The high-frequency falloff ω-&ggr; of earthquake displacement spectra and the b value of aftershock sequences are attributed to the character of spatially varying strength along fault zones. I assume that the high frequency energy of a main shock is produced by a self-similar distribution of subevents, where the number of subevents with radii greater than R is proportional to R-D, D being the fractal dimension. In this model, an earthquake is composed of a hierarchical set of smaller earthquakes. The static stress drop is parameterized to be proportional to R&eegr;, and strength is assumed to be proportional to static stress drop. I find that a distribution of subevents with D=2 and stress drop independent of seismic moment (&eegr;=0) produces a main shock with an ω-2 falloff, if the subevent areas fill the rupture area of the main shock. By equating subevents to ''islands'' of high stress of a random, self-similar stress field on a fault, I relate D to the scaling of strength on a fault, such that D=2-&eegr;. Thus D=2 corresponds to constant stress drop scaling (&eegr;=0) and scale-invariant fault strength. A self-similar model of aftershock rupture zones on a fault is used to determine the relationship between the b value, the size distribution of aftershock rupture zones, and the scaling of strength on a fault. The b value for aftershock sequences on a fault is found to equal (3-1.5&eegr;)/(3+&eegr;). Therefore this model indicates that the typically observed spectral falloffs of ω-2 and b values of 1 can be entirely caused by scale-invariant strength (&eegr;=0) along fault zones.