Processing of translational and rotational motions of surface waves: performance analysis and applications to single sensor and to array measurements

The analysis of rotational seismic motions has received considerable attention in the last years. Recent advances in sensor technologies allow us to measure directly the rotational components of the seismic wavefield. Today this is achieved with improved accuracy and at an affordable cost. The analysis and the study of rotational motions are, to a certain extent, less developed than other aspects of seismology due to the historical lack of instrumental observations. This is due to both the technical challenges involved in measuring rotational motions and to the widespread belief that rotational motions are insignificant. This paper addresses the joint processing of translational and rotational motions from both the theoretical and the practical perspectives. Our attention focuses on the analysis of motions of both Rayleigh waves and Love waves from recordings of single sensors and from an array of sensors. From the theoretical standpoint, analysis of Fisher information (FI) allows us to understand how the different measurement types contribute to the estimation of quantities of geophysical interest. In addition, we show how rotational measurements resolve ambiguity on parameter estimation in the single sensor setting. We quantify the achievable estimation accuracy by means of Cramér–Rao bound (CRB). From the practical standpoint, a method for the joint processing of rotational and translational recordings to perform maximum likelihood (ML) estimation is presented. The proposed technique estimates parameters of Love waves and Rayleigh waves from single sensor or array recordings. We support and illustrate our findings with a comprehensive collection of numerical examples. Applications to real recordings are also shown.