Paper summaries 2012 and earlier

Abstract: Wedges, such as accretionary prisms and thin‐skinned fold‐and‐thrust belts, occur frequently in nature and can be the site of devastating earthquakes. Critical wedge theory can be applied to these settings, but this steady‐state description of wedge deformation is at odds with the periodic occurrence of earthquakes. We discuss how critical wedge theory applies to the seismic cycle, and we use elastic wedge theory to constrain realistic stress states. Our goal is to determine the rupture behavior of an earthquake in a wedge. If rupture initiates on the basal sliding surface, will it stay confined to the basal surface, or will it propagate onto a fault branch interior to the wedge? This information can significantly alter the seismic hazard in areas where fault intersections occur. We answer this question using numerical models of dynamic rupture propagation through branched geometries for which the stress state is a pivotal input parameter. We apply wedge theory to constrain the stress state, but inherent to this theory is the assumption of a weak basal fault. We investigate the role of this assumption and determine that rupture is unlikely to propagate from a weak basal fault onto a strong branch fault without the aid of a physical process such as pore fluid migration along the branch. This framework is applied to the rupture of the 2008 Wenchuan earthquake. We find that we are able to reproduce the behavior at some fault intersections, but our 2D model is not able to reproduce all the behaviors, possibly due to the oblique nature of this event.

Abstract: The 2008 M_w 7.9 Wenchuan earthquake ruptured an imbricate thrust system in the Longmen Shan range, which forms the eastern boundary of the Tibetan Plateau. We use seismic reflection data and surface geology to construct geologic cross sections and a three-dimensional (3D) fault model in the range front. The rupture was complex, with slip on both the steeply dipping Beichuan fault and the more shallowly dipping Pengguan fault, which appear to merge at depth. In contrast, only the Beichuan fault ruptured in the north, with the transition near a lateral fault offset. Thus, the earthquake involved multiple thrust splays and breached a significant segment boundary. To investigate the tectonic setting of the earthquake, we extend our previous measurements of crustal shortening (Hubbard and Shaw, 2009) into the interior of the range and show that shortening correlates with topography. This suggests that upper-crustal shortening can produce the high topography of the Longmen Shan without calling on other uplift mechanisms. Based on this understanding, we model the thrust belt as a critical taper wedge, to assess what rock and fault strengths are required to explain the topographic slopes within the range front and basin. The low taper within the basin is consistent with a weak detachment (δ_f≈0.1), while a slightly stronger (δ_f≈0.3–0.4) detachment is necessary to explain the higher taper of the range front. This difference may relate to the localization of the detachment within a Triassic evaporite sequence within the basin, while the faults beneath the range front are rooted in Precambrian metasedimentary or igneous rocks. Critical taper theory implies that shortening in the range front where the 2008 Wenchuan earthquake occurred is many times greater than in the basin, consistent with our shortening measurements. We examine the implications of these findings for seismic hazard assessment in the region and in other active mountain belts around the world.

Abstract: The 2008 M_w 7.9 Wenchuan earthquake is a result of ongoing India-Tibet collision and reflects the growth of the Longmen Shan fold-and-thrust belt. In this paper, we construct a 3-D structural model of the geometry of the coseismic faults and related structures of the Wenchuan earthquake by integrating geological investigations, relocated aftershocks, and seismic reflection profiles. In the 3-D structural model, the differences between the southern and northern segments of the rupture are highlighted. The structural transition zone between the two segments contains a major geometric segment boundary, reflecting differences in the structural configuration of the thrust ramp and the tectonic evolution of the fault system, which appears to have localized significant damage from Anxian to Beichuan. Within the northern segment, we identify a transverse structure across which the Beichuan fault plunges under the Tangwangzhai syncline. This boundary corresponds to a marked change in the nature of the surface rupture and is illuminated by a microearthquake sequence perpendicular to the Longmen Shan thrust belt. In the southern segment, our investigations confirm that uplift due to active faulting and folding is largely responsible for the areas of steepest topography. On the basis of this association, the southwestern segment of the Longmen Shan, south of the Wenchuan earthquake, is likely active and presents a significant earthquake hazard, despite the lack of historical earthquakes in this region. This study illustrates the importance of building 3-D models to study active faulting and folding, as well as to assess earthquake hazard.

Abstract: The Longmen Shan mountain range, site of the devastating 12 May 2008 Wenchuan (M =  7.9) earthquake, defines the eastern margin of the Himalayan orogen and exhibits greater topographic relief than anywhere else in the Tibetan plateau. However, before the earthquake, geodetic and geologic surveys measured little shortening across the range front, inspiring a vigorous debate about the process by which the topography of the mountain belt is produced and maintained. Two endmember models have been proposed: (1) brittle crustal thickening, in which thrust faults with large amounts of slip that are rooted in the lithosphere cause uplift, and (2) crustal flow, in which low-viscosity material in the lower crust extrudes outward from the Tibetan plateau and inflates the crust north and east of the Himalayas. Here we use balanced geologic cross-sections to show that crustal shortening, structural relief, and topography are strongly correlated in the range front. This suggests that crustal shortening is a primary driver for uplift and topography of the Longmen Shan on the flanks of the plateau. The 2008 Wenchuan (M =  7.9) earthquake, which ruptured a large thrust fault along the range front causing tens of thousands of fatalities and widespread damage, is an active manifestation of this shortening process.

Abstract: The Mw 7.9 Wenchuan, China, earthquake ruptured two large thrust faults along the Long-menshan thrust belt at the eastern margin of the Tibetan Plateau. This earthquake generated a 240-km-long surface rupture zone along the Beichuan fault and an additional 72-km-long surface rupture zone along the Pengguan fault. Maximum vertical and horizontal offsets of 6.5 m and 4.9 m, respectively, were measured along the Beichuan fault. A maximum vertical offset of 3.5 m was measured along the Pengguan fault. Coseismic surface ruptures, integrated with aftershocks and industry seismic profiles, show that two imbricate structures have ruptured simultaneously, resulting in the largest continental thrust event ever documented. Large oblique thrusting observed during this earthquake indicates that crustal shortening is an important process responsible for the high topography in the region, as everywhere along the edge of Tibetan Plateau.

Abstract: This is the second in a series of papers about the dynamics of the forced van der Pol oscillator [J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 1--35]. The first paper described the reduced system, a two dimensional flow with jumps that reflect fast trajectory segments in this vector field with two time scales. This paper extends the reduced system to account for canards, trajectory segments that follow the unstable portion of the slow manifold in the forced van der Pol oscillator. This extension of the reduced system serves as a template for approximating the full nonwandering set of the forced van der Pol oscillator for large sets of parameter values, including parameters for which the system is chaotic. We analyze some bifurcations in the extension of the reduced system, building upon our previous work in [J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 1--35]. We conclude with computations of return maps and periodic orbits in the full three dimensional flow that are compared with the computations and analysis of the reduced system. These comparisons demonstrate numerically the validity of results we derive from the study of canards in the reduced system.