What can be learned from rotational motions excited by earthquakes?

One answer to the question posed in the title is that we will have more accurate data for arrival times of SH waves, because the rotational component around the vertical axis is sensitive to SH waves although not to P-SV waves. Importantly, there is another answer related to seismic sources, which will be discussed in this paper.
Generally, not only dislocations commonly used in earthquake models but also other kind of defects could contribute to producing seismic waves. In particular, rotational strains at earthquake sources directly generate rotational components in seismic waves. Employing the geometrical theory of defects, we obtain a general expression for the rotational motion of seismic waves as a function of the parameters of source defects.
Using this expression, together with one for translational motion, we can estimate the rotational strain tensor and the spatial variation of slip velocity in the source area of earthquakes. These quantities will be large at the edges of a fault plane due to spatially rapid changes of slip on the fault and/or a formation of tensile fractures.     

Evidence for different scaling of earthquake source parameters for large earthquakes depending on faulting mechanism

Scaling relationships between seismic moment, rupture length, and rupture width have been examined. For this purpose, the data from several previous studies have been merged into a database containing more than 550 events. For large earthquakes, a dependence of scaling on faulting mechanism has been found. Whereas small and large dip-slip earthquakes scale in the same way, the self-similarity of earthquakes breaks down for large strike-slip events. Furthermore, no significant differences in scaling could be found between normal and reverse earthquakes and between earthquakes from different regions. Since the thickness of the seismogenic layer limits fault widths, most strike-slip earthquakes are limited to rupture widths of between 15 and 30 km while the rupture length is not limited. The aspect ratio of dip-slip earthquakes is similar for all earthquake sizes. Hence, the limitation in rupture width seems to control the maximum possible rupture length for these events. The different behaviour of strike-slip and dip-slip earthquakes can be explained by rupture dynamics and geological fault growth. If faults are segmented, with the thickness of the seismogenic layer controlling the length of each segment, strike-slip earthquakes might rupture connected segments more easily than dip-slip events, and thus could produce longer ruptures than dip-slip events of the same width     

The two-point correlation function of the seismic moment tensor

Summary. We use the invariants of the two-point correlation function of the seismic moment to investigate the degree of irregularity of an earthquake fault, i.e. to study the rapidity with which a complex fault changes its direction of orientation. The two-point correlation function is a fourth-order tensor which has three scalar invariants in the isotropic case. Although the accuracy of present-day catalogues of fault plane solutions is rather low for our purpose, nevertheless the invariants of these correlation tensors confirm the generally     

Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering

10 M ≥ 6.7 earthquakes ruptured 1000 km of the North Anatolian fault (Turkey) during 1939–1992, providing an unsurpassed opportunity to study how one large shock sets up the next. We use the mapped surface slip and fault geometry to infer the transfer of stress throughout the sequence. Calculations of the change in Coulomb failure stress reveal that nine out of 10 ruptures were brought closer to failure by the preceding shocks, typically by 1–10 bar, equivalent to 3–30 years of secular stressing. We translate the calculated stress changes into earthquake probability gains using an earthquake-nucleation constitutive relation, which includes both permanent and transient effects of the sudden stress changes. The transient effects of the stress changes dominate during the mean 10 yr period between triggering and subsequent rupturing shocks in the Anatolia sequence. The stress changes result in an average three-fold gain in the net earthquake probability during the decade after each event. Stress is calculated to be high today at several isolated sites along the fault. During the next 30 years, we estimate a 15 per cent probability of a M ≥ 6.7 earthquake east of the major eastern centre of Ercinzan, and a 12 per cent probability for a large event south of the major western port city of Izmit. Such stress-based probability calculations may thus be useful to assess and update earthquake hazards elsewhere.     

The mean transmission properties of a fault with imperfect facial contact

A model of a fault where the two faces do not exactly conform is characterized by a distribution of approximately circular contacts; elsewhere, the faces are stress-free. This contrasts with most earlier models, which have assumed the contact geometry to be equivalent to a plane distribution of approximately circular cracks. The contact regions in the present model are taken to be sparsely distributed, and averaged interface conditions are derived that are accurate to second order. At lowest order they agree with established formulae for the normal stiffness of non-conforming surfaces. These averaged, or mean, conditions are expected to hold at wavelengths long compared with the radii and spacing distance of the contact points. Unsurprisingly, they are equivalent to the continuity conditions for a thin elastic layer whose properties are given here in terms of the parameters of the contact surface.     

Dynamic stress field of a kinematic earthquake source model with k-squared slip distribution

Source models such as the k -squared stochastic source model with k -dependent rise time are able to reproduce source complexity commonly observed in earthquake slip inversions. An analysis of the dynamic stress field associated with the slip history prescribed in these kinematic models can indicate possible inconsistencies with physics of faulting. The static stress drop, the strength excess, the breakdown stress drop and critical slip weakening distance D _c distributions are determined in this study for the kinematic k -squared source model with k -dependent rise time. Several studied k -squared models are found to be consistent with the slip weakening friction law along a substantial part of the fault. A new quantity, the stress delay, is introduced to map areas where the yielding criterion of the slip weakening friction is violated. Hisada's slip velocity function is found to be more consistent with the source dynamics than Boxcar, Brune's and Dirac's slip velocity functions. Constant rupture velocities close to the Rayleigh velocity are inconsistent with the k -squared model, because they break the yielding criterion of the slip weakening friction law. The bimodal character of D _c / D _tot frequency–magnitude distribution was found. D _c approaches the final slip D _tot near the edge of both the fault and asperity. We emphasize that both filtering and smoothing routinely applied in slip inversions may have a strong effect on the space–time pattern of the inferred stress field, leading potentially to an oversimplified view of earthquake source dynamics.