No abstract

It has been confirmed by comparison with particle velocities of surface waves of wave normal perpendicular to borehole axis measured by collocated seismic broadband array or borehole seismometers that high-sensitivity borehole tensor strainmeters could measure surface strain waves qualitatively. However, quantitative measurability of strain waves of wave normal being oblique to borehole axis by borehole tensor strainmeters is still a challenging problem. In this article, we introduce a scattering model of oblique-incidence seismic waves by an empty borehole to investigate the influence of incident-wave normal and polarization on theoretical-frequency-response bandwidth of borehole tensor strainmeters. Within the theoretical bandwidth of borehole tensor strainmeters, zero-frequency gains are introduced to build quantitative relation between instrumental strain waves of borehole tensor strainmeters and oblique-incidence seismic strain waves. Better understanding the influence of incident-wave normal and polarization on the relation between instrumental strain and strain components induced by the incident strain wave shows that incident-wave normal and polarization must be assessed by other instrumentation to promise quantitative measurement of incident strain waves by borehole tensor strainmeters, which would benefit in situ calibration of borehole tensor strainmeters.

The learning-based model predictive control (LB-MPC) is an effective and critical method to solve the path tracking problem in mobile platforms under uncertain disturbances. It is well known that the machine learning (ML) methods use the historical and real-time measurement data to build data-driven prediction models. The model predictive control (MPC) provides an integrated solution for control systems with interactive variables, complex dynamics, and various constraints. The LB-MPC combines the advantages of ML and MPC. In this work, the LB-MPC technique is summarized, and the application of path tracking control in mobile platforms is discussed by considering three aspects, namely, learning and optimizing the prediction model, the controller design, and the controller output under uncertain disturbances. Furthermore, some research challenges faced by LB-MPC for path tracking control in mobile platforms are discussed.

Borehole tensor strainmeters such as the RZB tensor strainmeter, YRY tensor strainmeter, and Gladwin tensor strainmeter are highly sensitive to ground deformation over periods of minutes to months, bridging the gap in the sensitivity and frequency between Global Positioning System and seismic measurements. To discuss the possibility of quantitatively measuring seismic strain waves by borehole tensor strainmeters, a model of the scattering of plane elastic P and S waves by an empty borehole is introduced to investigate the theoretical frequency response and corresponding bandwidth of an empty borehole for borehole tensor strainmeters. The calculation of scattering waves around the empty borehole gives the changes in the diameter of the borehole. Different gauge combinations are introduced to reflect the areal strain and the maximum shear strain of the incident waves. The theoretical frequency responses for different gauge combinations are determined by the nondimensional wavenumber of the incident wave, the Poisson’s ratio of the surrounding rock, and the difference between the azimuth angle of the first gauge and the incident angle of the incident wave. Theoretical‐frequency‐response analysis of different gauge combinations for an empty borehole confirms that different gauge combinations serve as low‐pass filters. The 1% bandwidth of the gauge combinations shows that borehole tensor strainmeters could quantitatively measure seismic strain waves in the acoustic frequency range if the instrumental effective bandwidth of the gauge is sufficiently large, which will advance high‐frequency seismology and benefit in situ calibration of borehole tensor strainmeters.

The scattering model of incident seismic waves by an empty borehole has been presented to investigate the theoretical frequency response and the corresponding bandwidth of borehole tensor strainmeters. Inner-diameter changes of the stainless steel instrument casing are measured by horizontal extensometers (gauges), after the borehole tensor strainmeter is installed at a certain depth of the borehole and boned by expansive grout with the surrounding rock. There is, however, no answer for the difference between this case and the empty case. In this paper, the scattering model of incident elastic seismic waves by a two-ring borehole is introduced to investigate the influence of the expansive grout on theoretical bandwidth for the measurement of strain waves by borehole tensor strainmeters. The calculation of wave fields in the surrounding rock and the two rings by wave function expansion gives the inner-diameter changes of the stainless steel instrument casing. Several cases show that the mechanical parameters of the expansive grout have great influence on the frequency responses of borehole tensor strainmeters for different gauge combinations, but little influence on the bandwidth, which means that the high-frequency bandwidth promises the quantitative measurability of strain waves in the acoustical frequency range for borehole tensor strainmeters.