Parsimonious Refraction Interferometry (PRI)

Objective

In this lab we will learn how to create densely populated refraction data set from only 2 opposites and few infill shot gathers.

Download the paper from here and traveltime picks https://csim.kaust.edu.sa/files/ErSE210/lab_PRI/DataPick4.zip for the field data exercise below.

Introduction

For a 2D survey, we now show that two opposite shot gathers and several short-offset infill shot gathers can be decomposed into many virtual-shot gathers that have many more traveltime picks available for inversion. In some cases, the virtual-shot gathers give as much refraction information as a full survey with N shots, where a shot is located at each of the N geophone locations. The result is a tomogram with a much denser ray coverage and better slowness resolution compared to that from the original data. We call this procedure parsimonious interferometry because it uses a stationary-phase principle to decompose the opposite traveltimes into many virtual traveltimes associated with shorter raypaths. Unlike the original pair of opposite shots, the virtual-shot locations are at all of the interior geophone locations.

Figure 1: Two-layer model where the black medium is faster than the top layer; the reciprocal sources are at A and D and are associated with the dashed red ray. The dashed blue raypath is associated with the virtual refraction ray that is excited by the virtual source (blue star) at C and terminates at B. The refraction traveltimes associated with the reciprocal shots (green and red stars) can be decomposed into the virtual refraction traveltime generated by the blue star.

Figure 2: a) The actual trvaeltime picks, b) two reciprocal and 5 infill shot gathers used as input to the proposed method, c) the virtual traveltimes calculated from PRI, and d) the difference between the actual and the virtual traveltime picks.

Procedure

Field data example

1. Download the field data example (Field Data). Download the reference traveltime picks https://csim.kaust.edu.sa/files/ErSE210/lab_PRI/DataPick4.zip for the field data exercise below.

2. Pick the first arrival traveltimes (reference traveltimes).

3. Use the two opposite CSGs (CSG # 1 and # 120) and 4 to 6 short-offset infills to calculate the virtual traveltimes

4. Calculate and plot the errors between reference and virtual traveltimes

5. Plot the histogram of the differences between reference and virtual traveltimes.