The coda quality factor of short‐period S waves (Qc) excited by local earthquakes in the Pyrenees has been measured as a function of the length of the coda window (LW) for different choices of the onset time of the coda (tW). In the 2–16 Hz frequency band, we observe a transient regime characterized by an increase of Qc with LW, followed by a stabilization around a plateau the value of which depends on the central frequency of the signal. Using Monte Carlo simulations of wave transport in a variety of random media (≈1200 models), we demonstrate that the lapse‐time dependence of Qc in the Pyrenees may be modeled by multiple anisotropic scattering of seismic waves, without invoking any depth dependence of the attenuation properties in the crust. In our model, anisotropic scattering is quantified by the ratio between the transport mean free path and the mean path (l*/l). At 6 Hz, the data require an anisotropy factor l*/l≥5, a transport mean free path l*≈400 km, and an intrinsic quality factor Qi≈800. From the frequency‐dependent plateau of Qc at large lapse time, we infer an intrinsic quality factor of the form Qi≈400f0.4 in the Pyrenees. We also show how the rapid increase of the lapse‐time dependence of Qc with frequency may be exploited to put constraints on the power spectrum of heterogeneities in the crust.