Methods and seismic shot generation and data collection systems utilizing refraction in horizontal stratified media for monotonically increased velocity determinations

A seismic shot generation and data collection system comprising a seismic source, a seismic receiver, a depth-domain velocity model, a monotonically increased velocity model, and a seismic data processor, wherein:

• the seismic source is positioned to direct seismic energy into a subsurface region comprising geological discontinuities to generate a seismic wave;
• the seismic receiver is positioned to receive seismic energy that is redirected by the geological discontinuities through reflection, refraction, or a combination thereof to detect the seismic wave;
• the depth-domain velocity model comprises a plurality of inverse modeled velocities based on first arrival data from the seismic wave detected by the seismic receiver and a refraction velocity v(z) associated with the plurality of inverse modeled velocities;
• the first arrival data comprises a plurality of time t and offset x values;
• the monotonically increased velocity model comprises a function, the function comprising a monotonically increased velocity v*(z);
• and
• the seismic data processor is communicatively coupled to the depth-domain velocity model and the monotonically increased velocity model and is operable to
• receive the first arrival data from the seismic wave generated by the seismic source and detected by the seismic receiver,
• determine the plurality of inverse modeled velocities of the depth-domain velocity model based on the plurality of time t and offset x values of the first arrival data,
• determine the refraction velocity v(z) for an estimated depth z based on the plurality of inverse modeled velocities,
• determine the monotonically increased velocity v*(z) from the monotonically increased velocity model by optimizing the function to minimize error through requiring the monotonically increased velocity v*(z) to be nearest to the refraction velocity v(z) and to be characterized by a positive slope such that the refraction velocity v(z) increases with depth,
• generate a subsurface image based on the estimated depth z and the determined monotonically increased velocity v*(z).

A method comprising:

• receiving first arrival data from a seismic wave generated by a seismic source and detected by a seismic receiver,
• determining a plurality of inverse modeled velocities of a depth-domain velocity model based on a plurality of time t and offset x values of the first arrival data,
• determining a refraction velocity v(z) for an estimated depth z based on the plurality of inverse modeled velocities,
• determining a monotonically increased velocity v*(z) from a monotonically increased velocity model by requiring the monotonically increased velocity v*(z) to be nearest to the refraction velocity v(z) and to be characterized by a positive slope such that the refraction velocity v(z) increases with depth, and
• generating a subsurface image based on the estimated depth z and the determined monotonically increased velocity v*(z).