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The low frequency of seismic waves severely limits the regulation of wave propagation in earthquake protection engineering applications. In recent years, locally resonant metamaterials have been introduced for seismic wave attenuation. A barrier based on locally resonant metamaterials consisting of rows of wells is proposed to reduce the transmission of Rayleigh waves during propagation, achieving earthquake protection. First, comparisons are made between the wells of the metamaterial, empty wells, solid steel wells, and a continuous steel wall. It is evident that locally resonant metamaterials exhibit better performance than that of the other materials. Simulations of the relationships between the attenuation of Rayleigh waves and the depth, number of rows, and working frequency of the wells are presented. With a barrier of ten rows of wells, where the diameter of each well is less than one-twentieth of the wavelength of the Rayleigh wave and the depth of the wells is nearly four-fifths of the wavelength, the maximum attenuation reaches up to 16.2 dB when all the wells share the same working frequency, and the bandwidth is broader, but the maximum value is less when the rows have different working frequencies. Depending on the demand for a higher value or a broader bandwidth of the Rayleigh wave attenuation, this barrier promotes flexible and achievable improvements by adding rows or decentralizing the working frequencies of the wells. The vast potential of seismic wave attenuation from locally resonant metamaterials is anticipated in the future.

Young’s elastic modulus and Poisson’s ratio of the cement in a cased borehole are important in the prediction of the cement sheath integrity under hydraulic fracturing. Although these mechanical properties can be derived in principle from the bulk velocities, the inversion of these velocities of the cement from the received full waveforms remains a challenging problem, especially the S-wave velocity. We have developed an inversion method based on the round-trip traveltimes of the leaked flexural waves (TTL) to invert the bulk velocities of the medium behind the casing. The traveltime difference between the casing wave and the delayed casing wave is the additional time for the leaked wave to travel in the interlayer to the formation and back to the casing. To demonstrate the effectiveness of this method, synthetic full waveforms with a changing interlayer are calculated when an ultrasonic acoustic beam is incident obliquely on the casing. The traveltimes of the wave packets are picked from the envelope curve of the full waveform and then used to invert the bulk velocities in the TTL method. The inverted S-wave velocity of cement is quite accurate with an error rate smaller than 3%, no matter whether the cement is of the ordinary, heavy, or light type. When the interlayer is mud, the P-wave is inverted with an error rate of less than 2%. The P-wave velocity is inverted roughly with an error rate of approximately 10% when the medium behind the casing is light cement.