  Although our existing one-dimensional (1D) model provides a successful
quantitative description of rupture events, a 1D description is somewhat
limited. We therefore derive a two-dimensional (2D) model which allows us to
investigate characteristics of earthquakes (EQs) and slow slip events (SSEs)
that are only apparent in a second dimension. We find that the leading edge of
an EQ rupture in the direction of the global shear stress (x-direction) is
wider in the plane of the crustal fault (y-direction) than the trailing edge.
The direction of the slip velocity is primarily in the x-direction. EQ ruptures
expand in both the x- and y-directions. In SSEs, the rupture also expands in
both directions for a short period of time, then, after pulses are formed,
there is no further expandsion, i.e., the pulse shape remains practically
unchanged. The 2D simulations show the seismic moment (M) versus time (T)
scaling law may be expressed by the relation , where . For EQs, is
approximately equal to 3, while for SSEs, tends to 1 as the pulses develop and
become fully established. The 2D model quantitatively describes the parameters
of a seismic pulse in episodic tremor and slip (ETS) phenomena and also
explains important features of non-volcanic tremor associated with this pulse,
such as reverse tremor migration. The 2D model confirms the basic findings
obtained previously by the 1D model: (i) The type of a seismic event, EQ or
SSE, and the type of a rupture, crack-like or pulse-like, are determined solely
by the fault strength, the ratio of the shear to normal stress, and the
gradient in this ratio; (ii) The shape of a rupture and position of the maximum
slip is determined by the spatial distribution of the initial stress.
