Resolving locked asperities and slip deficit in unlocked regions: A new inversion method applied in the South America subduction zone

Resolving locked asperities and slip deficit in unlocked regions: A new inversion method applied in the South America subduction zone

Matthew Herman, Rob Govers, Department of Earth Sciences, Utrecht University Pseudo-coupling Model

Trench_Origin

400 km

25º

Length

+x +y

+z

Fixed

x-z motion only

1 meter Width

100 km

1000 km

}

}

Trench

1 m

0 100 200 300 400 500 600 700 800 900 1000

Along-Strike (km)

0 100 200 300 400

Along-Dip (km)

0.0 0.2 0.4 0.6 0.8 1.0

Slip (m)

0.2 0.4 0.6 0.8 1.0

Slip (m)

Slip (m)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

Plate Interface Slip

Locked

Pseudo-coupled

Locked

Near the asperity, the

pseudo-coupled interface accumulates high slip deficit.

Farther from the asperity, the

plates slide at the relative velocity.

Outside the asperity, the interface is free to slide, but sliding is restricted by the adjacent locked zone.

Model Setup

We displace the top and bottom of the subducting plate 1 meter while holding the backstop of the upper plate fixed. No slip is allowed in locked asperities, but the rest of the interface is unlocked and can thus slide freely.

In this study, we incorporate the physics of pseudo-coupling into an inter-seismic inversion so that we can determine:

The continuous nature of tectonic plates implies that inter-seismic slip deficit must be continuous on the plate boundary. As a result, areas outside mechanically locked asperities can accumulate slip deficit even in the absence of shear resistance. We call this “pseudo-coupling” to distinguish it from mechanical coupling. Previously, we quantified its effect conceptually (Herman et al., 2018).

Where and how much of the subduction plate interface is locked?

What is the corresponding slip deficit accumulation rate?

Inversion Approach

(C)

(D)

0 100 200 300 400 500 600 700 800 900 1000

Along−Strike Distance (km)

0 100 200 300 400

Down−Dip Distance (km)

(C)

(D)

0 100 200 300 400 500 600 700 800 900 1000

0 100 200 300 400

Down−Dip Distance (km)

0.0 0.2 0.4 0.6 0.8 1.0

Slip (m)

0.0 0.2 0.4 0.6 0.8 1.0

Fault Slip (m)

0 100 200 300 400

Down−Dip Distance (km)

0.0 0.2 0.4 0.6 0.8 1.0

Fault Slip (m)

0 100 200 300 400 500 600 700 800 900 1000

Along−Strike Distance (km)

FEMInversion

Direct

Calculation FEM

Along-strike

Down-dip

Input

Fault Slip

0 100 200 300 400 500 600 700 800 900 1000

Along−Strike Distance (km)

0 100 200 300 400 100 2030 4050 6070

Slip (mm/yr)

Best Fault Slip

0 100 200 300 400 500 600 700 800 900 1000

0 100 200 300 400

Horizontal Distance From Trench (km)

χ² misfit: 8.31e−01

Surface

Displacements

0 100 200 300 400 500 600 700 800 900 1000

0 100 200 300 400

1 2 5 10 20 50 100

χ2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Iteration

Probability Locked

0 100 200 300 400 500 600 700 800 900 1000

0 100 200 300 400

Horizontal Distance From Trench (km)

0.0 0.2 0.4 0.6 0.8 1.0

Locked Prob.

Misfit vs. Iteration

Accepted

Rejected

Model

We search for distributions of locked and unlocked patches that produce good fits to inter-seismic surface velocities. Since there are potentially many good fitting solutions, we implement an algorithm (Metropolis-Hastings) to determine the probability that each patch is locked. Key to this approach is that the fault slip distribution and corresponding velocities are based on the physics of pseudo- coupling in every iteration of the search.

Initialize locked and unlocked

patches

Calculate pseudo-coupling

and surface velocities Calculate proposed model velocity misfit: χ

_pro²

Randomly flip

< 5% locked and unlocked patches

Lower χ

²

than

current model? Calculate p=exp(χ

_pro²

-χ

_curr²

)

rand(0-1)<p?

Set proposed model as current

model

Keep current model

Yes

No

Yes

No Propose model

(Repeat many times)

Proof of Concept The search involves running

10,000+ models. Each requires calculating the slip distribution and computing the misfit with respect to the observed velocities.

To accelerate the search, we use an analytical solution for directly minimizing the shear stresses to calculate slip around locked patches instead of an FEM . This produces similar fault slip and horizontal surface motions as the FEM. Biases associated with vertical displacements preclude their use in this model.

Inversion Algorithm Workflow

0 100 200 300 400 500 600 700 800 900 1000

0 100 200 300 400 500 600

Surface

Displacements

1922

1906 1906

1877 1868

1835 1822

1819 1784

1751 1746

1730 1687

1604

Nazca Plate South America Plate

South America Subduction Zone

The oceanic Nazca plate subducts eastward beneath

the continental South America plate from Chile to

Colombia. This subduction zone has hosted 12 Mw 7.5+

earthquakes in the past 25 years (red symbols indicate these earthquake epicenters and red lines show 2, 5, and 10 meter slip contours).

There is also a centuries-long historical record of great earthquakes (Kelleher, 1972) (rupture extents of these events are indicated by red bars west of the trench; Mw 8.0+ events are labeled with their dates).

The upper plate is densely instrumented by continuous and campaign GNSS stations measuring surface motions. We use the inter-seismic velocity field (measured before the Mw 7.5+ earthquakes) as the constraints on the plate interface locking distribution. We also test how much of the velocities can be explained by forearc sliver motions.

Seismotectonics

Geodetic Observations _i ⁱⁱ

iii iv

Locking Rigid Total Pre.

Observed

20 mm/yr

95%

−76˚ −74˚ −72˚ −70˚ −68˚ −66˚ −64˚ −62˚

−38˚

−36˚

−34˚

−32˚

−30˚

−28˚

−26˚

−24˚

−22˚

−20˚

0 20 40 60 80

Back−slip (mm/yr)

i

21 mm/yr^Median:

0 20 40 60 80

Back−slip (mm/yr)

ii

36 mm/yr^Median:

0 20 40 60 80

Back−slip (mm/yr)

iii

27 mm/yr^Median:

0 20 40 60 80

Back−slip (mm/yr)

iv

26 mm/yr^Median:

i ii

iii

iv

v

−82˚ −80˚ −78˚

−18˚

−16˚

−14˚

−12˚

−10˚

−8˚

−6˚

−4˚

−2˚

0˚

2˚

4˚

0 10 20 30 40 50 60 70

Back−Slip (mm/yr)

0 20 40 60 80

Back−slip (mm/yr)

i

26 mm/yr^Median:

0 20 40 60 80

Back−slip (mm/yr)

ii

22 mm/yr^Median:

0 20 40 60 80

Back−slip (mm/yr)

iii

3 mm/yr^Median:

0 20 40 60 80

Back−slip (mm/yr)

iv

25 mm/yr^Median:

0 20 40 60 80

Back−slip (mm/yr)

v

_{34 mm/yr}^Median:

−76˚ −74˚ −72˚ −70˚ −68˚ −66˚ −64˚ −62˚

−38˚

−36˚

−34˚

−32˚

−30˚

−28˚

−26˚

−24˚

−22˚

−20˚

0.0 0.2 0.4 0.6 0.8 1.0

Fraction Locked

Median: 0.24

0.0 0.2 0.4 0.6 0.8 1.0

Fraction Locked

Median: 0.10

0.0 0.2 0.4 0.6 0.8 1.0

Fraction Locked

Median: 0.21

−82˚ −80˚ −78˚

−18˚

−16˚

−14˚

−12˚

−10˚

−8˚

−6˚

−4˚

−2˚

0˚

2˚

4˚

0.0 0.2 0.4 0.6 0.8 1.0

Probability Locked

0.0 0.2 0.4 0.6 0.8 1.0

Fraction Locked

Median: 0.08

0.0 0.2 0.4 0.6 0.8 1.0

Fraction Locked

Median: 0.01

0.0 0.2 0.4 0.6 0.8 1.0

Fraction Locked

Median: 0.16

Locking Probability Slip Deficit Rate

Frequency

Frequency

0.0 0.1 0.2 0.3 0.4

Angular Velocity (°/Ma)

Chile Sliver

Frequency

Frequency

0.0 0.1 0.2 0.3 0.4

Angular Velocity (°/Ma)

Peru Sliver

Frequency

Frequency

0.0 0.1 0.2 0.3 0.4

Angular Velocity (°/Ma)

Ecuador−Colombia Sliver

Colombia-Ecuador

Northern Peru

Southern Peru

Northern Chile

Central Chile

Southern Chile 5-10% of area locked

Slip deficit rate: 10-60 mm/yr Sliver translation: 1-2 mm/yr

1-2% of area locked

Slip deficit rate: < 5 mm/yr Sliver translation: 2-3 mm/yr

14-18% of area locked

Slip deficit rate: 25-70 mm/yr 2001 Mw 8.4

2007 Mw 8.0

20-30% of area locked

Slip deficit rate: 20-70 mm/yr 2014 Mw 8.1

10% of area locked

Slip deficit rate: 15-75 mm/yr 2015 Mw 8.3

Sliver translation: 3-4 mm/yr

20-30% of area locked

Slip deficit rate: 30-75 mm/yr 2010 Mw 8.8

There are systematic

variations in the locking probability along strike.

Locking correlates well with locations of great megathrust events.

Recent earthquakes

nucleate in and around the edges of

high-probability locked zones. They rupture

into regions with slip deficit rates of 50%

or more of the

convergence rate.

The largest events rupture through

multiple asperities.

High

pseudo-coupling

Medium pseudo-coupling Low pseudo-coupling

Upper plate Trench

Subducting Plate

Inter-seismic

Slip Deficit

Co-seismic

Slip Magnitude

Fully locked asperities accumulate slip deficit at the convergence rate.

Earthquakes begin in and around these regions.

Seismicity No seismicity

Trench

Large, multi-asperity ruptures release the full accumulated slip deficit, allowing other pseudo- coupled regions to slip in concert with the

seismogenic zone.

In smaller earthquakes, slip can propagate outside of locked zones. Depending on geometry, the shallow interface may also slip.

Outside asperities, the interface appears partially coupled over a large area, accumulating slip deficit at a significant rate.

Conclusions

• Maximum of 30% of plate interface area is locked

• Earthquakes initiate inside or near edges of high probability locked zones

• Mw 8+ earthquakes occur in regions with at least 10% of fault area locked

• Large earthquakes may propagate outside of

high-probability locked zones into regions with slip deficit rate ≥ 25-50% of convergence rate

• Slip deficit rate near trench is ≥ 25% of convergence rate

• Forearc sliver motion ~1/2 that of previous studies