Properties of earthquake source physics can be inferred from the comparison between seismic observations and results of dynamic rupture models. Although simple self-similar rupture models naturally explain the space and time observations at the scale of the whole earthquake, several observational studies based on the analysis of source time functions (STFs) suggest that they are unable to reproduce the initial accelerating phases of the rupture. We here propose to reproduce the observed transient moment accelerations, without affecting the global self-similarity of the rupture, to constrain their possible physical origins. Simulated STFs are generated from dynamic simulations with heterogeneous slip-weakening distance Dc. Heterogeneity is introduced on the fault plane through a fractal number-size distribution of circular patches, in which Dc takes a value proportional to their radius. As a consequence of the stochastic spatial distribution of the patches, rupture development exhibits a large variability, and delays between initiation and main rupture activation frequently occur. This variability, together with the dynamic correlation between rupture velocity and slip velocity inside each broken patch, successfully perturbs the self-similar properties: rather than growing quadratically with time, STFs have an higher apparent time exponent, close to the observed value of 2.7. In a broader perspective, our simulations show that to respect observed STF shapes, realistic dynamic models should generate bursts of seismic moment, most likely by episodes where slip and rupture velocity are correlated. Such a behavior appears to emerge more naturally when considering heterogeneities in the friction parameters rather than in the initial stress.

Observation of the seismic process for a large earthquake population is of key interest to detect potential magnitude‐dependent behaviors and, more generally, to quantify how seismic rupture develops. In contrast with studies focusing on the first radiated waves, we here propose to characterize the growing phase leading to the main seismic moment release episode(s), which we refer to as the development phase. Our analysis uses the 2,221 teleseismic source time functions (STFs) of shallow dip‐slip earthquakes provided by the global SCARDEC database and consists in measuring the moment acceleration during the development phase at prescribed moment rates. This approach is therefore insensitive to hypocentral time uncertainties and aims at quantifying how seismic ruptures accelerate, independently of when they accelerate. Our results first show that rupture acceleration does not exhibit any magnitude‐dependent signal emerging above the intrinsic measurements variability. We thus use the full STF catalog to characterize the moment rate trueṀd of the development phase and show that, on average, trueṀdfalse(tfalse)∝tnd with nd equal to 2.7. This time evolution therefore does not follow the steady t2 growth expected for classical circular crack models, which indicates that stress drop and/or rupture velocity transiently vary during the development phase. We finally illustrate with a synthetic STF catalog that, due to initial rupture variability, approaches based on hypocentral time are not expected to fully characterize the behavior of the development phase.