System for determination of measured depth (MD) in wellbores from downhole pressure sensors using time of arrival techniques

A computer implemented method for estimating measured depth of a borehole, comprising an act of causing one or more processors to execute instructions stored on a non-transitory memory such that upon execution, the one or more processors perform operations of:

• continuously obtaining time series measurements from an environmental sensor package, the times series measurements comprising source signals and reflected signals;
• determining initial estimates of a time delay and path attenuation amplitude from the time series measurements;
• determining an L2 error for the initial estimates of the time delay and the path attenuation amplitude;
• performing iterative minimization of the L2 error until a set of source signal parameters converge, resulting in a least squares estimate of the source signal and the reflected signals;
• using the least squares estimate to obtain time delay values;
• and
• using the time delay values, continuously generating an estimate of a measured depth of the borehole.

A computer program product for estimating measured depth of a borehole, the computer program product comprising:

• computer-readable instructions stored on a non-transitory computer-readable medium that are executable by a computer having one or more processors for causing the processor to perform operations of:
• continuously obtaining time series measurements from an environmental sensor package, the times series measurements comprising source signals and reflected signals;
• determining initial estimates of a time delay and path attenuation amplitude from the time series measurements;
• determining an L2 error for the initial estimates of the time delay and the path attenuation amplitude;
• performing iterative minimization of the L2 error until a set of source signal parameters converge, resulting in a least squares estimate of the source signal and the reflected signals;
• using the least squares estimate to obtain time delay values;
• and
• using the time delay values, continuously generating an estimate of a measured depth of the borehole.