Tsunami excitation by inland/coastal earthquakes: the Green function approach

International audienceIn the framework of the linear theory, the representation theorem is derived for an incompressible liquid layer with a boundary of arbitrary shape and in a homogeneous gravity field. In addition, the asymptotic representation for the Green function, in a layer of constant thickness is obtained. The validity of the approach for the calculation of the tsunami wavefield based on the Green function technique is verified comparing the results with those obtained from the modal theory, for a liquid layer of infinite horizontal dimensions. The Green function approach is preferable for the estimation of the excitation spectra, since in the case of an infinite liquid layer it leads to simple analytical expressions. From this analysis it is easy to describe the peculiarities of tsunami excitation by different sources. The method is extended to the excitation of tsunami in a semiinfinite layer with a sloping boundary. Numerical modelling of the tsunami wavefield, excited by point sources at different distances from the coastline, shows that when the source is located at a distance from the coastline equal or larger than the source depth, the shore presence does not affect the excitation of the tsunami. When the source is moved towards thecoastline, the low frequency content in the excitation spectrum ecreases, while the high frequencies content increases dramatically. The maximum of the excitation spectra from inland sources, located at a distance from the shore like the source depth, becomes less than 10% of that radiated if the same source is located in the open ocean. The effect of the finiteness of the source is also studied and the excitation spectrum is obtained by integration over the fault area. Numerical modelling of the excitation spectra for different source models shows that, for a given seismic moment, the spectral level, as well as the maximum value of the spectra, decreases with increasing fault size. When the sources are located in the vicinity of a shore, the synthetic mareograms calculated at distances greater than the source depth show that the maximum tsunami amplitude decays with decreasing source-to-shore distance. The rate of decay is dependent on the dip, length and depth of the fault. The tsunami intensity, defined as maximum peak-to-peak amplitude, decays with the inland distance of the source from the coast. At an inland distance equal to the source depth, it becomes 4?5 times less than that from a source in the open ocean. If the source is located under the coastline, the intensity of tsunami is approximately the same as for oceanic sources

Spektralna svojstva potresa na dodiru tektonskih ploča

Earthquakes are investigated with epicentres located along divergent and along convergent plate boundaries. Two criteria are applied in order to distinguish between earthquakes featuring anomalous “long-periodic” and “short-periodic” radiation of body-waves: 1) deviation of the corner period Tc of the P-waves from the regression between Tc and the moment magnitude Mw; and 2) the values of stress drop Dsigma. It is found that earthquakes along divergent boundaries radiate the seismic energy mainly at longer periods, and, vice versa, that such along convergent boundaries radiate energy mainly at shorter periods. The average stress drop for the former earthquakes is estimated thereby to be 33 bars and for latter – 89 bars. In a regional scale, for earthquakes in the Japan-Kuril area it is found that the corner periods for strike-slip events are larger than those for thrust events. The results confirm the findings of investigations based on the creepex distribution along divergent and convergent boundaries, as well as the findings related to the dependence of creepex on the source mechanism.Proučavani su potresi na konvergentnim i divergentnim mjestima dodira tektonskih ploča. Potresi karakterizirani anomalno dugoperiodičkom odnosno kratkoperiodičkom radijacijom prostornih valova razlučeni su na osnovi devijacije graničnog perioda Tc P-valova (regresijom Tc i momentne magnitude Mw), te razmatranjem iznosa pada napetosti na rasjedu, Dsigma. Ustanovljeno je da potresi na konvergentnim granicama zrače seizmičku energiju uglavnom na duljim periodima nego oni na divergentnim granicama. Prosječni pad napetosti za potrese duž konvergentnih granica iznosi 33 bara, a za one na divergentnim 89 bara. Na području Japana i Kurilskih otoka »strike-slip« potresi imaju veći granični period od »dip-slip« potresa. Rezultati su u skladu s istraživanjima creepex razdiobe duž konvergentnih i divergentnih granica, kao i ovisnosti creepex-a o žarišnom mehanizmu

Tsunami excitation by inland/coastal earthquakes: the Green function approach

In the framework of the linear theory, the representation theorem is derived for an incompressible liquid layer with a boundary of arbitrary shape and in a homogeneous gravity field. In addition, the asymptotic representation for the Green function, in a layer of constant thickness is obtained. The validity of the approach for the calculation of the tsunami wavefield based on the Green function technique is verified comparing the results with those obtained from the modal theory, for a liquid layer of infinite horizontal dimensions. The Green function approach is preferable for the estimation of the excitation spectra, since in the case of an infinite liquid layer it leads to simple analytical expressions. From this analysis it is easy to describe the peculiarities of tsunami excitation by different sources. The method is extended to the excitation of tsunami in a semiinfinite layer with a sloping boundary. Numerical modelling of the tsunami wavefield, excited by point sources at different distances from the coastline, shows that when the source is located at a distance from the coastline equal or larger than the source depth, the shore presence does not affect the excitation of the tsunami. When the source is moved towards thecoastline, the low frequency content in the excitation spectrum ecreases, while the high frequencies content increases dramatically. The maximum of the excitation spectra from inland sources, located at a distance from the shore like the source depth, becomes less than 10% of that radiated if the same source is located in the open ocean. The effect of the finiteness of the source is also studied and the excitation spectrum is obtained by integration over the fault area. Numerical modelling of the excitation spectra for different source models shows that, for a given seismic moment, the spectral level, as well as the maximum value of the spectra, decreases with increasing fault size. When the sources are located in the vicinity of a shore, the synthetic mareograms calculated at distances greater than the source depth show that the maximum tsunami amplitude decays with decreasing source-to-shore distance. The rate of decay is dependent on the dip, length and depth of the fault. The tsunami intensity, defined as maximum peak-to-peak amplitude, decays with the inland distance of the source from the coast. At an inland distance equal to the source depth, it becomes 4–5 times less than that from a source in the open ocean. If the source is located under the coastline, the intensity of tsunami is approximately the same as for oceanic sources

Efficacy and safety of oral semaglutide in patients with type 2 diabetes and moderate renal impairment (PIONEER 5): a placebo-controlled, randomised, phase 3a trial

Background: Oral semaglutide is the first oral glucagon-like peptide-1 (GLP-1) receptor agonist for glycaemic control in patients with type 2 diabetes. Type 2 diabetes is commonly associated with renal impairment, restricting treatment options. We aimed to investigate the efficacy and safety of oral semaglutide in patients with type 2 diabetes and moderate renal impairment. Methods: This randomised, double-blind, phase 3a trial was undertaken at 88 sites in eight countries. Patients aged 18 years and older, with type 2 diabetes, an estimated glomerular filtration rate of 30–59 mL/min per 1·73 m2, and who had been receiving a stable dose of metformin or sulfonylurea, or both, or basal insulin with or without metformin for the past 90 days were eligible. Participants were randomly assigned (1:1) by use of an interactive web-response system, with stratification by glucose-lowering medication and renal function, to receive oral semaglutide (dose escalated to 14 mg once daily) or matching placebo for 26 weeks, in addition to background medication. Participants and site staff were masked to assignment. Two efficacy-related estimands were defined: treatment policy (regardless of treatment discontinuation or rescue medication) and trial product (on treatment without rescue medication) in all participants randomly assigned. Endpoints were change from baseline to week 26 in HbA1c (primary endpoint) and bodyweight (confirmatory secondary endpoint), assessed in all participants with sufficient data. Safety was assessed in all participants who received at least one dose of study drug. This trial is registered on ClinicalTrials.gov, number NCT02827708, and the European Clinical Trials Registry, number EudraCT 2015-005326-19, and is now complete. Findings: Between Sept 20, 2016, and Sept 29, 2017, of 721 patients screened, 324 were eligible and randomly assigned to oral semaglutide (n=163) or placebo (n=161). Mean age at baseline was 70 years (SD 8), and 168 (52%) of participants were female. 133 (82%) participants in the oral semaglutide group and 141 (88%) in the placebo group completed 26 weeks on treatment. At 26 weeks, oral semaglutide was superior to placebo in decreasing HbA1c (estimated mean change of −1·0 percentage point (SE 0·1; −11 mmol/mol [SE 0·8]) vs −0·2 percentage points (SE 0·1; −2 mmol/mol [SE 0·8]); estimated treatment difference [ETD]: −0·8 percentage points, 95% CI −1·0 to −0·6;

Inverse problems of geophysics

This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given