Reliable estimate of the anelastic attenuation factor-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> from seismic records is highly desirable for improving seismic resolution. However, the conventional equivalent-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> or horizontal interval-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> estimation ignores that <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-distribution should hold the same ability for the subsurface structure characterization as seismic data. To pursue an accurate <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-model, we propose a technique for joint reflectivity and structural interval-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> estimation by using nonstationary sparse inversion. We designed a structural interval-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> model by dividing the seismic data into several structural layers with the interpreted horizon(s). Attenuations in each layer are close to each other and can be described by an equivalent-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> or gradient-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>. Based on the attenuation theory, the nonstationary sparse inversion is solved iteratively, where, at each iteration, the equivalent-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> of only one layer is optimized by searching for the corresponding optimum inverted reflectivity, leading to a structural interval-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> model. The main advantages of our method are its objectivity and accuracy because of the integration of the prior structural information from interpreted horizons into joint reflectivity-estimation and <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-estimation. The test of synthetic and field data clearly illustrates that the proposed method enables high-precision structural interval-<inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula> estimation and sufficiently compensates for <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-related attenuation.