Lecture 2: The Slowness-Enhanced Back-Projection Improving Imaging - - PowerPoint PPT Presentation

Lecture 2: The Slowness-Enhanced Back-Projection

Improving Imaging Quality

Objective: Improving Resolution Solution: MUSIC method

High Resolution Low Resolution Low Accuracy High Accuracy

Objective: Reduce Spatial Biases Solution: Slowness Calibration

• Travel-time correction in back-projections
• Hypocenter alignment
• Slowness Enhanced back-projection
• Unzipping of bottom of seismogenic zone in the Gorkha

Earthquake

• Absence of deep penetration in the Tohoku earthquake
• Early and Persistent supershear rupture of the 2018 Palu

earthquake

• Wide step-over of the 2017 Chiapas earthquake

Outlines

70 75 80 85 90 95°E 40 35 30 25 1934 1947 1950 1885 1905 1803 1930 1897 1833 1819 2001 2 million 500,000 200,000 Urban population ? Bhuj Calcutta Dhaka Kathmandu Delhi Islamabad 5 km 500 km Locking line Potential magnitude 10 8.2 8.1 8.0 7.8 8 6 4 2

Certain possible

N Tibet Lockin Locked Sliding Himalaya 100 km India

N Tibet

Contraction uplift

Locking line S N Tibet Locked Sliding Himalaya 100 km India

Potential slip, m Potential magnitude 10 8.2 8.1 8.0 7.8 8 6 4 2

Certain possible

Tectonic View of the Indo-Asian Collision Zone

Bilham et al., Science, 2001

Mountain Building and Megathrust Earthquakes

Credit: Seismo Lab, Caltech

Tectonic Background

Avouac et al., 2015

Data and Processing

120˚E 150˚E 30˚S 80˚N

120˚E 150˚E 150˚W 100˚W 50˚W 60˚N 80˚N

87˚

150˚W 100˚W 50˚W 0˚ 40˚N 60˚N

North America (NA) Australia (AU) Europe (EU)

Broad-band seismograms filtered between 0.5 -2 Hz; Epicentral distance between 50 and 95 degrees; MUSIC back-projection technique; Reference window strategy;

Back-projections of Three Large Continental Arrays

84˚ 85˚ 86˚ 87˚ 27˚ 28˚ 29˚

1

84˚ 86˚ 28˚

Kathmandu

50 km 30 60 Time (s) AU 30 60 EU 30 60 NA

120˚E 150˚E 30˚S 150˚W 100˚W 50˚W 60˚N 80˚N 0˚ 40˚N 60˚N

85˚ 86˚ 28˚ 86˚ 28˚

Kathmandu

50 km 28˚ 28˚

North America (NA) Europe (EU) Australia (AU)

Back-projections of Three Large Continental Arrays

86˚ 28˚ 50 km 28

M5.5 M6.7 M6.3 M5.7 AU NA EU

North America (NA) Europe (EU) Australia (AU)

Aftershock Test

Back-projection

Tohoku Earthquake Meng et al., GRL (2011)

Introduced by Ishii, Shearer et al (2005) Principle: 1. Identify coherent wave arrivals across a dense tele-seismic array 2. Use their differential arrival times to infer source locations 3. Repeat as the earthquake unfolds, in

• rder to track the rupture

High-resolution is obtained by exploiting high-frequency waves (~1Hz) Source region Seismic array Seismic rays

Methods Group Three

Back-projection Data Travel-time correction Beamforming (e.g. Wang and Mori ) Hypocenter Alignment (Ishii et al) Finite Fault Inversion

Processing Improvements

Relative relocation Array processing Filtering Location/Direction searching Correlation Stacking (Borcea et al) MUSIC (Meng et al) Hybrid Back-projection (Yagi et al) Compressive Sensing (Yao et al) High-frequency source images

Anatomy of the Back-projection Method

Principles of Back-projection

BP ξ,t

( ) =

uj t +Tj

0 ξ

( )

( )

j

∑

BP equation: Seismogram Station index Time Source location Travel time

Introducing Uncertainty of Travel time

Tj

0 ξ

( ) = Tj

cal ξ

( )+δTj ξ ( )

Theoretic travel time Travel time error Hypocenter Alignment

δTj ξ

( ) ! δTj ξh ( ) = Tj

0 ξh

( )−Tj

cal ξh

( )

Hypocenter Not always true !

Empirical aftershock calibrations of Back-projection

Ishii et al., 2007 Interpolation by weighted sum of aftershock travel-time errors! Challenges:

• 1. Sparseness of large aftershocks.
• 2. Aftershocks are mostly distributed away from large co-seismic slip

Introducing slowness correction

Distance across path D i s t a n c e a l

• n

g p a t h

ξh ξ

γ j

Tj

cal ξ

( ) = Tj ξh ( )+ sjγ j ⋅ ξ − ξh ( )

Far-field travel-time approximation Introducing the slowness correction term

δTj ξ

( ) ! δTj ξh ( )+δsjγ j ⋅ ξ −ξh ( )

Revised Back-projection Formula

BP ξ,t

( ) =

uj t +Tj

0 ξ

( )

( )

j

∑

= uj t +Tj

cal ξ

( )+δTj ξh ( )+δsjγ j ⋅ ξ − ξh ( )

( )

j

∑

= uj t +Tj

0 ξh

( )+ sj +δsj

( )γ j ⋅ ξ − ξh

( )

( )

j

∑

Accounting for travel time errors away from hypocenter!

Source of Slowness Error

" P (s/o)

• 0.01

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Depth (km)

200 400 600 800 1000 1200 1400 1600 1800

Slowness (ray parameter) error as a function of velocity change at different depths

85˚ 86˚ 28˚ 86˚ 28˚

Kathmandu

50 km 85˚ 86˚ 28˚ 86˚ 28˚

Kathmandu

86˚ 28˚ 50 km 28 86˚ 28˚

M5.5 M6.7 M6.3 M5.7 AU NA EU

Back-projections with Slowness Calibration

20 40 60

Time (s)

40 80 120

Distance (km)

5km/s 2km/s 1km/s

85˚ 86˚ 28˚

Kathmandu

50 km 0.0 0.5 1.0 Power

85˚ 86˚ 28˚

Kathmandu

50 km 3 Slip(m) 30 60 Time (s)

Time (s)

c

Distance (km)

Synthetic tests of kinematic rupture scenarios

85˚ 86˚ 27˚ 28˚

Kathmandu

50 km 40 80 Time (s) 85˚ 86˚ 27˚ 28˚

Kathmandu

50 km 85˚ 86˚ 27˚ 28˚

Kathmandu

50 km 85˚ 86˚ 27˚ 28˚

Kathmandu

50 km 85˚ 86˚ 27˚ 28˚

Kathmandu

50 km 85˚ 86˚ 27˚ 28˚

Kathmandu

50 km

Consistency Between BP and Finite Fault Models

Credit: Diego Melgar and Lingsen Meng

Unzipping of the Lower Edge of the Locked Megathrust

Avouac et al., 2015

Stress Loading at the Bottom of the Coupling Zone

Stevens and Avouac, 2015

Nucleation Propagation Arrest

Intermediate event unzipping part of the lower edge

• f the couple zone

Extracted from Junle Jiang and Nadia Lapusta’s dynamic earthquake cycle simulations

Pre-stress Final stress

Unzipping of the Lower Edge of the Locked Megathrust

Credit: Junle Jiang and Nadia Lapusta

Earthquake Cycles in Tohoku Region

Allmon et al., 2011 Historical earthquakes 2011 Tohoku Earthquake

Summary

• Multi-Array back-projections of the Gorkha earthquake

provides a unique opportunity to understand the spatial uncertainties of BP imaging.

• A slowness error term calibrated by aftershocks needs to be

introduced to achieve consistency between BPs of different arrays.

• Refined source imaging reveals a narrow unilateral

eastward rupture unzipping the lower bottom of the locked portion of the MHT.

• The Gorkha earthquake is possibly a intermediate event

during the interseismic period of larger earthquakes.