Mechanisms of geometrical seismic attenuation

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In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q) observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient.In particular, geometrical attenuation was found to be positive for most waves traveling dnd champagne sparkles within the lithosphere.Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values.

In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models.For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing) and negative (for focusing).In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive.

For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q».However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics.The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically.

When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency.These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.<br />   .

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MECHANISMS OF GEOMETRICAL SEISMIC ATTENUATION

Mechanisms of geometrical seismic attenuation

Mechanisms of geometrical seismic attenuation

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