Lingsen Meng

Research  /  02

Source imaging

Back-projection imaging

A large earthquake radiates high-frequency waves from wherever its rupture front is at each moment. Back-projection turns a dense seismic array into an antenna that points at those sources, and so tracks the rupture in space and time without assuming a fault model. Much of our methodological work has been to make these images sharper and more reliable.

Delay and stack

Take a trial source location. For each station, predict the travel time from that point, shift the recording by it, and sum. If the trial point is where the waves came from, the shifted traces line up and add constructively; if not, they partly cancel. Scanning a grid of trial points in successive short time windows gives the brightest radiators as a function of time, which trace the rupture front.

Beamforming in one picture

Schematic
A wavefront crosses the array; traces are aligned on predicted travel times and stacked.
Synthetic wavelets in a homogeneous medium. Shifting by the travel times from the true source aligns the traces and gives a large stack; the same shifts computed for a wrong trial point give a small one.

Radiators of recent large earthquakes

Each dot is the location of peak high-frequency radiation in one time window, from slowness-enhanced back-projection (SEBP) of teleseismic P waves. Colour gives time after origin and size the normalised beam power. The inset plots distance from the epicentre against time; its slope is the rupture speed. Different arrays see the same rupture from different directions, so switching arrays is a quick test of robustness.

Back-projection playback

Published data
time after origin 0 – · marker area ∝ beam power · star = epicentre

Sources: Mandalay, Xu et al. (2025) Science, data doi:10.5281/zenodo.17113746; Noto, Xu et al. (2024) Science, doi:10.5281/zenodo.12786109; Türkiye, Xu et al. (2023) Commun. Earth Environ., doi:10.5281/zenodo.10040732 (CH = Chinese array); Maduo, Xu et al. (2023) JGR, doi:10.5281/zenodo.7761908. Palu: single-array MUSIC back-projection of the Australian-array data shipped with the public MUSICBP code, with the beam-power map of each 10 s window; consistent with Bao et al. (2019), whose figure uses multi-array SEBP; windows with normalised power below 0.34 are hidden. The Venezuela result belongs to a submitted manuscript and has not been peer reviewed. Coastlines: Natural Earth.

Making back-projection sharper and more reliable

MUSIC back-projection

Beamforming blurs sources that radiate at the same time from nearby points. We brought the MUltiple SIgnal Classification (MUSIC) method into back-projection, with multitaper cross-spectra to handle non-stationary seismic signals. It sharpens the image of the rupture process considerably (Meng et al., 2011, GRL; 2012, JGR).

30 35 40 45 50 55 Back-azimuth (°) −25 −20 −15 −10 −5 0 Normalised power (dB) true sources, 3° apart Beamforming MUSIC
Computed for this pageSynthetic test. Two plane waves arriving 3° apart at a 25-station array of 140 km aperture (1 Hz, slowness 0.08 s/km, added noise). The conventional beam merges them into one peak; the MUSIC pseudo-spectrum separates them. Computed for this page with tools/make_figures.py.

Reference windows against the “swimming” artefact

Conventional sliding-window back-projection produces transients that migrate across the image toward the array, because earthquake waveforms are impulsive rather than stationary. Aligning each window on a reference window instead of absolute time suppresses this artefact without losing resolution (Meng et al., 2013, Earth Planets Space).

Slowness calibration with aftershocks (SEBP)

Different arrays can image the same earthquake differently, mainly because 3-D Earth structure distorts travel times in an array-specific way. Besides aligning the first arrival on the hypocentre, we correct the slowness, i.e. how travel time changes with source position, using aftershocks with known locations. This makes images from different arrays agree (Meng, Zhang & Yagi, 2016, GRL), and the regional version reduces spatial bias further (Zhang et al., 2023, JGR). The public code is in MUSICBP (SEBP branch).

Depth: 3-D back-projection

Teleseismic rays are steep, so back-projection resolves position well but depth poorly. Combining P with the depth phase pP, whose ray paths cross, recovers depth. For the 2013 Mw 8.3 Okhotsk deep-focus earthquake it shows a mostly horizontal rupture deepening southward, consistent with failure on sub-parallel planes in an en-echelon pattern (Meng et al., 2014, GRL).

Southern Hemisphere: PKIKP back-projection

Most large arrays are in the Northern Hemisphere, out of teleseismic range of many southern earthquakes. The core phase PKIKP at 150–180° reaches resolution comparable to P-wave back-projection, validated on the 2010 Chile, 2021 Haiti and 2021 Kermadec earthquakes (Xu, Meng & Chu, 2025, JGR).

Map and depth sections of 3-D back-projection radiators of the 2013 Okhotsk deep earthquake
Original figure · Meng et al. 2014, GRL2013 Okhotsk deep earthquake. Radiators from P and pP back-projection in map view (a) and along two depth sections (b, c), coloured by time. From Meng et al. (2014), GRL.
Back-projection of the 2012 off-Sumatra earthquake showing rupture on orthogonal fault branches
Original figure · Meng et al. 2012, Science2012 Mw 8.6 off-Sumatra earthquake. Back-projection radiators coloured by time reveal rupture on four orthogonal fault planes, including branching onto faults under compressional stress and a jump across a ~20 km offset. From Meng et al. (2012), Science.

Arrays for earthquake early warning

Early-warning systems that treat an earthquake as a point underestimate large ruptures while they are still growing. Small-aperture arrays near active faults can back-project in real time and follow rupture length, duration and directivity as they develop, which could extend finite-source warning to M > 7 events; we demonstrated the idea with the 2004 Parkfield and 2010 El Mayor–Cucapah earthquakes (Meng, Allen & Ampuero, 2014, BSSA). Multi-array local back-projection later imaged the 2019 Ridgecrest sequence (Xie, Bao & Meng, 2021, JGR), and a high-frequency distance metric from back-projection improves ground-motion prediction (Feng & Meng, 2018, GRL).

Key papers

Back-projection code