ALBERT

Description: 〈span〉〈div〉SUMMARY〈/div〉Backprojection (BP) of teleseismic 〈span〉P〈/span〉 waves is a powerful tool to study the evolution of seismic radiation of large earthquakes. The common interpretations on the BP results are qualitative comparisons with earthquake kinematic observations, such as the evolution of slip on the fault and rupture velocity. However, the direct relation between the BP images and physical properties of the earthquake rupture process remains unclear and is needed for further application of this technique. In this study, we start from a theoretical formulation of the BP images, which is linear in the frequency domain, and carry on a synthetic exercise with kinematic source representations and virtual receivers embedded in a homogeneous full-space. We find that the fundamental linear formulation of the BP method is most correlated with the true kinematic source properties: in frequency domain the BP images are proportional to the images of slip motion through a scaling matrix $\mathbf {F}(\omega )$ that accounts for radiation pattern and source–receiver geometry and that acts as a spatial smoothing operator. Overall, the synthetic BP images match relatively well the kinematic models and our exercise validates that the BP image can be directly used to track the spatiotemporal propagation of rupture front. However, because $\mathbf {F}(\omega )$ is not strictly an identity matrix due to limited station coverage in space (azimuth and distance) and to the limited frequency bands of the seismograms, it remains difficult to recover the details in the rupture fronts from BP images. We define a resolvability parameter ε〈sub〉〈span〉I〈/span〉〈/sub〉(ω) built from $\mathbf {F}(\omega )$ that incorporates fault geometry, radiation pattern and wave propagation (source–array geometry) to quantify the ability of the BP method to resolve details of the rupture on the fault. ε〈sub〉〈span〉I〈/span〉〈/sub〉(ω) successfully captures the similarity between BP images and kinematic source. We analyse the resolvability of most tectonically active regions and the most commonly used seismic arrays. Based on this global resolvability analysis, we propose an empirical relation between the seismic frequency, resolvable area and earthquake magnitude. It provides general guidelines to choose the lowest frequency in seismic waveform (e.g. about 0.3 Hz for 〈span〉M〈/span〉〈sub〉w〈/sub〉 8 and 1 Hz for 〈span〉M〈/span〉〈sub〉w〈/sub〉 7 earthquakes) and to interpret the BP image in terms of the source kinematics. In general, this work attempts to provide a clear interpretation of the BP images in light of the real earthquake rupture process and give a systematic evaluation of seismic data limitations.〈/span〉