
• receiving, data input comprising a maximum misfit value and maximum iteration value;
• determining, a Laplace-Fourier transform of the recorded seismic wave field;
• setting, a current 1D velocity model to the initial 1D velocity model;
• setting, an iteration value n to zero;
• regenerating, the current 1D velocity model to generate inverted data representing the subsurface area by:
• (i) generating, a modeled synthetic wave field in the Laplace-Fourier domain using the current 1D velocity model;
• (ii) comparing the modeled synthetic wave field with the recorded seismic wave field to determine a misfit value;
• (iii) if the determined misfit value is less than the maximum misfit value, outputting the current 1D velocity model as the final 1D velocity model;
• (iv) if the determined misfit value is greater than the maximum misfit value, and if the iteration value is equal to or greater than the maximum iteration value, outputting the current 1D velocity model as the final velocity model;
• and
• (v) if the determined misfit value is greater than the maximum misfit value, and if the iteration value is less than the maximum iteration value, generating a corrected current 1D velocity model using a gradient of a misfit function and setting the iteration value to n+1, and repeating steps (i) through (v).

A system comprising:

• one or more non-transitory machine-readable storage media storing instructions for producing a seismic wave velocity model of a subsurface area, and
• one or more processing devices to execute the instructions to perform operations comprising:
• receiving, by a processor of a computing system, from a seismic receiver, seismic data input comprising a recorded seismic wave field;
• receiving, by the processor, an initial 1D velocity model of the subsurface area;
• receiving, by the processor, data input comprising a maximum misfit value and maximum iteration value;
• determining, by the processor, a Laplace-Fourier transform of the recorded seismic wave field;
• setting, by the processor, a current 1D velocity model to the initial 1D velocity model;
• setting, by the processor, an iteration value n to zero;
• regenerating, by the processor, the current 1D velocity model to generate inverted data representing the subsurface area by:
• (i) generating, by the processor, a modeled synthetic wave field in the Laplace-Fourier domain using the current 1D velocity model;
• (ii) comparing the modeled synthetic wave field with the recorded seismic wave field to determine a misfit value;
• (iii) if the determined misfit value is less than the maximum misfit value, outputting the current 1D velocity model as the final 1D velocity model;
• (iv) if the determined misfit value is greater than the maximum misfit value, and if the iteration value is equal to or greater than the maximum iteration value, outputting the current 1D velocity model as the final velocity model;
• and
• (v) if the determined misfit value is greater than the maximum misfit value, and if the iteration value is less than the maximum iteration value, generating a corrected current 1D velocity model using a gradient of a misfit function and setting the iteration value to n+1, and repeating steps (i) through (v).