Basic Concepts ofL1Norm Minimization for Surveying Applications

Marshall, J. Le; Bethel, James

doi:10.1061/(asce)0733-9453(1996)122:4(168)

Cited by 37 publications

(25 citation statements)

References 3 publications

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“…Equation is solved by minimizing the L1 norm of the residuals. The advantage of the L1 norm over the more widely used L2 norm is that it is less sensitive to outliers and thus reduces their impact on the estimated parameters [ Marshall and Bethel , ]. To determine the temporal evolution of the volume change, we additionally use a linear Kalman filter [ Grewal and Andrews , ] to generate time series of the volume change for each PCDs [ Shirzaei and Walter , ].…”

Section: Methodsmentioning

confidence: 99%

Deep and shallow sources for the Lusi mud eruption revealed by surface deformation

Shirzaei

Rudolph

Manga

2015

Geophysical Research Letters

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The Lusi mud eruption, in East Java, Indonesia, began in May 2006 and continues to the present. Previous analyses of surface deformation data suggested an exponential decay of the pressure in the mud source but did not constrain the location, geometry, and evolution of the possible source(s) of the erupting mud and fluids. To map the surface deformation, we employ multitemporal interferometric synthetic aperture radar and analyze a well‐populated L‐band data set acquired by the Advanced Land Observing Satellite (ALOS) between May 2006 and April 2011. We then apply a time‐dependent inverse modeling scheme. Volume changes occur in two regions beneath Lusi, at 0.3–2.0 km and 3.5–4.75 km depth. The cumulative volume change within the shallow source is ~2–3 times larger than that of the deep source. The observation and model suggest that a shallow source plays a key role by supplying the erupting mud, but that additional fluids do ascend from depths >4 km on eruptive timescales.

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Section: Methodsmentioning

confidence: 99%

Deep and shallow sources for the Lusi mud eruption revealed by surface deformation

Shirzaei

Rudolph

Manga

2015

Geophysical Research Letters

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“…To associate the daily time series of surface displacement with the kinematics of the spatiotemporal distribution of the afterslip, we implement a time-dependent inverse modeling scheme . This method consists of two main operators; (1) a robust optimization operator using the L1-norm minimization as a minimum spatial mean error estimator (Marshall and Bethel, 1996), and (2) a linear Kalman filter (LKF) (Grewal and Andrews, 2001) to generate the time series of the afterslip for each triangular dislocation of the fault-interface mesh as a minimum temporal mean square error estimator. These two steps are implemented iteratively (Shirzaei and Walter, 2010).…”

Section: Time-dependent Afterslip Modelmentioning

confidence: 99%

Seismic versus aseismic slip: Probing mechanical properties of the northeast Japan subduction zone

Shirzaei

Bürgmann

Uchida

et al. 2014

Earth and Planetary Science Letters

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“…This provided us with a larger group of pixels (Figure 3c) which may be more affected by phase noise. This step‐wise increase in observation points did not lead to significant global unwrapping errors [ Marshall and Bethel , 1996], since we used an L1 norm minimization approach for phase unwrapping [ Costantini , 1998] and we reduced the spatial aliasing by removing the ADM. Hereafter we unwrapped the residual phase and restored the ADM, so that eventually the complete unwrapped data set was obtained (Figure 3e). As a test, we unwrapped the filtered interferograms without removing the ADM and noted significant unwrapping errors.…”

Section: Application To Llaima Volcanomentioning

confidence: 99%

Inflation and deflation at the steep-sided Llaima stratovolcano (Chile) detected by using InSAR

Bathke

Shirzaei²,

Walter

2011

Geophys. Res. Lett.

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Llaima volcano, Chile, is a typical basaltic‐to‐andesitic stratovolcano in the southcentral Andes. Llaima had at least four explosive eruptions in the decade 2000 – 2010, however little is known about the physical processes and magma storage at this volcano. In this study we present an InSAR deformation field at Llaima from 2003 – 2008, covering both the post‐eruptive and syn‐eruptive periods. The satellite InSAR data are significantly affected by environmental decorrelation due to steep topography, snow and vegetation; because of this, we applied a model‐assisted phase unwrapping approach. The analysis of these data suggests two main deformation episodes: subsidence associated with the post‐eruptive period, and uplift associated with the syn‐eruptive period. Maximum summit subsidence and uplift are ∼10 cm and ∼8 cm, respectively. Through inverse modeling of both periods, a deflating and inflating magma body can be inferred, located at a depth of 4 – 12 km, subject to a volume decrease of 10 – 46 × 106 m3 during the subsidence period, followed by a volume increase of 6 – 20 × 106 m3 during the uplift period. Therefore, this study presents the first evidence of magma‐driven deformation at Llaima volcano, and suggests that eruption periods are associated with the inflation and deflation of a deep magma body that can be monitored by using space geodesy.

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Basic Concepts ofL₁Norm Minimization for Surveying Applications

Cited by 37 publications

References 3 publications

Deep and shallow sources for the Lusi mud eruption revealed by surface deformation

Deep and shallow sources for the Lusi mud eruption revealed by surface deformation

Seismic versus aseismic slip: Probing mechanical properties of the northeast Japan subduction zone

Inflation and deflation at the steep-sided Llaima stratovolcano (Chile) detected by using InSAR

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