Numerical implementation of wave mode of definition of bottom hole coordinates (Q2729330)

The article is a contribution to the methods of defining the bottom hole coordinates that is one of necessary components of geophysical exploration and drilling activities. The author notes that the raise of accuracy of defining the coordinates of a drift makes it possible to improve the quality of interpretation of the logging information and to reduce the time and costs of the drilling activity.NEWLINENEWLINE The aim of the article is to produce a procedure of estimating the drift parameters for any number of sensors \(\geq 4\).NEWLINENEWLINE In the Cartesian coordinate system \(x\), \(y\), \(z\), let the axes \(x\), \(y\) be directed along the surface of ground, and the axis \(z\) downwards to the center of the Earth. Denote by \(v\) the mean velocity of the seismic propagation wave. It is assumed that the sensors, recording (or emitting) seismic signals on the ground surface or in small holes, have coordinates \((x_i,y_i,z_i)\). Let \(t_i\) be the time of propagation of a seismic signal from the source in a bottom hole (for example, chisels) up to the \(i\)-point (or vice versa). It is required to find (estimate) the coordinates \((x^*,y^*,z^*)\) of a bottom hole and the velocity \(v\).NEWLINENEWLINE The problem is solved in the framework of the acoustic method for defining the wave mode of the coordinate of the bottom hole which consists in measuring the time of wave propagation of a certain physical nature from the point of applying the action (or the measurement point) above the ground up to the bottom hole. The calculation scheme of the least square method with regularization is implemented for finding an approximate solution to the above-mentioned problem which makes it possible to obtain confidence intervals for the coordinates \((x,y,z)\) of the bottom hole and the mean propagation velocity \(v\) of a seismic wave.