Q models (seismology)

In seismology, a Q model represents the spatial distribution of seismic attenuation, often referred to as "Q," within the Earth. Q, or the quality factor, is a dimensionless parameter that describes the amount of energy loss per cycle of seismic wave propagation due to intrinsic attenuation mechanisms like friction and thermal relaxation. A Q model provides a three-dimensional picture of this attenuation, mapping variations in Q values as a function of location (latitude, longitude, and depth) within the Earth's interior or a specific region of interest.

Q models are crucial for several reasons. First, attenuation strongly influences the amplitude and shape of seismic waves. Therefore, correcting for attenuation effects using a Q model is necessary for accurate amplitude-based studies, such as earthquake source parameter estimation and seismic imaging. Second, variations in Q can reveal information about the Earth's composition, temperature, and physical state. High Q values generally indicate low attenuation, often associated with cold, dry, and solid regions like the lithosphere. Low Q values indicate high attenuation, often associated with hot, partially molten, or fluid-rich regions like the asthenosphere or regions containing magma. Third, Q models can be used in conjunction with seismic velocity models to improve our understanding of the Earth's rheology and dynamic processes.

Construction of Q models typically involves analyzing seismic waveforms, such as body waves (P and S waves) and surface waves. Several methods are employed, including:

• Spectral ratio methods: These methods compare the amplitude spectra of seismic waves that have traveled through different paths, allowing the estimation of the difference in attenuation.
• T methods:* This approach uses the parameter T*, which represents the integrated attenuation along the ray path, to infer Q values.
• Waveform modeling: This technique involves simulating seismic wave propagation through various Q models and comparing the synthetic waveforms with observed data. The Q model that best fits the data is then selected.
• Surface wave attenuation measurements: Analysis of the decay of surface wave amplitudes with distance can be used to estimate frequency-dependent Q values for the upper mantle and crust.

The resulting Q models are often presented as maps or three-dimensional volumes showing the distribution of Q values at different depths. These models can be global, regional, or local in scale, depending on the data used and the purpose of the study. The resolution and accuracy of a Q model are limited by the availability and quality of seismic data, as well as the chosen methodology. Despite these limitations, Q models provide essential constraints on our understanding of the Earth's structure, composition, and dynamics.