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

Lecture 2: The Slowness-Enhanced Back-Projection

Improving Imaging Quality Low Resolution High Resolution High Accuracy Low Accuracy Objective: Improving Resolution Objective: Reduce Spatial Biases Solution : MUSIC method Solution: Slowness Calibration

Outlines • 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

Tectonic View of the Indo-Asian Collision Zone S N Contraction uplift Tibet Himalaya Himalaya N 40 India N Locking line Tibet India Lockin 5 km Tibet 500 km Locked Locked Sliding Sliding 0 100 km 100 km Potential magnitude Potential magnitude 10 10 35 Potential slip, m Locking Certain possible Certain possible 8.2 8 8.2 8 line 8.1 6 8.1 6 1885 8.0 4 1905 4 8.0 2 7.8 2 7.8 Islamabad 0 30 0 ? Urban 1803 population Delhi Kathmandu 2 million 1950 500,000 1947 1833 200,000 1934 1930 25 1897 1819 Dhaka 2001 Bhuj Calcutta 70 75 80 85 90 95°E Bilham et al., Science, 2001

Mountain Building and Megathrust Earthquakes Credit: Seismo Lab, Caltech

Tectonic Background Avouac et al., 2015

Data and 30 ˚ S Processing 120 ˚ E 150 ˚ E Australia (AU) 80 ˚ N 120 ˚ E 150 ˚ E 80 ˚ N Broad-band seismograms filtered between 0.5 -2 Hz; Epicentral distance between 50 and 95 degrees; MUSIC back-projection technique; 60 ˚ N Reference window strategy; North America (NA) 150 ˚ W 100 ˚ W 50 ˚ W 150 ˚ W 100 ˚ W 50 ˚ W 60 ˚ N 40 ˚ N 87 ˚ 0 ˚ Europe (EU)

Back-projections of Three Large Continental Arrays 29˚ Time (s) AU EU NA 50 km 60 60 60 30˚S 30 30 30 0 0 0 1 120˚E 150˚E 80˚N 28˚ 28˚ 60˚N Kathmandu 150˚W 100˚W 50˚W 60˚N 27˚ 40˚N 84˚ 84˚ 85˚ 86˚ 86˚ 87˚ 0˚

Back-projections of Three Large Continental Arrays North America (NA) 50 km Europe (EU) 28 ˚ 28 ˚ 28 ˚ 28 ˚ Kathmandu Australia (AU) 85 ˚ 86 ˚ 86 ˚

Aftershock Test M5.5 North America (NA) M6.7 28 ˚ 28 M6.3 M5.7 AU Europe (EU) NA EU Australia (AU) 50 km 86 ˚

Back-projection Introduced by Ishii, Shearer et al (2005) Principle: Tohoku Earthquake 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 order to track the rupture Source Seismic region array Seismic rays Meng et al., GRL (2011) High-resolution is obtained by exploiting high-frequency waves (~1Hz)

Anatomy of the Back-projection Method Methods Array Relative Finite Fault Back-projection processing relocation Inversion Processing Location/Direction Filtering High-frequency Travel-time Data searching source images correction Group Three Improvements Hypocenter Beamforming Correlation Compressive Hybrid MUSIC Alignment (e.g. Wang and Stacking Sensing Back-projection (Meng et al) (Ishii et al) Mori ) (Borcea et al) (Yao et al) (Yagi et al)

Principles of Back-projection Travel time Source location Seismogram 0 ξ BP equation: ( ) ∑ ( ) = ( ) BP ξ , t u j t + T j Station index Time j Introducing Uncertainty of Travel time 0 ξ cal ξ ( ) = T j ( ) + δ T j ξ ( ) T j Theoretic travel time Travel time error Hypocenter Alignment 0 ξ h cal ξ h ( ) ! δ T j ξ h ( ) = T j ( ) − T j ( ) δ T j ξ Not always true ! Hypocenter

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 Far-field travel-time approximation γ j cal ξ ( ) = T j ξ h ( ) + s j γ j ⋅ ξ − ξ h ( ) T j h t Introducing the slowness correction term a p g ξ n o ( ) ! δ T j ξ h ( ) + δ s j γ j ⋅ ξ − ξ h ( ) δ T j ξ l a e c n a Accounting for travel time errors away t s i D from hypocenter! Revised Back-projection Formula 0 ξ ξ h ( ) ∑ ( ) = ( ) BP ξ , t u j t + T j j Distance across path cal ξ ( ) ∑ ( ) + δ T j ξ h ( ) + δ s j γ j ⋅ ξ − ξ h ( ) u j t + T j = j 0 ξ h ( ) ∑ ( ) γ j ⋅ ξ − ξ h ( ) + s j + δ s j ( ) = u j t + T j j

Source of Slowness Error 0 200 400 600 Depth (km) 800 1000 1200 1400 1600 1800 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 " P (s/ o ) Slowness (ray parameter) error as a function of velocity change at different depths

Back-projections with Slowness Calibration M5.5 M6.7 28 ˚ 28 ˚ 28 M6.3 M5.7 AU NA EU 50 km 86 ˚ 86 ˚ 50 km 28 ˚ 28 ˚ 28 ˚ 28 ˚ Kathmandu Kathmandu 85 ˚ 86 ˚ 86 ˚ 85 ˚ 86 ˚ 86 ˚

Power Slip(m) Time (s) 50 km 1.0 50 km Time (s) 60 3 0.5 30 0 0 0.0 28 ˚ 28 ˚ c Kathmandu Kathmandu 85 ˚ 86 ˚ 85 ˚ 86 ˚ Distance (km) 60 40 Time (s) 20 2km/s 1km/s 0 5km/s 0 40 80 120 Distance (km)

Synthetic tests of kinematic rupture scenarios Time (s) 80 50 km 50 km 40 0 28 ˚ 28 ˚ Kathmandu Kathmandu 27 ˚ 27 ˚ 85 ˚ 86 ˚ 85 ˚ 86 ˚ 50 km 50 km 28 ˚ 28 ˚ Kathmandu Kathmandu 27 ˚ 27 ˚ 85 ˚ 86 ˚ 85 ˚ 86 ˚ 50 km 50 km 28 ˚ 28 ˚ Kathmandu Kathmandu 27 ˚ 27 ˚ 85 ˚ 86 ˚ 85 ˚ 86 ˚

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

Unzipping of the Lower Edge of the Locked Megathrust Intermediate event unzipping part of the lower edge of the couple zone Extracted from Junle Jiang and Nadia Lapusta’s dynamic earthquake cycle simulations Nucleation Pre-stress Propagation Final stress Arrest Credit: Junle Jiang and Nadia Lapusta

Earthquake Cycles in Tohoku Region Historical earthquakes 2011 Tohoku Earthquake Allmon et al., 2011

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.