Guerrero Deformation Modeling

Modeling and Inversion of Guerrero GPS Data:

Motivation:

The Guerrero segment of the Cocos-North America plate boundary, between Acapulco and Zihuatanejo, is one of only two segments that has not experienced a shallow interplate earthquake since seismic instruments were installed in 1923. Since the last large earthquake in that region (in 1911), the Cocos plate has moved more than five meters relative North America. Recently, we have observed evidence for several aseismic fault slip events or "silent earthquakes" in continuous GPS data from the region [Lowry et al., 2001; Kostoglodov et al., 2003; Larson et al., 2004; Iglesias et al., 2004; Yoshioka et al., 2004; Lowry et al., 2005].

GPS measurements in Guerrero consist entirely of episodic surveys prior to 1997, and only eight continuous GPS sites were operating during the 2002 event. The possible presence of transient slip events in the early portion of the geodetic record greatly complicates interpretation and modeling of the survey data. Geodetic studies during interseismic periods typically assume that, in the absence of large earthquakes, displacements measured at infrequent intervals represent a steady-state velocity. Transient aseismic slip typically occurs on timescales of a few weeks to a year (and ~3-4 months in Guerrero), so it is aliased by infrequent survey measurements. In principle however, nonlinear slip dynamics should be recognizable in infrequently sampled measurements, so long as (1) the data are represented as a position time series rather than as a velocity vector, (2) spatial and temporal sampling are adequate to distinguish steady-state from transient motions, and (3) transient motions are sufficiently large to distinguish from error in the GPS positions.

Unfortunately, campaign data from Guerrero were collected before the possibility of transient deformation had been recognized. Transients are evident in 1996, 1998, 1999, 2000, 2001, 2002, 2003 and 2004, from campaign data collected in 1992, 1995, 1996, 1998, 2000 and 2001. The first continuous GPS site began measurement in 1996, a second in 1997, and most of the rest of the continuous sites were installed in 1999, 2000, or 2003. Not all campaign sites were occupied at all epochs, and only one site (ACAP) was sampled sufficiently to separate all of the eight recognized transients from the steady-state site velocity. Guerrero state is just one of many subduction zones where tens to hundreds of thousands of dollars were spent to collect campaign GPS measurements before continuous GPS measurements indicated transient slip behavior. Ideally, we would like to make use of these early data rather than to simply discard them.

Squeezing More from the Data:

Modeling the displacement time series at a particular site requires (at a minimum) two parameters to describe the steady-state slope and intercept plus one parameter to describe the total displacement during each transient event. However, our data are not adequate to separate steady-state from transients at many of the sites. To circumvent this problem, we recognize that (1) total deformation between any two sampling epochs must equal the sum of steady-state for that period plus any transient displacements, and (2) displacements and/or velocities due to deep slip must be very similar at closely-spaced sites. Hence we can substitute spatial redundancy for temporal redundancy at some campaign sites.

I model steady-state velocity as spatially variable coupling between the Cocos and North American plates. (A more detailed description of the steady-state slip modeling is given in Larson et al. [2004]). The coupling model can be thought of as a smooth interpolator of steady-state velocity estimates from well-sampled sites to poorly-sampled sites that enables a more robust estimate of transient displacement at those sites. The velocity field from steady-state coupling must vary smoothly because surface deformation has a spatial wavelength roughly twice the depth of the source, and the Guerrero plate interface is deep (ranging from 20 km depth at the coast to more than 80 km below inland sites such as IGUA and YAIG). Consequently, closely-spaced GPS sites must have very similar steady-state velocities and similar transient displacements.

Transient slip is modeled in two very different ways to provide a sense of the range of possible solutions. In one model, I assume slip is uniform within a single rectangular region or patch on the plate boundary, and solve via grid search for the length, width, location, slip and timing parameters that best fit the GPS data. A more detailed description of this approach is given here and in Larson et al. [2004]. In the second modeling approach, I solve for variable slip on a discretized representation of the plate boundary and limit the solution space by requiring that the slip in each event is less than the slip deficit accumulated by frictional coupling (minus transient slip) since the beginning of GPS observation. A more detailed description of the discretized modeling approach, and a comparison of the two modeling approaches, is given in Lowry et al. [2005]. In general, constraints on the discretized model force smaller slip (and hence smaller moment release) in each event, and discretized models locate slip nearer to the GPS sites (which are situated predominantly on the Guerrero coastline).

Best-fit models of steady-state slip are given here for both the

single patch

and discretized

models. The color indicates steady-state slip (ranging from perfectly coupled, red, to free slip, white). Gray vectors are the modeled surface velocities, and blue vectors are the "observed" velocities estimated from residuals of the respective transient models. The ellipses on the observed velocities are 95% confidence, from formal errors scaled to produce a chi-square parameter of one. The two models differ primarily in that the single patch model estimates more steady-state slip at shallow depth. This results primarily from a need to offset the lack of transient slip at those depths in the single patch models.

Best-fit results of both the single patch and discretized models of transient slip are also given for each of the

1996,

1998,

1999,

2000,

2001,

2002,

2003,

and 2004

slow slip events. In the case of the single patch models (left panels), the black rectangle denotes the best-fit slip model, and the grayscale indicates the minimum misfit of all the models that produced slip at a given location. White corresponds to regions where no model produced slip which could fit the data at better than 95% confidence. Also shown as black vectors are "observed" transient displacements relative to NOAM, at those sites where temporal sampling was adequate to separate the transient deformation from the steady state and other transient displacements. These were calculated by inverting for parameters of a line superimposed by hyperbolic tangent functions during each of the transient episodes. The latter functions were fit directly to the position time series without filtering through a slip model so they give an "independent" estimate of displacement during the transient event. Ellipses are 95% uncertainty from formal errors of the tanh model, scaled by repeatability relative to the model. The corresponding best-fit model vectors are shown as white vectors. Note that the sites for which black vectors are shown are not the only sites at which the GPS data constrain the result; these are just the sites where the transient displacement could be independently estimated. In the discretized models (right panels), the grayscale denotes total transient slip on each discrete patch and the thin vectors show the magnitude and direction of slip.

An alternative inverse solution, in which coseismic displacements during earthquakes are modeled and removed prior to inverting for transient and steady-state slip, is given here for the 1992-2001 period only. The results are quite similar with and without the inclusion of displacement models for earthquakes other than the 1995 Mw=7.3 Copala event. Slip during the Copala earthquake is treated as an unknown parameter to be solved for in each model.

Time series of GPS positions, corrected for rigid rotation of the North American plate, are also shown for each of the sites relative to MDO1 and/or ACAP below. Red circles are daily coordinate solutions with 95% confidence indicated by cyan bars. Blue represents the best-fit model from inversion, and yellow indicates the periods of transient episodes.

ACAP relative MDO1 (single patch)

ACAP relative MDO1 (discretized)

AYUT relative MDO1 (single patch)

AYUT relative MDO1 (discretized)

C345 relative MDO1 (single patch)

C345 relative MDO1 (discretized)

CAYA relative MDO1 (single patch)

CAYA relative MDO1 (discretized)

CHIL relative MDO1 (single patch)

CHIL relative MDO1 (discretized)

COYU relative MDO1 (single patch)

COYU relative MDO1 (discretized)

CRUZ relative MDO1 (single patch)

CRUZ relative MDO1 (discretized)

DOAR relative MDO1 (single patch)

DOAR relative MDO1 (discretized)

GC01 relative MDO1 (single patch)

GC01 relative MDO1 (discretized)

IGUA relative MDO1 (single patch)

IGUA relative MDO1 (discretized)

INEG relative MDO1 (single patch)

INEG relative MDO1 (discretized)

LAJA relative MDO1 (single patch)

LAJA relative MDO1 (discretized)

LOMA relative MDO1 (single patch)

LOMA relative MDO1 (discretized)

OAXA relative MDO1 (single patch)

OAXA relative MDO1 (discretized)

PAPA relative MDO1 (single patch)

PAPA relative MDO1 (discretized)

PENJ relative MDO1 (single patch)

PENJ relative MDO1 (discretized)

PINO relative MDO1 (single patch)

PINO relative MDO1 (discretized)

POCH relative MDO1 (single patch)

POCH relative MDO1 (discretized)

POSW relative MDO1 (single patch)

POSW relative MDO1 (discretized)

SANM relative MDO1 (single patch)

SANM relative MDO1 (discretized)

TCOL relative MDO1 (single patch)

TCOL relative MDO1 (discretized)

TETI relative MDO1 (single patch)

TETI relative MDO1 (discretized)

TIGR relative MDO1 (single patch)

TIGR relative MDO1 (discretized)

UNIO relative MDO1 (single patch)

UNIO relative MDO1 (discretized)

YAIG relative MDO1 (single patch)

YAIG relative MDO1 (discretized)

ZIHP relative MDO1 (single patch)

ZIHP relative MDO1 (discretized)

AYUT relative ACAP (single patch)

AYUT relative ACAP (discretized)

BAR1 relative ACAP (single patch)

BAR1 relative ACAP (discretized)

C345 relative ACAP (single patch)

C345 relative ACAP (discretized)

CAYA relative ACAP (single patch)

CAYA relative ACAP (discretized)

CHIL relative ACAP (single patch)

CHIL relative ACAP (discretized)

CPDR relative ACAP (single patch)

CPDR relative ACAP (discretized)

CRUZ relative ACAP (single patch)

CRUZ relative ACAP (discretized)

DI16 relative ACAP (single patch)

DI16 relative ACAP (discretized)

EMU1 relative ACAP (single patch)

EMU1 relative ACAP (discretized)

GC01 relative ACAP (single patch)

GC01 relative ACAP (discretized)

LAGU relative ACAP (single patch)

LAGU relative ACAP (discretized)

LAJA relative ACAP (single patch)

LAJA relative ACAP (discretized)

LOMA relative ACAP (single patch)

LOMA relative ACAP (discretized)

MONA relative ACAP (single patch)

MONA relative ACAP (discretized)

PAPA relative ACAP (single patch)

PAPA relative ACAP (discretized)

PENJ relative ACAP (single patch)

PENJ relative ACAP (discretized)

PIED relative ACAP (single patch)

PIED relative ACAP (discretized)

POCH relative ACAP (single patch)

POCH relative ACAP (discretized)

SANM relative ACAP (single patch)

SANM relative ACAP (discretized)

TAXT relative ACAP (single patch)

TAXT relative ACAP (discretized)

TCOL relative ACAP (single patch)

TCOL relative ACAP (discretized)

TETI relative ACAP (single patch)

TETI relative ACAP (discretized)

TIGR relative ACAP (single patch)

TIGR relative ACAP (discretized)

TLAC relative ACAP (single patch)

TLAC relative ACAP (discretized)

UNIO relative ACAP (single patch)

UNIO relative ACAP (discretized)

ZIHP relative ACAP (single patch)

ZIHP relative ACAP (discretized)