Propagation of errors due to incorrect positions of sources and detectors in wave‐field tomography

Tomographic data processed by 2D inversion programs can produce fairly large distortions due to incorrect source and/or detector positions. This problem is very serious in high‐frequency electromagnetic tomography (GPR), due to the dimensions of the transmitter and receiver antennae. The errors can even be larger when coupled antennae are used (receiver and transmitter inside the same box) whose positions are not clearly known. Similar errors can be involved in seismic tomography, for instance when the mechanical connection between transducers and sample is defective.

In this paper the problem has been studied using synthetic data which were calculated for different acquisition geometries. Synthetic data have been distorted assuming a position error in the whole set of sensors, transmitters or receivers. Tests have been carried out using a homogeneous, isotropic medium and various simple inhomogeneous models, characterized by different geometric boundaries.

The responses for all the models have been calculated (both forward and inverse problems) assuming straight raypaths, also in the case of velocity variations. The calculated traveltimes were processed using an LSQR algorithm implemented in an iterative inversion program, containing two damping factors to reduce total and local velocity contrasts. The inversion results have been reproduced graphically and the analysis of residuals has been carried out. Finally, propagation of these residuals, both in time and velocity, is discussed.