Structural modeling of the Western Transverse Ranges: An imbricated thrust ramp architecture

Active fold-and-thrust belts can potentially accommodate large-magnitude earthquakes, so understanding the structure in such regions has both societal and scientific importance. Recent studies have provided evidence for large earthquakes in the Western Transverse Ranges of California, USA. However, the diverse set of conflicting structural models for this region highlights the lack of understanding of the subsurface geometry of faults. A more robust structural model is required to assess the seismic hazard of the Western Transverse Ranges. Toward this goal, we developed a forward structural model using Trishear in MOVE® to match the first-order structure of the Western Transverse Ranges, as inferred from surface geology, subsurface well control, and seismic stratigraphy. We incorporated the full range of geologic observations, including vertical motions from uplifted fluvial and marine terraces, as constraints on our kinematic forward modeling. Using fault-related folding methods, we predicted the geometry and sense of slip of the major faults at depth, and we used these structures to model the evolution of the Western Transverse Ranges since the late Pliocene. The model predictions are in good agreement with the observed geology. Our results suggest that the Western Transverse Ranges comprises a southward-verging imbricate thrust system, with the dominant faults dipping as a ramp to the north and steepening as they shoal from ∼16°–30° at depth to ∼45°–60° near the surface. We estimate ∼21 km of total shortening since the Pliocene in the eastern part of the region, and a decrease of total shortening west of Santa Barbara down to 7 km near Point Conception. The potential surface area of the inferred deep thrust ramp is up to 6000 km2, which is of sufficient size to host the large earthquakes inferred from paleoseismic studies in this region.


INTRODUCTION
Active fold-and-thrust belts produce destructive earthquakes, such as the M 7.9 Wenchuan earthquake in 2008 and the M 7.3 Gorkha earthquake in 2015 (Hayes et al., 2016). Estimating the geometry of faults at depth is important for risk assessment because the deep connectivity in thin-skinned fold-and-thrust belts determines the plausible sizes of earthquakes that a system can host (Wells and Coppersmith, 1994). Furthermore, many structural predictive models have been developed because this class of structures acts as potential hydrocarbon traps (e.g., Suppe, 1983;Suppe and Medwedeff, 1990;Erslev, 1991;Groshong, 1994;Poblet and McClay, 1996). The Western Transverse Ranges ( Fig. 1) of southern California is an active fold-and-thrust belt (Namson and Davis, 1988;Shaw and Suppe, 1994) in a highly populated region, with 18 million people inhabiting the Los Angeles Basin along its southern margin. Recent studies of coastal uplift and borehole transects across a fold scarp have revealed that very large and rapid uplift events have occurred along the Pitas Point/Ventura fault system (Fig. 1B, localities a and b;Hubbard et al., 2014), the offshore part of which is referred to as the Pitas Point fault and the onshore part of which is referred to as the Ventura fault. The observed uplift events were estimated to be the result of Mw 7.5-8 earthquakes (Rockwell et al., 2016;McAuliffe et al., 2015). For instance, Holocene coastal marine terraces near Punta Gorda between Ventura and Santa Barbara, California, record four uplift events in the past 6.7 k.y., with an average of 10 m per uplift event (Rockwell et al., 2016), Punta Gorda (Fig. 1B, locality a) is situated on the axis of the Pitas Point/Ventura Avenue anticline along a section where the Pitas Point fault is mostly or completely blind, so much or all of the fault slip is translated into uplift through folding and back-thrusting. Similarly, the onshore Ventura fault has produced up to 6 m of vertical deformation per event (McAuliffe et al., 2015). These uplift events are comparable to the magnitude of uplift observed in the 1999 M 7.6 Chi-Chi earthquake in Taiwan (Ma et al., 1999), and scaling relations (Wells and Coppersmith, 1994) suggest that these are the result of large earthquakes. Considering the complex structural geology in the upper several kilometers of the Western Transverse Ranges, the observed uplifts were suggested to be the result of multisegment thrust fault ruptures (Hubbard et al., 2014). However, this explanation has been questioned based on arguments of fault complexity (Sorlien and Nicholson, 2015).
Various structural models (e.g., Yeats et al., 1988;Namson and Davis, 1988;Shaw and Suppe, 1994;Hubbard et al., 2014;Sorlien and Nicholson, 2015) have been advanced over the years to describe the complex fault architecture in the Western Transverse Ranges. Nevertheless, there are ongoing debates regarding these proposed models, mainly centered on the direction of dip of the primary structures and their senses of slip. As a result, series of competing, alternative models for these structures are represented LEVY ET AL. | Structural modeling of the Western Transverse Ranges RESEARCH in the Southern California Earthquake Center's (SCEC) Community Fault Model (CFM; Nicholson et al., 2017;Plesch et al., 2007) and used in regional hazards assessments.
In this work, we incorporated published geological observations, including late Quaternary geologic vertical motions, to be used as interpretive constraints on a kinematic forward model for the Western Transverse Ranges. We started with the detailed regional mapping by Dibblee (2002) and incorporated subsurface data from the numerous oil wells in the region, as well as offshore seismic re ection pro les and their interpretations (Sorlien and Nicholson, 2015) and published geological observations (Davis and Namson, 1998;Hubbard et al., 2014;Jackson, 1981;Namson and Davis, 1988;Sarna-Wojcicki and Yerkes, 1982;Schlueter, 1976;Yeats, 1983). From these sources, we constructed seven geologic cross sections of the upper few kilometers, with sections across the eastern Ventura Basin westward to near Point Conception (Fig. 2). We then applied forward modeling using the Trishear module in Move® (https://www.mve.com/) to replicate or match the primary structural elements of the Western Transverse Ranges, as shown in the geologic cross section, with the intent of developing a crustal-scale model of the entire seismogenic portion of the crust. Incorporated into this modeling was information on the local and regional vertical motions, which aided in constraining the fault dip at depth. The nal result is a retrodeformable, area-balanced kinematic model that matches and accounts for the sur cial and shallow subsurface geology, the local and regional structural relief, and late Quaternary vertical motions as determined from geologic studies of uplifted and deformed marine and uvial terrace sequences. We applied this model to test the possibility that the Western Transverse Ranges hosts a fault system that may be capable of generating earthquakes responsible for the large uplift events observed in the region.

GEOLOGICAL BACKGROUND
The Western Transverse Ranges are composed of continental plutonic and metamorphic basement in the east and juxtaposed or accreted oceanic ophiolitic-Franciscan basement complex in the west, both overlain by an ~13-km-thick section of Cretaceous and Cenozoic sedimentary and volcanic deposits (Fig. 3;Dibblee, 1982a). In the Mesozoic and early Cenozoic, the Transverse Ranges block, or blocks, occupied the forearc region of a subduction zone collecting continental shelf sediments (Atwater, 1998). During the Oligocene, the Paci c plate made contact with North America (Atwater, 1998), and the tectonic regime in the Western Transverse Ranges changed as the San Andreas transform plate boundary (Fig. 1A) evolved over time (Crowell, 1979). In the middle Miocene, the con guration had a transtensional geometry that was responsible for localized extension, rotation, and left-lateral shearing (Atwater, 1998). Later, beginning in the Pliocene, the region began to undergo shortening (Atwater, 1998;Dibblee, 1982b;Rockwell, 1983); this shortening regime continues to the present (Rockwell, 1988;Rockwell et al., 1988;Marshall et al., 2013   S a n t a Yn ez An tic lin orium S a n A n d re a s F a u lt   (Miller et al., 2005) Continuous deposition of continental shelf sediments as the WTR occupied the forearc region of a subduction zone (Atwater, 1998). No recognized angular unconformities in the Ventura basin Tectonic regime Inception of shortening and formation of the fold thrust belt (Atwater, 1998;Dibblee, 1982b;Rockwell, 1983) Extension, rotation, left lateral shearing and volcanism (10-8 Ma) (Atwater, 1998 Figure 3. Stratigraphic column of the Western Transverse Ranges (WTR) modi ed from Dibblee (1982b). Thickness is presented in meters in the numerical column. This is a generalized stratigraphy, and some units have fault contacts as can be seen in Figure 2. For stratigraphic columns in different localities, we refer to Dibblee (1982b). We added a column that describes the tectonic regime.
that the region has mostly experienced continuous subsidence. Bird and Rosenstock (1984) presented a case to explain the regional subsidence with a model of mantle downwelling and incipient subduction, which might explain the mechanism required to accommodate such a thick stratigraphic sequence. While the deposition of the terrestrial Oligocene Sespe sediments might imply uplift, global sea level changed during that period due to the formation of the large ice sheets in Antarctica (Miller et al., 2005).
Deposition in the Santa Barbara/Ventura Basin, south of the range (Figs. 2, 3, and 4), has been nearly continuous since the Eocene, and it accelerated in the Pliocene (Dibblee, 1982b;Yeats and Rockwell, 1991). Northward from the Santa Ynez fault system, the Eocene sequence thins rapidly, as do the Oligocene Sespe Formation and the Rincon and Vaqueros Formations (Dibblee, 1982b). An angular unconformity is locally present between the middle Miocene (Mohnian) Monterey Formation and older strata (Figs. 2, 3, and 4), which suggests a prelate Miocene period of erosion that may have resulted from local uplift during Miocene extension. There are two models that describe the Miocene period of rotation and local extension, as indicated by paleomagnetic measurements (e.g., Horna us, 1985;Horna us et al., 1986Horna us et al., , 1982Nicholson et al., 1994;Schwartz 2018). One model suggests that the Western Transverse Ranges rotated clockwise by 110° as a large coherent block (Horna us et al., 1982;Nicholson et al., 1994). Dibblee (1982b), referring to this earlier work (Horna us et al., 1982), stated that so much rotation and the space problem with large adjacent blocks would be dif cult if not impossible to account for from the geology. Alternatively, Schwartz (2018) suggested that the Miocene rotation more likely occurred as rotation of microplates. In either case, the paleomagnetic measurements show that most  of the rotation accrued between 12 and 8 Ma (Horna us et al., 1986;Schwartz, 2018), and therefore the rotation observed in the Western Transverse Ranges predated the current shortening regime, which began during the Pliocene. Figure 2 presents a compilation of a large number of geologic maps of the Western Transverse Ranges (Dibblee, 2002). A rst-order observation is that topography is being built to the north, and the structural relief from north to south is ~11 km with the north side up, as Cretaceous rocks are exposed along the Santa Ynez anticlinorium and Quaternary rocks are exposed to the south in the Ventura anticline and in the Ventura Basin (Figs. 2, 3, and 4).
The most obvious feature along the Santa Ynez mountain range is the ~160-km-long, E-W-trending Santa Ynez anticlinorium. This anticlinorium has a mostly overturned south limb, with a 5-km-thick section of overturned Eocene marine and Oligocene strata. East of Ojai Valley (Fig. 1B), the south limb is cut by the south-verging San Cayetano fault, which is interpreted as the emergent portion of the associated thrust underneath this fold (Namson and Davis, 1988). Where the San Cayetano fault is emergent, the fault displaces early Eocene rocks in the hanging wall against Quaternary rocks in the footwall with as much as 9 km of stratigraphic separation at the surface (Rockwell, 1988), although additional shortening by folding may require a larger basement offset.
The nomenclature in the Western Transverse Ranges is a source for confusion, so it is important to clarify that the Santa Ynez fault, in many locations, is too far north from the anticlinorium to be interpreted as the fault that produced this large fold (Fig. 2). Furthermore, the Santa Ynez fault currently exhibits mainly left-lateral strikeslip motion (Darrow and Sylvester, 1983), and it has a very steep dip that varies from dipping to the north to dipping to the south along its strike. Although its late Quaternary slip history is strikeslip motion, the Santa Ynez fault has sustained as much as 1-3 km of dip slip, which presumably occurred prior to its current role partitioning the majority of the strike slip accommodated within the Western Transverse Ranges.
There are a variety of structural interpretations for this region (Fig. 5). Yeats et al. (1988) presented balanced cross sections with a dominant north-verging structure, the Sisar décollement, at 8 km depth, south of the Red Mountain and San Cayetano faults. In their model (Fig. 5A), both the Ventura Avenue anticline and the Sulphur Mountain anticline, the latter of which is located between the Lion and South Sulphur Mountain faults (Fig. 1A), were formed by a south-dipping thrust system that roots to a décollement ~8 km under the surface. Namson and Davis (1988) presented their model ( Fig. 5B) based on fault-propagation fold and fault-bend fold methods (Suppe,1983). They proposed the presence of a detachment at 12-15 km depth and associated the San Cayetano thrust with the Santa Ynez anticlinorium. From seismological observations, a northdipping low-angle fault was interpreted that might also relate to Namson and Davis' (1988) décollement at depths of ~12 km (Corbett and Johnson, 1982;Hauksson et al., 2016;Huang et al., 1996). South of the anticlinorium, the main thrust in the Namson and Davis (1988) model dips south, in what seems to be a structure that is comparable to the Sisar décollement presented by Yeats et al. (1988). Namson and Davis (1988) interpreted the South Sulphur Mountain anticline to result from the south-dipping Lion fault, and the Ventura Avenue anticline has a number of small layer-parallel faults, dipping alternately south and north, associated with it in their model. Hubbard et al. (2014) applied fault-related folding theories (Shaw et al., 2005;Suppe, 1983;Suppe and Medwedeff, 1990) and used well and seismic re ection data in the Ventura Basin to construct a model of the Ventura Avenue anticline. They incorporated the Ventura fault as the structure producing the Ventura Avenue anticline, and they connected this fault with the Red Mountain, Lion, and San Cayetano faults, with a at thrust within the Rincon shale at ~7 km depth. The linkage between the detachment and San Cayetano fault yields a ramp-at-ramp geometry for the Pitas Point/Ventura fault. In this model, the structure forming Sulphur Mountain is also interpreted as a south-dipping fault. This model is represented as one version in the SCEC CFM5.2 ( Fig. 5C; Plesch et al., 2007;Nicholson et al., 2017). Sorlien and Nicholson (2015) presented several interpreted seismic cross sections in the offshore Ventura-Santa Barbara Basin but did not extend or interpret faults below the depth of imagery, i.e., ~6-7 km. Their sections demonstrate that the offshore Pitas Point fault system is aligned with the onshore Ventura fault and anticline. One of the versions of the SCEC CFM presents high-angle reverse oblique faults as the dominant structures producing the Western Transverse Ranges ( Fig. 5D; Nicholson et al., 2017). Faults are connected as a regional ower structure in this version, and there is no blind San Cayetano fault west of Ojai Valley. This version appears to attribute the formation of the Santa Ynez anticlinorium to a south-dipping Santa Ynez fault, but this cannot be correct because the anticlinorium is overturned (verges) to the south, and the fault is far to the north.

TIMING AND STYLE OF DEFORMATION
The formation of the Santa Ynez anticlinorium probably initiated during the late Pliocene or early Quaternary (Dibblee, 1982a), and folding ceased before 200 ka (Rockwell, 1988). The age of initiation of the San Cayetano fault is not directly constrained. Rockwell (1983) documented that uplift to the north initiated by ca. 3.2 Ma, based on analysis of microfauna in the Lower Pliocene Pico Formation, which also contained clasts of the Miocene Monterey Formation that were derived from the north. These may have been shed from folding and uplift north of the Santa Ynez range, or from the anticlinorium itself. The south-verging, overturned Red Mountain anticline and north-dipping Red Mountain fault began motion by at least 1 Ma (Yerkes and Lee, 1987). The current dip on the Red Mountain fault is anomalous in that it dips steeply (70°) to the north, which is unfavorable for accommodation of shortening.
Folding of the onshore Ventura Avenue anticline is estimated to have begun around ca. 300-200 ka (Rockwell et al., 1984) and continues to the present (Hubbard et al., 2014;McAuliffe et al., 2015;Rockwell et al., 2016). In the offshore to the west, the same fold trend initiated motion earlier in the Quaternary and appears to be progressively older toward the west (Sorlien and Nicholson, 2015). This makes sense if the primary cause of folding in the Western Transverse Ranges is associated with the continued development of the Big Bend in the San Andreas fault (Crowell, 1979), as the westernmost Transverse Ranges toward Point Conception are now translated west of the Big Bend such that the shortening should have been earlier, and the current rate should be much lower. We discuss this further later in this paper.
The late Quaternary vertical motions are an important consideration in the development of a defendable structural model. North of the Arroyo Parida fault, terraces of the Ventura River (Fig. 1B, locality c) indicate regional uplift (without folding) at ~1 mm/yr across the southern ank of the Santa Ynez anticlinorium for at least the past 200 k.y. (Rockwell et al., 1984). Similarly, the Santa Ynez Valley north of the anticlinorium is rising at a similar rate of ~1 mm/yr (Fig. 1B, locality d; Farris, 2017). These observations argue for a regional uplift rate north of the Arroyo Parida fault of ~1 mm/ yr, which must be accounted for in any viable structural model.
Farther west in the Santa Barbara region (Fig.  1B), current contractional deformation is also localized south of the Arroyo Parida-Mission Ridge fault, although the main topographic relief is to the north in the Santa Ynez Mountains  (Gurrola et al., 2014). Southward, active deformation extends offshore into Santa Barbara Basin, with active folding of the Pitas Point/ Ventura Avenue, Red Mountain, Oak Ridge, and Mid-Channel anticlinal trends (Perea et al., 2017;Shaw and Suppe, 1994;Sorlien and Nicholson, 2015). The ca. 57 ka marine terraces demonstrate an uplift rate of ~1 mm/yr at Isla Vista (Fig. 1B, locality e; Gurrola et al., 2014) and at least 0.3 mm/yr farther west (Fig.  1B, locality f) between Gaviota and Point Conception (Rockwell et al., 1992). The apparent decrease in rate to the west is consistent with observed lower rates of shortening based on global positioning system (GPS) data (Marshall et al., 2013).

RESEARCH
The most rapid rates of uplift in the entire region are associated with the Ventura-San Miguelito anticline at Punta Gorda (Fig. 1B, locality a), where the long-term rate is estimated at 6-7 mm/yr (Rockwell et al., 2016). This is also where four Holocene marine terraces have been identi ed, with each terrace interpreted to correspond to an abandoned abrasion surface due to uplift produced by an earthquake (Rockwell et al., 2016). The highest Holocene terrace is preserved at ~38 m above modern sea level near the fold crest and is interpreted to represent the cumulative uplift from four large earthquakes (Rockwell et al., 2016). In addition, analysis of GPS data showed that this region has the highest rate of shortening ( g. 5 in Marshall et al., 2013). Finally, results from a geodetic study showed an uplift signal north of the Santa Ynez range, which is consistent with interseismic strain accumulation on active thrusts in the Western Transverse Ranges (Hammond et al., 2018).

CROSS SECTIONS
We constructed seven geological cross sections over a 140 km length of the Western Transverse Ranges, from near Fillmore westward to near Point Conception (Figs. 2 and 4), using surface geology and dip data (Dibblee, 2002), subsurface well control (see Appendix), and seismic and previous geologic sections ( Davis and Namson, 1998;Hubbard et al., 2014;Jackson, 1981;Namson and Davis, 1988;Sarna-Wojcicki and Yerkes, 1982;Schlueter, 1976;Sorlien and Nicholson, 2015;Yeats, 1983). Each cross section (Fig. 4) presents near-surface observations, and interpretations where surface data were projected downward to a small extent. Interpretations of thickness are based on calculations of true thickness from the geological maps (Dibblee, 2002) and from the stratigraphic columns presented in Dibblee (1982a). The overturned south limb of the anticlinorium is apparent in sections 1-5. To the west, in crosssection 6 and 7, the south limb is not overturned, but the anticlinorium still appears to be the largest structure.
The rst-order observations of uplift in the north and subsidence in the south point to a southward-directed motion for the main faults at depth. These southward-verging faults are interpreted to accommodate the observed shortening and uplift. The models that consider the south-dipping faults as the dominant structures, such as the inferred Sisar detachment, which has been interpreted primarily as a tool to balance cross sections (Yeats et al., 1988), are thus inconsistent with the well-documented vertical motions of the region. Observationally, the Ventura-Santa Barbara Basin is subsiding at a high rate of 2-3 mm/yr, whereas onshore north of the basin, there are observations that argue for relatively high rates of uplift.
One aspect of our geological interpretation that is signi cantly different from previous interpretations (Fig. 5) relates to the fault that produces the South Sulphur Mountain anticline; the subsurface is poorly constrained by well control because most of the oil production has been from shallow strata. The regional orientation and alignment of the structures (Fig. 2), along with the overturned south ank (verges south) and stratigraphic relief, suggest that this anticline was produced by a north-dipping fault. In cross section 2 (Fig. 4), we interpret it as a south-verging structure, with the South Sulphur Mountain fault as the main thrust and the Lion fault as a back thrust, rather than the previously suggested interpretation of a dominant southdipping fault (Hubbard et al., 2014;Namson and Davis, 1988;Yeats et al., 1988), which did not include the observed overturned south ank ( Fig. 2; Dibblee, 2002). Finally, our model seeks to explain the southward younging or serial development of the rst-order structures, from early development of the Santa Ynez anticlinorium to the late Quaternary evolution of the onshore Ventura Avenue anticline, as described in the next section.

EVOLUTION OF THE FOLD-AND-THRUST SYSTEM SINCE THE PLIOCENE
When considering all of the observations referred to above on the timing and location of folding, it is apparent that the Western Transverse Ranges are a southward-propagating fold-and-thrust belt, as rst suggested by Rockwell (1983), and that it is evolving in a fashion similar to other forward-propagating fold-and-thrust belts (Boyer and Elliott, 1982;Butler, 1987;DeCelles et al., 2001;Jordan et al., 1993;Morley, 1988;Wiltschko and Dorr, 1983), as also demonstrated in laboratory experiments (e.g., Storti et al., 1997;Smit et al., 2003). Onshore near Ventura, current deformation is localized between the Arroyo Parida fault (Rockwell et al., 1984) and the Ventura fault (Hubbard et al., 2014;McAuliffe et al., 2015), with the majority of shortening taken up by the Ventura Avenue anticline and associated Ventura fault. Offshore, east of Santa Barbara, the pattern is a little more complex based on new seismic re ection (CHIRP) data (Perea et al., 2017). The interpretation of these data suggests that the deformation has jumped from east to west and from south to north, from the Pitas Point/Ventura Avenue anticline and Pitas Point fault to the Red Mountain anticline and then to the Mesa-Rincon Creek fold system (located in Fig. 1B between locality e and Santa Barbara). Close to Ventura, the most active structures are the Pitas Point/Ventura Avenue anticline and Pitas Point fault, whereas the Mesa-Rincon Creek fold system is the most active structure close to Santa Barbara (Perea et al., 2017).
We conclude that a blind extension of the San Cayetano fault west of Ojai Valley produced the mostly overturned Santa Ynez anticlinorium as the rst location of the thrust front, as rst suggested by Namson and Davis (1988). North of the Santa Ynez range, the Pine Mountain fault might predate the San Cayetano fault, but the lack of age data or associated stratigraphic observations does not allow us to resolve this question at this time, and total shortening from this structure is minor compared to that of the anticlinorium to the south. The observation that folding had ceased prior to 200 ka implies that the blind San Cayetano fault west of Ojai Valley (Fig. 1B) is no longer active. By at least 1 Ma (Yerkes and Lee, 1987), the thrust front propagated south, rst to the Red Mountain and South Sulphur Mountain faults, and then, in the late Quaternary, to the currently active but mostly blind Pitas Point/Ventura fault, with the Pitas Point/Ventura Avenue and related anticlines developing in the hanging wall. The Red Mountain fault continues to play a role in the offshore Santa Barbara Basin, but onshore, we interpret the late Quaternary deformation and steep dip of the fault to be the result of passive exural slip due to folding in the back limb of the Ventura Avenue anticline, similar to the schematic development of the imbricate thrust system presented by Poblet and Lisle (2011). This sequence of events for the onshore Ventura Basin is consistent with other well-documented fold-and-thrust belts worldwide, where propagation of the thrust front develops "in sequence" with the direction of vergence of the primary structures. Figure 6 illustrates our proposed model for the evolution of the first-order Pliocene structure of the Western Transverse Ranges fold-and-thrust belt.

MODEL ASSUMPTIONS
We made a number of assumptions to model the geometry and evolution of faults at depth. The stratigraphy in the model is simpli ed, and the thicknesses of the units are xed, although in the real world, there are local changes due to the Miocene period of rotation and extension. Considering that our goal was to model the overall rst-order, Pliocene and younger contractional deformation of the Western Transverse Ranges, we suggest that the resulting mismatches from not incorporating these stratigraphic details are minor.
The second assumption is that out-of-plane motion can be neglected. Some faults in the Western Transverse Ranges have accommodated some strike-slip motion during the late Quaternary, and the larger earthquakes in the Central Transverse Ranges, to the east of the study area, have exhibited up to 30% left-lateral strike-slip motion (cf. the 1971 San Fernando earthquake). However, the orientation of shortening relative to the stress eld generated by the Big Bend of the San Andreas fault argues that the maximum compressive stress is N-S ( Rodgers, 1975), and this is borne out by modern geodetic observations that demonstrate primarily NNW-SSE shortening across the Western Transverse Ranges (Marshall et al., 2013), which, if anything, should produce a very minor rightlateral component of motion on E-W-striking faults. Thus, the amount of strike-slip relative to the rate of shortening is expected to be small, but we address it further here to avoid the common criticism of two-dimensional (2-D) modeling where there is a potential component of strikeslip motion.
The three high-angle strike-slip faults that may impact our forward modeling are the Big Pine, Santa Ynez, and Arroyo Parida faults (Fig.  1B). There are few data on the recent activity of the Big Pine fault, although it is suf ciently north of the main structures that any strike-slip motion will have negligible effect. The Santa Ynez fault has been studied to some degree with paleoseismic trenches; Sylvester (1983, 1984) excavated a "box trench" (two perpendicular and two parallel trenches across a fault) to estimate 5-10 m of left-lateral displacement of basal terrace gravels, which are overlain by several meters of sediment and capped by a middle Holocene soil, which in turn provides a minimum age of displacement of ca. 5 ka. The next higher terrace (Qt2) has an estimated soil age of ca. 16 ka, placing a maximum age on the basal gravels. Thus, the maximum late Quaternary slip rate range for the Santa Ynez fault is estimated to be 0.3-2 mm/yr. The Arroyo Parida fault displays no evidence of lateral slip in late Pleistocene terraces of the Ventura River (Fig. 1B, locality g; Rockwell et al., 1984), although a minor component could have been missed at the scale of mapping (1:20,000). Near Carpinteria (Fig. 1B, locality  h), uvial channels incised into bedrock in the Santa Ynez range display left de ections where the channels cross the Arroyo Parida fault. However, the bedrock channels must predate the last interglacial marine terraces, which cut across rock downstream from the fault crossings and are likely considerably older. Based on these observations, it does not appear that the Arroyo Parida fault has sustained much, if any, late Quaternary lateral slip at the Ventura River, and it likely has a low rate of well less than 1 mm/yr near Carpinteria and Santa Barbara. We consider both the Santa Ynez and Arroyo Parida faults as the structures that accommodate the partitioned strike-slip motion in the Western Transverse Ranges.
Seismological data also argue for a component of lateral slip, as most of the larger Transverse Ranges earthquakes exhibited oblique slip, based on observations from surface ruptures (Keller and DeVecchio, 2013) or focal mechanism solutions (Corbett and Johnson, 1982), although many of these observations are far to the east. In summary, there is a lateral component of shear in the Western Transverse Ranges, but considering a rate that is most likely less than 2 mm/yr, versus a contraction rate of that is close to 10 mm/yr, the lateral slip is considerably subordinate to the rate of shortening. Considering that the shortening of the Western Transverse Ranges initiated at ca. 3-2 Ma, there has been only a few kilometers of lateral shear during the period of contraction. In contrast, the Paleogene sedimentary rocks show lateral continuities on the scale of tens of kilometers with gradual thinning to the north in the direction of contraction. Therefore, the lateral component of strains should have only a minor effect on forward modeling that assumes pure contraction, especially for the pre-Miocene strata, which record the major shortening associated with the Santa Ynez anticlinorium.
Similarly, the thicknesses of most of the Neogene rocks to the top of Miocene are relatively constant, although there are exceptions due to extensional faulting during the Miocene, which are accounted for in the model. This is evident from the relatively constant thickness of marine units that form the Santa Ynez range from Point Conception to at least the Ventura River, with local areas of complexity. Based on the above discussion, we assume that the effects of out-of-plane motion are negligible for our forward modeling, as presented below.

ESTIMATE OF DIP FOR THE FAULT AT DEPTH
There is a considerable debate as to whether the structures in the Western Transverse Ranges are controlled solely by high-angle reverse oblique faults (Nicholson et al., 2017) or whether there is a regional detachment or gently dipping thrust ramp that underlies the region (e.g., Namson and Davis, 1988;Shaw and Suppe, 1994).  Figure 9; similar steps were performed for the other cross sections, and the nal result was compared to surface and near-surface observations (Fig. 10).
As mentioned in the geological background section, Namson and Davis (1988) presented evidence for placing a décollement at a depth of 12-15 km depth, and seismological observations support this interpretation (Corbett and Johnson, 1982;Hauksson et al., 2016;Huang et al., 1996). Hubbard et al. (2014) proposed the existence of a at at ~7 km, in contrast to previous models with a south-dipping detachment under the basin (Namson and Davis, 1988;Yeats et al., 1988). Hubbard et al.'s (2014) at was interpreted to connect a high-angle deep ramp of the San Cayetano fault to the Pitas Point/ Ventura fault system via the "southern San Cayetano fault." Recent work has established that the southern branch of the San Cayetano exists, and it is the likely surface linkage between the San Cayetano and Ventura faults (Hughes et al., 2018). The geometry presented by Hubbard et al. (2014), which includes an ~30°N-dipping thrust ramp that extends downward from the at, was favored over the high-angle reverse faults model by mechanical modeling (Marshall et al., 2017). The north-dipping thrust ramp proposed by Hubbard et al. (2014) provides a reasonable mechanism to explain uplift in the Western Transverse Ranges. However, it has yet to be tested against the observed regional uplift of ~1 mm/yr north of the Arroyo Parida fault (Rockwell et al., 1984) and in Santa Ynez Valley (Farris, 2017), or the lack of late Quaternary folding of the Santa Ynez range. Therefore, we explored this further, and we suggest that this deeper ramp must be more gently dipping to the north to account for the regionally observed uplift.
We estimated the plausible dip range by accounting for the rates of vertical and horizontal motion using a simplistic kinematic model (Fig. 7A) that assumed that the observed uplift north of the zone of active folding is a result of slip on the underlying, deep low-angle thrust. Regional subsidence due to mantle downwelling (Bird and Rosenstock, 1984) is also accounted for in the model. The subsidence rate was evaluated assuming that the Upper Quaternary coarse clastic sediments in Ventura Basin were originally at or close to the surface and that their current depth is the result of subsidence. Their ages have been previously de ned by the presence of tephras and fossil extinction horizons (Yeats, 1983), so a subsidence rate could be calculated. Using the top of the Repetto member of the Pico Formation onshore between the Ventura and Oak Ridge faults results in a subsidence rate of ~2.6 mm/yr for the onshore central trough of Ventura Basin. For the offshore, the depth to the top of the Repetto member resolves a rate of ~2.5 mm/yr. The 2.5 mm/yr rate was used in our model as an estimate of the regional subsidence rate, although this rate might be considered as a maximum rate, in case subsidence is faster in the basin due to sediment loading, which is likely the case. In such a case, the calculated dip angle that we used may also be a maximum dip angle.
We employed shortening rates of 6.5-10 mm/ yr determined from previous geologic and geodetic studies (Marshall et al., 2013;Rockwell et al., 1988) and our estimate of the change in line length of a horizon at the top of the Pico Formation in the Ventura area, south of the Red Mountain fault (Fig. 4, cross-section 3). The required dip of the lower fault ramp based on our model is shown by the intersection of each line and the 1 mm/yr uplift rate (Fig. 7B). The range of plausible dips is 16°-30° when accounting for the uncertainties in the shortening and uplift rates. In our models, we used a dip of 20° for the deep ramp, which is similar to the dip inferred for the fault that produced the Fillmore earthquake swarm based on microseismicity (Hauksson et al., 2016), as well as the dip of the fault that produced the 1978 M 6 Santa Barbara earthquake (Corbett and Johnson, 1982).

FORWARD MODELING
In order to test the interpretation of a southward-propagating fault system and estimate the rst-order geometry of the deep faults of the fold-and-thrust belt, we applied fault-bend folding (Suppe, 1983) and Trishear (Erslev, 1991) forward modeling. The results of the models were compared with and tested against the geologic cross sections presented in Figure 4. This comparison allowed us to assess whether a large deep thrust ramp may plausibly represent a continuous fault surface along strike that is capable of hosting large earthquakes.
We generated a series of kinematic forward models using the Trishear (Erslev, 1991) module in MOVE ® by Midland Valley Exploration Ltd. (https://www.mve.com/) to match the surface and near-surface geology. We modeled a southward-propagating fault system by iterative steps. That is, we rst produced slip on a fault to the north of the Santa Ynez anticlinorium to match some of the deformation in the hanging wall of the San Cayetano fault. We then "propagated" the deformation southward by initiating slip on a new fault to represent the San Cayetano fault, followed by the Red Mountain-South Sulphur Mountain fault, and nally the Pitas Point/ Ventura fault system. We iterated this with various fault con gurations until we matched the surface geology as interpreted in our geologic cross sections.
The order of faulting has an important impact on the patterns of resulting deformation, so representation of the regional evolution of structures in our models, as described above, provided an important constraint. Earlier stages of our models represent initial conditions that were then modi ed by subsequent faulting and folding. After each modeling step, we made an adjustment to the fault geometry and displacement parameters until we reached a satisfying result under the different constraints of age, geometry, and amount of shortening; hence, this was an iterative process. In Figure 6, we present the steps we applied for cross section 2 (Fig. 4); a similar procedure was performed for each of the other cross sections.
We used the same parameters for the different modeled sections except for fault spacing and fault displacement. The extent to which the thrust front propagated toward the south through time is apparent in Figure 2 h-horizontal shortening rate; u-uplift rate; s-subsidence rate. We assumed that competing rates of uplift and regional subsidence will equal the observed rate of uplift where there is no folding. (B) Plot of dip vs. observed uplift rate for different shortening rates and a subsidence rate of 2.5 mm/yr. The prediction for fault dip is at the intersection of the results (red and blue curves) with the 1 mm uplift line (black), which is the reported regional uplift. See text for further information.
Ventura faults changes along strike. The amount of slip, or contraction, used in the models varied as overall shortening decreased to the west, so slip was reduced for cross sections 5, 6, and 7 to match the amount of deformation represented in the surface and near-subsurface geology.
The parameters we used for the nal model are: For the San Cayetano fault, we used a propagation to slip ratio of 1, we used 20 Trishear zones, and we did not apply an offset for the Trishear angle. For the Red Mountain/South Sulphur Mountain fault, we used a propagation to slip ratio of 0.8 with 8 Trishear zones, and an offset of 0.6 for the Trishear angle. For the Pitas Point/Ventura fault, we used propagation to slip ratio of 0.3, 1 Trishear zone, and an offset of 0.9 for the Trishear angle. The propagation to slip ratio for each fault was selected to match the shape of the fold as best we could through trial and error; we did not thoroughly explore the sensitivity of this parameter. Figure 8 presents additional models using different dips than our preferred model for the lower ramp in order to demonstrate the sensitivity of relief and fold shape on the geometry of the lower ramp.

RESULTS
The model (Fig. 6) illustrates the concept of southward thrust propagation over time, attendant fault dip, and expected patterns of uplift and folding, with uplift of the hanging wall and the locus of folding migrating southward through time. The comparison of the model predictions with the geological cross sections shows a good rst-order match and demonstrates that the models capture the rst-order patterns of folding and structural relief (Figs. 9 and 10). Despite having a rather large spacing between cross sections, the similar fault geometry inferred at depth, along with the interpreted structural evolution through time, reproduces the surface dips of the anticlinorium and the younger anticlines to the south as the thrust front progressed south along the 140 km length of the range covered by the cross sections. Furthermore, the structural relief and stratigraphy in the forward models match  well with the geologic cross sections constructed using classical techniques.
In our modeling, we included the sequence of events and ages of structures, as presented or determined in previous studies. There is some shortening represented by folding north of the San Ynez range, mostly associated with the Pine Mountain fault (Fig. 2), but the rst major thrust front along the length of the Santa Ynez anticlinorium resulted from initiation of motion on the San Cayetano fault. This was followed by propagation of the thrust fault southward to the Red Mountain-South Sulphur Mountain fold and later to the Pitas Point/Ventura fault, all of which formed the imbricated thrust and ramp architecture as depicted in Figure 9. In crosssections 2 through 5 (Figs. 9 and 10), there is a at between the emergent Red Mountain and Ventura frontal faults, as modeled and interpreted by others (Hubbard et al., 2014;Namson and Davis, 1988;Shaw and Suppe, 1994;Yeats et al., 1988,) and we reproduced the low-angle at in our modeling. In fact, we tried to eliminate this midcrustal at and found that it was required in order to retain connectivity and simultaneously reproduce the surface geometry. The presence of the at is also favored by mechanical models that analyzed geodetic data for the presence or absence of a midcrustal at (Marshall et al., 2017).
Cross-section 1 (Fig. 10) required a simple geometry, compared to the other cross sections, without a ramp-at-ramp structure. This was expected because there is no major fold south of the San Cayetano fault near Fillmore (Fig.  1B); a simpler structural con guration required a simpler structural evolution and model. It might be expected that the marginal cross section would exhibit a different geometry close to the lateral boundaries of the system. That said, a young fold emerges out of the late Quaternary alluvium west of Fillmore and south of the San Cayetano fault (Rockwell, 1988;Hughes et al., 2018) that was too small to model at the scale of the model, but it does represent the very recent southward propagation of the San Cayetano fault, as demonstrated by Hughes et al. (2018).
Based on these models, we estimated that ~21 km of total shortening has accrued since contraction began in the Pliocene in the eastern part of the Ventura Basin (cross-sections 1-4). The required shortening decreases to ~13 km in cross-section 5, ~11 km in cross-section 6, and ~7 km at the westernmost cross-section 7 near Point Conception. The average shortening rate implied by this amount of shortening, considering the age uncertainty, is 6.5-9.1 mm/yr for cross sections 1-4, in close agreement with geodetic estimates, which suggest an average current shortening rate of 7 mm/yr (Marshall et al., 2013), and geologic estimates of 8-10 mm/ yr . Another factor of note is that the geodetic estimates of shortening in the westernmost Western Transverse Ranges (area of cross-section 7) are much lower than near Ventura (Marshall et al., 2013), consistent with our estimate that only a third of the shortening is required to produce the observed structures for the area of cross-section 7.
This reduction in shortening westward is consistent with the observation that the anticlinorium is not overturned west of cross-section 5 (Figs. 2 and 4), which also argues for a lesser amount of total shortening. The alternative is to place the main fault deeper, but the observation that the depth of microseismicity in the Western Transverse Ranges seems to shallow from east to west indicates that the seismogenic depth also shallows from east to west (Nazareth and Hauksson, 2004). This contradicts deepening the location of the main lower ramp and thus supports our decision to match the observed folding patterns with a westward decrease in slip.
The westward decrease in the amount of shortening is likely the result, in part, of the position of the westernmost Transverse Ranges relative to the Big Bend of the San Andreas fault, which has evolved over time. Early in the history of contraction (late Pliocene?), the region around Point Conception would have been far to the east of its current position because of less total slip on the San Andreas fault. Therefore, the contraction in the west may be older, resulting from the previous location of this region directly south of the Big Bend in the San Andreas fault. Furthermore, the Big Bend of the San Andreas, which is inferred to be a major factor in contraction in the Western Transverse Ranges, has evolved over time as slip accrued on the Garlock fault (Fig. 1A) from extension in the Great Basin (Davis and Burch el, 1973). Full agreement between model prediction and geologic observations is unrealistic for a number of reasons. First, changes in thickness are observed as units thin to the north, and it is dif cult to model this aspect accurately in Trishear. In addition, secondary structures and additional deformation resulting from minor back thrusts and from out-of-plane strike-slip faulting are dif cult to quantify, although the amount of strike-slip motion is minor compared to dip slip, and the initial geometry of the Paleogene section was relatively simple. Finally, the superposition of the present compressional deformation regime on the Miocene extensional regime is another factor that introduces additional complications. For example, the Miocene growth strata and sections that were eroded make it dif cult to compare the observed geology to a simple layered model. The simpli cations we made, mainly using a layer cake model, might affect the amount of total shortening we used in the model. In the case that the Lower Eocene or Cretaceous units already had some relief from north to south, a lower dip or slip on the modeled faults would have been required, and vice versa. Because we have no way to constrain the paleorelief of these units, we cannot quantify this uncertainty, although there are no clastic deposits eroded from the Eocene strata in the Miocene units, which argues against subaerial exposure of the Eocene strata to the north. Considering those issues, and accepting the limitations of our inherent assumptions, we suggest that our structural models reproduce the geometry and kinematics of the major thrust sheets, and they are consistent with all large-scale observations along the transects (Figs. 9 and 10).

THREE-DIMENSIONAL FAULT SURFACE
Considering that the depth of the brittle-ductile transition in the Western Transverse Ranges is as deep as 18-20 km, based on depth distribution of the seismic moment release (Nazareth and Hauksson, 2004), we can estimate the fault surface area for the underlying thrust. Figure 11 presents an interpolated fault surface (using the spline curve method) for that portion of the crust that lies in the seismogenic zone. In this threedimensional (3-D) model, we connected the various fault lines with the assumption that the active deep fault connects to the frontal foldand-thrust zone as one continuous thrust surface. Based on this model, we estimated that the surface area of the fault is ~6000 km 2 . If the entire ~140 km length of the fault system fails in a single event, an earthquake in the Mw 7.8 range is possible, based on scaling relations (Leonard, 2010). As the slip rate, and therefore expected slip per event, decrease to the west, this is likely a maximum estimate of the plausible earthquake magnitude.
This magnitude of potential earthquake, or at least a magnitude in the Mw 7.5-7.8 range, is supported by the aforementioned recent studies of coastal uplift, borehole excavations, and structural analysis (Hubbard et al., 2014;McAuliffe et al., 2015;Rockwell et al., 2016). The Holocene coastal marine terraces near Punta Gorda between Ventura and Santa Barbara record Holocene uplift events that average 10 m (Rockwell et al., 2016). Similarly, the onshore Ventura fault has produced up to 6 m of vertical deformation per event (McAuliffe et al., 2015). These amounts of uplift in a single event are only known worldwide from large earthquakes.
The evidence for large displacements or uplift led Hubbard et al. (2014) to propose that some ruptures must involve multiple segments to accommodate the expected surface area of such uplifts. They argued that rupture of just the emergent portion of the San Cayetano and Ventura faults was too small to explain such large events, and thus proposed multisegment ruptures that extended east and/or west. Our interpretation for the surface area of the thrust is about twice that of Hubbard et al. (2014) due to the shallower dip of the lower ramp down to 18-20 km depth and extension of the fault system to the west. Thus, our fault representation is of suf cient size to host the class of earthquakes that independent paleoseismic data indicate have occurred within the system.
One other aspect is worth noting. The low dip that we infer for the underlying thrust ramp in our model predicts that a geodetic uplift signal should be observable to the north of the Santa Ynez range, contrary to that from the steeper dips inferred for other models (Sorlien and Nicholson, 2015;Nicholson et al., 2017). Our model is consistent with the geodetic uplift signal north of the Santa Ynez range (Hammond et al., 2018), which indicates that the deep thrust related to the shortening at the brittleductile transition zone is in the same area as we predict.

CONCLUSIONS
Based on our new kinematic forward modeling effort, we propose that the primary structures of the Western Transverse Ranges result from a southward-verging system of folds and thrust faults that have evolved through time. In our model, the lower ramp dips ~20° (with possible range of 16°-30°) to the north, to explain the regional uplift of 1 mm/yr, and the upper ramp dips ~45°-60° to the north, based on well data. Based on seven forward models (Figs. 9 and 10) that explain well the observed surface geology and interpreted cross sections, we infer that the deep structure is best represented by a large, continuous thrust sheet that connects the various geological structures observed at the surface. The presence of this large, interpreted fault can explain the large deformations that have been documented for the Pitas Point/ Ventura fault system at the coast. The potential surface area of a rupture in the seismogenic zone may be as large as ~6000 km 2 ; such a scenario could yield an earthquake as large as M 7.8 (Hubbard et al., 2014;McAuliffe et al., 2015;Rockwell et al., 2016). Further, we predict that the rate of shortening drops signicantly in the offshore from east to west, which implies that displacement per event also likely falls off to the west.
Finally, our approach of accounting for observations that constrain the model but do not serve as inputs might be applied in other fold-and-thrust belts worldwide. Independent information on fault slip rates, uplift and shortening rates, relative timing of structures, geodetic data, and other independent information help to guide the development and restrict the degrees of freedom for structural models of the entire seismogenic crust, as in our models for the Western Transverse Ranges.

APPENDIX: WELL DATA
In Appendix Table A1, we include the API numbers and coordinates for the wells we incorporated into our cross sections. Some of the wells were interpreted by the studies cited in our work, while others had a well log available through the Department of Conservation, California, website (https:// maps.conservation.ca.gov/doggr/well nder/#close). elevation m m Figure 11. Interpolation of the predicted active fault surface. Surface was interpolated from the modeled fault lines using spline curve method down to the seismogenic depth (18 km; Nazareth and Hauksson, 2004). The surface area of the fault is estimated at ~6000 km 2 , which can potentially host a high 7 magnitude earthquake according to scaling relations (Leonard, 2010).