Geology topics

Roland Bürgmann

Publications and source records attributed to Roland Bürgmann.

18 recordsLinked to original sources

USGS2026

Temporal and spatial changes in seismic attenuation associated with inferred fluid migration in the 2016 central Apennines earthquake sequence

Prior work suggests that high‐frequency seismic attenuation acts as a highly sensitive proxy for crustal permeability and fluid mobility in fractured media. We test the hypothesis that the fault system responsible for the 2016–2017 Amatrice–Visso–Norcia–Capitignano sequence acted as an impermeable seal, compartmentalizing pressurized fluids until dynamic rupture triggered widespread fluid diffusion. By tracking across the sequence the spatiotemporal evolution of the S ‐wave anelastic attenuation parameter, we identify large, positive low‐frequency attenuation anomalies emerging within the hanging wall following the Amatrice mainshock and strictly preceding subsequent large ruptures. Conversely, we observe weaker, negative anomalies in the footwall, anticorrelated in time with those of the hanging wall, revealing a massive asymmetry in fluid redistribution and permeability evolution across the fault system. Furthermore, aftershock migration rates reveal distinct linear alignments in a distance‐reduced time space, allowing us to explicitly track and quantify episodes of lateral and upward fluid migration. These physically consistent patterns suggest that stress‐driven fluid diffusion directly weakens adjacent fault patches, dictating the spatiotemporal migration of seismicity. We conclude that near‐real‐time monitoring of seismic attenuation may help detect fluid redistribution in active fault systems and may provide useful information for time‐dependent seismic hazard assessment.

central Apennines↗

USGS2025

Probing lower-crustal fault properties with frequency-dependent tidal tremor triggering

The way seismicity responds to periodic stress perturbations offers crucial insights into the processes that can trigger an earthquake. Laboratory and theoretical analyses have shown that the period of imposed forcing and source properties affect the sensitivity to triggering, but frequency-dependent triggering of tectonic faults is poorly understood. The rate of low-frequency earthquakes (LFEs) near Parkfield, California has been found to be strongly correlated with solid earth tides. Tidal forcing acts over multiple frequencies, and the sensitivity to tidal triggering of LFEs therefore provides a unique opportunity to probe the physics of earthquake triggering and underlying fault properties. Here, we find that the response of LFEs to solid earth tides at diurnal and semi-diurnal frequencies is highly variable but spatially coherent along the San Andreas Fault. Using rate-state friction modeling, we find that the variation of the amplitude of tidal modulation is mainly affected by the spatial variation of the background effective normal stress, whereas the spatially varied tidal modulation at diurnal and semi-diurnal frequencies is mainly affected by the fault frictional property. The spatial variations of the LFE response reveal a heterogeneous lower-crustal geologic structure and complex physical faulting processes below the rupture zone of eventual great earthquakes.

California↗

USGS2020

Four-dimensional surface motions of the Slumgullion landslide and quantification of hydrometeorological forcing

Landslides modify the natural landscape and cause fatalities and property damage worldwide. Quantifying landslide dynamics is challenging due to the stochastic nature of the environment. With its large area of ~1 km 2 and perennial motions at ~10–20 mm per day, the Slumgullion landslide in Colorado, USA, represents an ideal natural laboratory to better understand landslide behavior. Here, we use hybrid remote sensing data and methods to recover the four-dimensional surface motions during 2011–2018. We refine the boundaries of an area of ~0.35 km 2 below the crest of the prehistoric landslide. We construct a mechanical framework to quantify the rheology, subsurface channel geometry, mass flow rate, and spatiotemporally dependent pore-water pressure feedback through a joint analysis of displacement and hydrometeorological measurements from ground, air and space. Our study demonstrates the importance of remotely characterizing often inaccessible, dangerous slopes to better understand landslides and other quasi-static mass fluxes in natural and industrial environments, which will ultimately help reduce associated hazards.

Colorado↗

USGS2019

Dynamically triggered changes of plate interface coupling in Southern Cascadia

In Southern Cascadia, precise Global Navigation Satellite System (GNSS) measurements spanning about 15 years reveal steady deformation due to locking on the Cascadia megathrust punctuated by transient deformation from large earthquakes and episodic tremor and slip events. Near the Mendocino Triple Junction, however, we recognize several abrupt GNSS velocity changes that reflect a different process. After correcting for earthquakes and seasonal loading, we find that several dozen GNSS time series show spatially coherent east‐west velocity changes of ~2 mm/yr and that these changes coincide in time with regional M > 6.5 earthquakes. We consider several hypotheses and propose that dynamically triggered changes in megathrust coupling best explain the data. Our inversions locate the coupling changes slightly updip of the tremor‐producing zone. We speculate that fluid exchange surrounding the tremor region may be important. Such observations of transient coupling changes are rare and challenging to explain mechanistically but have important implications for earthquake processes on faults.

California↗

USGS2019

Interseismic quiescence and triggered slip of active normal faults of Kīlauea Volcano’s south flank during 2001-2018

The mobile south flank of Kīlauea Volcano hosts two normal fault systems, the Koa'e fault system (KFS) and the Hilina fault system (HFS). In historical time, at least three M>6.5 earthquakes have occurred on the basal detachment of the Kīlauea Volcano's south flank, with the most recent being the 4 May 2018 M6.9 earthquake. Here we analyze kinematic Global Positioning System data collected from 2001 to 2017 and interferometric synthetic aperture radar data before, during, and after the 2018 M6.9 earthquake to determine the crustal motion across the HFS and KFS faults. Our results indicate that the HFS faults did not significantly slip during the interseismic period from 2007 to 2011. Despite its substantial magnitude, interferometric synthetic aperture radar (InSAR) data show that the 2018 M6.9 earthquake triggered subcentimeter level slip along sections of the previously mapped HFS branches. Up to 20 cm of offset occurred on what appears to be a newly formed (or previously unknown) fault near the eastern end of the HFS. During the 3 months following the M6.9 earthquake, up to ~30 cm of slip occurred along the KFS, which helps accommodate rapid large‐scale subsidence of Kīlauea's summit region as large volumes of summit reservoir magma fed the lower East Rift Zone eruption. The HFS appears to activate only in concert with large earthquakes on the basal detachment. The KFS, on the other hand, moves both seismically during small local earthquakes and aseismically in response to nearby earthquakes and caldera subsidence.

Hawaii↗

USGS2018

Interseismic ground deformation and fault slip rates in the greater San Francisco Bay Area from two decades of space geodetic data

The detailed spatial variations of strain accumulation and creep on major faults in the northern San Francisco Bay Area (North Bay), which are important for seismic potential and evaluation of natural hazards, remain poorly understood. Here we combine interferometric synthetic aperture radar data from the ERS‐1/2 and Envisat satellites between 1992 and 2010 with continuous and campaign GPS data to obtain a high spatial and temporal coverage of ground deformation of the North Bay. The SAR data from both ascending and descending orbits are combined to separate horizontal and vertical components of the deformation. We jointly invert the horizontal component of the mean velocities derived from these data to infer the deep strike‐slip rates on major locked faults. We use the estimated deep rates to simulate the long‐wavelength deformation due to interseismic elastic strain accumulation along these locked faults. After removing the long‐wavelength signal from the InSAR horizontal mean velocity field, we estimate fault‐parallel surface creep rates of up to 2 mm/year along the central section of the Rodgers Creek fault and surface creep rates ranging between 2 and 4 mm/year along the Concord fault. No surface creep is geodetically resolved along the West Napa and Green Valley fault zones. We identified characteristically repeating earthquakes on the Rodgers Creek fault, the West Napa fault, the Green Valley fault, and the Concord fault. Nontectonic deformation in the Geysers geothermal field and in Late Cenozoic basins (Rohnert Park and Sonoma basins) are also observed, likely due to hydrological and sediment‐compaction processes, respectively.

Journal of Geophysical Research B: Solid Earth↗

USGS2018

Constraints on friction, dilatancy, diffusivity, and effective stress from low-frequency earthquake rates on the deep San Andreas Fault

Families of recurring low-frequency earthquakes (LFEs) within nonvolcanic tremor on the San Andreas Fault in central California are sensitive to tidal stresses. LFEs occur at all levels of the tides, are strongly correlated and in phase with the ~200 Pa shear stresses, and weakly and not systematically correlated with the ~2 kPa tidal normal stresses. We assume that LFEs are small sources that repeatedly fail during shear within a much larger scale, aseismically slipping fault zone and consider two different models of the fault slip: (1) modulation of the fault slip rate by the tidal stresses or (2) episodic slip, triggered by the tides. LFEs are strongly clustered with duration much shorter than the semidiurnal tide; they cannot be significantly modulated on that time scale. The recurrence times of clusters, however, are many times longer than the semidiurnal, leading to an appearance of tidal triggering. In this context we examine the predictions of laboratory-observed triggered frictional (dilatant) fault slip. The undrained end-member model produces no sensitivity to the tidal normal stress, and slip onsets are in phase with the tidal shear stress. The tidal correlation constrains the diffusivity to be less than ~1 × 10 −6 /s and the product of the friction and dilatancy coefficients to be at most 5 × 10 −7 , orders of magnitude smaller than observed at room temperature. In the absence of dilatancy the effective normal stress at failure would be about ~55 kPa. For this model the observations require intrinsic weakness, low dilatancy, and lithostatic pore fluid.

Journal of Geophysical Research↗

USGS2018

Kinematics of the 2015 San Ramon, California earthquake swarm: Implications for fault zone structure and driving mechanisms

Earthquake swarms represent a sudden increase in seismicity that may indicate a heterogeneous fault-zone, the involvement of crustal fluids and/or slow fault slip. Swarms sometimes precede major earthquake ruptures. An earthquake swarm occurred in October 2015 near San Ramon, California in an extensional right step-over region between the northern Calaveras Fault and the Concord–Mt. Diablo fault zone, which has hosted ten major swarms since 1970. The 2015 San Ramon swarm is examined here from 11 October through 18 November using template matching analysis. The relocated seismicity catalog contains ∼4000 events with magnitudes between − 0.2 < M d < 3.6 "> −0.2< M d <3.6 . The swarm illuminated three sub-parallel, southwest striking and northwest dipping fault segments of km-scale dimension and thickness of up to 200 m. The segments contain coexisting populations of different focal-mechanisms, suggesting a complex fault zone structure with several sets of en échelon fault orientations. The migration of events along the three planar structures indicates a complex fluid and faulting interaction processes. We searched for correlations between seismic activity and tidal stresses and found some suggestive features, but nothing that we can be confident is statistically significant.

California↗

USGS2017

Surface slip during large Owens Valley earthquakes

The 1872 Owens Valley earthquake is the third largest known historical earthquake in California. Relatively sparse field data and a complex rupture trace, however, inhibited attempts to fully resolve the slip distribution and reconcile the total moment release. We present a new, comprehensive record of surface slip based on lidar and field investigation, documenting 162 new measurements of laterally and vertically displaced landforms for 1872 and prehistoric Owens Valley earthquakes. Our lidar analysis uses a newly developed analytical tool to measure fault slip based on cross‐correlation of sublinear topographic features and to produce a uniquely shaped probability density function (PDF) for each measurement. Stacking PDFs along strike to form cumulative offset probability distribution plots (COPDs) highlights common values corresponding to single and multiple‐event displacements. Lateral offsets for 1872 vary systematically from ∼1.0 to 6.0 m and average 3.3 ± 1.1 m (2σ). Vertical offsets are predominantly east‐down between ∼0.1 and 2.4 m, with a mean of 0.8 ± 0.5 m. The average lateral‐to‐vertical ratio compiled at specific sites is ∼6:1. Summing displacements across subparallel, overlapping rupture traces implies a maximum of 7–11 m and net average of 4.4 ± 1.5 m, corresponding to a geologic M w ∼7.5 for the 1872 event. We attribute progressively higher‐offset lateral COPD peaks at 7.1 ± 2.0 m, 12.8 ± 1.5 m, and 16.6 ± 1.4 m to three earlier large surface ruptures. Evaluating cumulative displacements in context with previously dated landforms in Owens Valley suggests relatively modest rates of fault slip, averaging between ∼0.6 and 1.6 mm/yr (1σ) over the late Quaternary.

Book↗

USGS2016

Spatial variations in fault friction related to lithology from rupture and afterslip of the 2014 South Napa, California, earthquake

Following earthquakes, faults are often observed to continue slipping aseismically. It has been proposed that this afterslip occurs on parts of the fault with rate-strengthening friction that are stressed by the mainshock, but our understanding has been limited by a lack of immediate, high-resolution observations. Here we show that the behavior of afterslip following the 2014 South Napa earthquake varied over distances of only a few kilometers. This variability cannot be explained by coseismic stress changes alone. We present daily positions from continuous and survey GPS sites that we re-measured within 12 hours of the mainshock, and surface displacements from the new Sentinel-1 radar mission. This unique geodetic data set constrains the distribution and evolution of coseismic and postseismic fault slip with exceptional resolution in space and time. We suggest that the observed heterogeneity in behavior is caused by lithological controls on the frictional properties of the fault plane.

California↗

USGS2016

Three-dimensional surface deformation derived from airborne interferometric UAVSAR: Application to the Slumgullion Landslide

In order to provide surface geodetic measurements with “landslide-wide” spatial coverage, we develop and validate a method for the characterization of 3-D surface deformation using the unique capabilities of the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) airborne repeat-pass radar interferometry system. We apply our method at the well-studied Slumgullion Landslide, which is 3.9 km long and moves persistently at rates up to ∼2 cm/day. A comparison with concurrent GPS measurements validates this method and shows that it provides reliable and accurate 3-D surface deformation measurements. The UAVSAR-derived vector velocity field measurements accurately capture the sharp boundaries defining previously identified kinematic units and geomorphic domains within the landslide. We acquired data across the landslide during spring and summer and identify that the landslide moves more slowly during summer except at its head, presumably in response to spatiotemporal variations in snowmelt infiltration. In order to constrain the mechanics controlling landslide motion from surface velocity measurements, we present an inversion framework for the extraction of slide thickness and basal geometry from dense 3-D surface velocity fields. We find that the average depth of the Slumgullion Landslide is 7.5 m, several meters less than previous depth estimates. We show that by considering a viscoplastic rheology, we can derive tighter theoretical bounds on the rheological parameter relating mean horizontal flow rate to surface velocity. Using inclinometer data for slow-moving, clay-rich landslides across the globe, we find a consistent value for the rheological parameter of 0.85 ± 0.08.

Colorado↗

USGS2016

Lithospheric rheology constrained from twenty-five years of postseismic deformation following the 1989 Mw 6.9 Loma Prieta earthquake

The October 17, 1989 M w 6.9 Loma Prieta earthquake provides the first opportunity of probing the crustal and upper mantle rheology in the San Francisco Bay Area since the 1906 M w 7.9 San Francisco earthquake. Here we use geodetic observations including GPS and InSAR to characterize the Loma Prieta earthquake postseismic displacements from 1989 to 2013. Pre-earthquake deformation rates are constrained by nearly 20 yr of USGS trilateration measurements and removed from the postseismic measurements prior to the analysis. We observe GPS horizontal displacements at mean rates of 1–4 mm/yr toward Loma Prieta Mountain until 2000, and ∼2 mm/yr surface subsidence of the northern Santa Cruz Mountains between 1992 and 2002 shown by InSAR, which is not associated with the seasonal and longer-term hydrological deformation in the adjoining Santa Clara Valley. Previous work indicates afterslip dominated in the early (1989–1994) postseismic period, so we focus on modeling the postseismic viscoelastic relaxation constrained by the geodetic observations after 1994. The best fitting model shows an elastic 19-km-thick upper crust above an 11-km-thick viscoelastic lower crust with viscosity of ∼6 × 10 18 Pas, underlain by a viscous upper mantle with viscosity between 3 × 1018 and 2 × 10 19 Pas. The millimeter-scale postseismic deformation does not resolve the viscosity in the different layers very well, and the lower-crustal relaxation may be localized in a narrow shear zone. However, the inferred lithospheric rheology is consistent with previous estimates based on post-1906 San Francisco earthquake measurements along the San Andreas fault system. The viscoelastic relaxation may also contribute to the enduring increase of aseismic slip and repeating earthquake activity on the San Andreas fault near San Juan Bautista, which continued for at least a decade after the Loma Prieta event.

California↗

USGS2014

The profound reach of the 11 April 2012 M 8.6 Indian Ocean earthquake: Short‐term global triggering followed by a longer‐term global shadow

The 11 April 2012 M 8.6 Indian Ocean earthquake was an unusually large intraoceanic strike‐slip event. For several days, the global M ≥4.5 and M ≥6.5 seismicity rate at remote distances (i.e., thousands of kilometers from the mainshock) was elevated. The strike‐slip mainshock appears through its Love waves to have triggered a global burst of strike‐slip aftershocks over several days. But the M ≥6.5 rate subsequently dropped to zero for the succeeding 95 days, although the M ≤6.0 global rate was close to background during this period. Such an extended period without an M ≥6.5 event has happened rarely over the past century, and never after a large mainshock. Quiescent periods following previous large ( M ≥8) mainshocks over the past century are either much shorter or begin so long after a given mainshock that no physical interpretation is warranted. The 2012 mainshock is unique in terms of both the short‐lived global increase and subsequent long quiescent period. We believe that the two components are linked and interpret this pattern as the product of dynamic stressing of a global system of faults. Transient dynamic stresses can encourage short‐term triggering, but, paradoxically, it can also inhibit rupture temporarily until background tectonic loading restores the system to its premainshock stress levels.

Bulletin of the Seismological Society of America↗

USGS2013

Inferring fault rheology from low-frequency earthquakes on the San Andreas

Families of recurring low-frequency earthquakes (LFEs) within nonvolcanic tremor (NVT) on the San Andreas fault in central California show strong sensitivity to shear stress induced by the daily tidal cycle. LFEs occur at all levels of the tidal shear stress and are in phase with the very small, ~400 Pa, stress amplitude. To quantitatively explain the correlation, we use a model from the existing literature that assumes the LFE sources are small, persistent regions that repeatedly fail during shear of a much larger scale, otherwise aseismically creeping fault zone. The LFE source patches see tectonic loading, creep of the surrounding fault which may be modulated by the tidal stress, and direct tidal loading. If the patches are small relative to the surrounding creeping fault then the stressing is dominated by fault creep, and if patch failure occurs at a threshold stress, then the resulting seismicity rate is proportional to the fault creep rate or fault zone strain rate. Using the seismicity rate as a proxy for strain rate and the tidal shear stress, we fit the data with possible fault rheologies that produce creep in laboratory experiments at temperatures of 400 to 600°C appropriate for the LFE source depth. The rheological properties of rock-forming minerals for dislocation creep and dislocation glide are not consistent with the observed fault creep because strong correlation between small stress perturbations and strain rate requires perturbation on the order of the ambient stress. The observed tidal modulation restricts ambient stress to be at most a few kilopascal, much lower than rock strength. A purely rate dependent friction is consistent with the observations only if the product of the friction rate dependence and effective normal stress is ~ 0.5 kPa. Extrapolating the friction rate strengthening dependence of phyllosilicates (talc) to depth would require the effective normal stress to be ~50 kPa, implying pore pressure is lithostatic. If the LFE source is on the order of tens of meters, as required by the model, rate-weakening friction rate dependence (e.g., olivine) at 400 to 600°C requires that the minimum effective pressure at the LFE source is ~ 2.5 MPa.

California↗

USGS2013

Annual modulation of non-volcanic tremor in northern Cascadia

Two catalogs of episodic tremor events in northern Cascadia, one from 2006 to 2012 and the other from 1997 to 2011, reveal two systematic patterns of tremor occurrence in southern Vancouver Island: (1) most individual events tend to occur in the third quarter of the year; (2) the number of events in prolonged episodes (i.e., episodic tremor and slip events), which generally propagate to Vancouver Island from elsewhere along the Cascadia subduction zone, is inversely correlated with the amount of precipitation that occurred in the preceding 2 months. We rationalize these patterns as the product of hydrologic loading of the crust of southern Vancouver Island and the surrounding continental region, superimposed with annual variations from oceanic tidal loading. Loading of the Vancouver Island crust in the winter (when the land surface receives ample precipitation) and unloading in the summer tends to inhibit and enhance downdip shear stress, respectively. Quantitatively, for an annually variable surface load, the predicted stress perturbation depends on mantle viscoelastic rheology. A mechanical model of downdip shear stress on the transition zone beneath Vancouver Island—driven predominantly by the annual hydrologic cycle—is consistent with the 1997–2012 tremor observations, with peak-to-peak downdip shear stress of about 0.4 kPa. This seasonal dependence of tremor occurrence appears to be restricted to southern Vancouver Island because of its unique situation as an elongated narrow-width land mass surrounded by ocean, which permits seasonal perturbations in shear stress at depth.

Journal of Geophysical Research B: Solid Earth↗

USGS2012

Illumination of rheological mantle heterogeneity by the M7.2 2010 El Mayor-Cucapah earthquake

Major intracontinental strike-slip faults tend to mark boundaries between lithospheric blocks of contrasting mechanical properties along much of their length. Both crustal and mantle heterogeneities can form such boundaries, but the role of crustal versus mantle strength contrasts for localizing strain sufficiently to generate major faults remains unclear. Using the crustal velocity field observed through the Global Positioning System (GPS) in the epicentral area of the M7.2 2010 El Mayor-Cucapah earthquake, Baja California, we find that transient deformation observed after the event is anomalously small in areas of relatively high seismic velocity in the shallow upper mantle (∼50 km depth). This pattern is best explained with a laterally heterogeneous viscoelastic structure that mimics the seismic structure. The mantle of the Southern Colorado River Desert (SCRD) and Peninsular Ranges (PR), which bound the fault system to its east and west, respectively, have anomalously high viscosity and seismic velocity. We hypothesize that compared with the rest of the San Andreas fault (SAF) system to its north, the strike-slip fault system in northern Baja California is narrow because of the presence of the PR and SCRD high-viscosity regions which bound it.

Arizona, Baja California, California, Sonora↗

USGS2011

Geodetic slip model of the 2011 M9.0 Tohoku earthquake

The three-dimensional crustal displacement field as sampled by GPS is used to determine the coseismic slip of the 2011 M9.0 Tohoku Earthquake. We employ a spherically layered Earth structure and use a combination of onland GPS, out to ∼4000 km from the rupture, and offshore GPS, which samples the high-slip region on the interplate boundary along the Japan trench. Inversion of the displacement field for dip slip, assuming an interplate boundary of variable dip and striking 195°, yields a compact slip maximum of about 33 m located 200 km east of Sendai. The geodetic moment is 4.06 × 10 22 N m, corresponding to M w = 9.0. The area of maximum slip is concentrated at a depth of about 10 km, is updip of the rupture areas of the M ≳ 7 Miyagi-oki earthquakes of 1933, 1936, 1937, and 1978, and roughly coincides with the rupture area of the M7.1 1981 Miyagi-oki earthquake. The overlap of the 2011 slip area with several preceding ruptures suggests that the same asperities may rupture repeatedly with M ≳ 7 events within several decades of one another.

Geophysical Research Letters↗

USGS2002

Steady subsidence of Medicine Lake volcano, northern California, revealed by repeated leveling surveys

Leveling surveys of a 193‐km circuit across Medicine Lake volcano (MLV) in 1954 and 1989 show that the summit area subsided by as much as 302 ± 30 mm (−8.6 ± 0.9 mm/yr) with respect to a datum point near Bartle, California, 40 km to the southwest. This result corrects an error in the earlier analysis of the same data by Dzurisin et al. [1991] , who reported the subsidence rate as −11.1 ± 1.2 mm/yr. The subsidence pattern extends across the entire volcano, with a surface area of nearly 2000 km 2 . Two areas of localized subsidence by as much as 20 cm can be attributed to shallow normal faulting near the volcano's periphery. Surveys of an east–west traverse across Lava Beds National Monument on the north flank of the volcano in 1990 and of a 23‐km traverse across the summit area in 1999 show that subsidence continued at essentially the same rate during 1989–1999 as 1954–1989. Volcano‐wide subsidence can be explained by either a point source of volume loss (Mogi) or a contracting horizontal rectangular dislocation (sill) at a depth of 10–11 km. Volume loss rate estimates range from 0.0013 to 0.0032 km 3 /yr, depending mostly on the source depth estimate and source type. Based on first‐order quantitative considerations, we can rule out that the observed subsidence is due to volume loss from magma withdrawal, thermal contraction, or crystallizing magma at depth. Instead, we attribute the subsidence and faulting to: (1) gravitational loading of thermally weakened crust by the mass of the volcano and associated intrusive rocks, and (2) thinning of locally weakened crust by Basin and Range deformation. The measured subsidence rate exceeds long‐term estimates from drill hole data, suggesting that over long timescales, steady subsidence and episodic uplift caused by magmatic intrusions counteract each other to produce the lower net subsidence rate.

California↗