Error estimation in multitemporal InSAR deformation time series, with application to Lanzarote, Canary Islands

Interferometric Synthetic Aperture Radar (InSAR) is a reliable technique for measuring crustal deformation. However, despite its long application in geophysical problems, its error estimation has been largely overlooked. Currently, the largest problem with InSAR is still the atmospheric propagation errors, which is why multitemporal interferometric techniques have been successfully developed using a series of interferograms. However, none of the standard multitemporal interferometric techniques, namely PS or SB (Persistent Scatterers and Small Baselines, respectively) provide an estimate of their precision. Here, we present a method to compute reliable estimates of the precision of the deformation time series. We implement it for the SB multitemporal interferometric technique (a favorable technique for natural terrains, the most usual target of geophysical applications). We describe the method that uses a properly weighted scheme that allows us to compute estimates for all interferogram pixels, enhanced by a Montecarlo resampling technique that properly propagates the interferogram errors (variance-covariances) into the unknown parameters (estimated errors for the displacements). We apply the multitemporal error estimation method to Lanzarote Island (Canary Islands), where no active magmatic activity has been reported in the last decades. We detect deformation around Timanfaya volcano (lengthening of line-of-sight ∼ subsidence), where the last eruption in 1730–1736 occurred. Deformation closely follows the surface temperature anomalies indicating that magma crystallization (cooling and contraction) of the 300-year shallow magmatic body under Timanfaya volcano is still ongoing.Peer reviewe

Patient baseline characteristics and data on surgery in the two groups.

<p>Data are presented as median (range) (not normally distributed data), as mean ± SD (normally distributed data) or as</p><p>absolute numbers (with the percentage (%) of the whole). * p<0.05</p><p>[95% CI]  =  95% Confidence intervall on the mean</p><p>CABG  =  coronary artery bypass grafting; CPB  =  cardiopulmonary bypass, MI  =  myocardial infarction, PRBC = packed red blood cells.</p

Receiver operating characteristic curve (all patients).

<p>Receiver operating characteristic curve for the significance of postoperative (admission to ICU) selenium, GPx, ADMA and CK-MB concentrations in all patients to predict the development of organ dysfunction in the postoperative period. AUC, area under the receiver operating curve.</p

Outcome characteristics of the two groups.

<p>Data are presented as median (range) (not normally distributed data), as mean ± SD (normally distributed data) or as absolute numbers (with the percentage (%) of the whole). CABG  =  coronary artery bypass grafting; CPB  =  cardiopulmonary bypass, MI  =  myocardial infarction.</p

Flowchart.

<p>According to the <i>CONSORT-statement</i> for randomised clinical trials. From the initially screened 60 patients, 46 patients received the allocated intervention. 6 patients had to be excluded from further analysis.</p

Perioperative inflammatory response and myocardial damage.

<p><b>A</b>) Comparison of serum IL-6 levels between the on-pump group (open circles) and the OPCAB-group (closed circles) at baseline (preoperative) and at ICU admission (postoperative). Data are presented as mean ± standard deviation. *<i>p</i><0.05, **<i>p</i><0.01 versus baseline, analyzed with 2-way ANOVA. <b>B</b>) Correlation of whole blood selenium levels and IL-6 levels in serum, between the two groups. Data are depicted as linear regression (black line) with 95% confidence intervals (long dashed line). <b>C</b>) Comparison of serum CK-MB levels between the on-pump group (open circles) and the OPCAB-group (closed circles) at baseline (preoperative) and at ICU admission (postoperative). Data are presented as mean ± standard deviation. *<i>p</i><0.05, **<i>p</i><0.01 versus baseline, analyzed with 2-way ANOVA. <b>D</b>) Correlation of whole blood selenium levels and CK-MB in serum between the two groups. Data are depicted as linear regression (black line) with 95% confidence intervals (long dashed line).</p

Receiver operating characteristic curve (OPCAB group).

<p>Receiver operating characteristic curve for the significance of postoperative (admission to ICU) selenium, GPx, ADMA and CK-MB concentrations in the OPCAB group to predict the development of organ dysfunction in the postoperative period. AUC, area under the receiver operating curve.</p