Deformation-induced topographic effect due to shallow dyke: Etna December 2018 fissure eruption case study

Gravitational effect of surface deformation is in 4D microgravimetry treated as the deformation-induced topographic effect (DITE). The DITE field is computed using Newtonian volumetric integration which requires high resolution digital elevation model (DEM) and vertical displacement field in areal form. If only elevation changes on benchmarks of the gravimetric network are available, instead of the vertical displacement field, the DITE on benchmarks can be evaluated only approximately, using a planar Bouguer or a normal free-air-effect (nFAE) approximation. Here we analyze the adequacy and accuracy of these two approximations in a case study for the December 2018 fissure eruption on Etna accompanied by significant surface deformation caused primarily by a relatively shallow dyke. The outcome is that in volcanic areas of similar morphology as that over the Etna summit area, and for surface deformation fields due to relatively shallow dykes, neither the Bouguer nor the nFAE approximation of the DITE is accurate enough. In such situations the residual gravity changes should be computed with both the Bouguer and nFAE corrections and interpreted as two marginal cases. In addition we analyze also a correction for the effect of benchmark elevation change based on the topographically modelled (predicted) vertical gradient of gravity (VGG) meant to approximate the in-situ VGG values at benchmarks. This correction does not appear suitable to approximate the DITE in conditions of our case study or in broader sense.

Comparison of different topographic mass integration schemes in topographic reduction and its impact on geoid modeling: a case study in the Colorado area

<p>Topographic reduction is one of the most imperative steps in geoid modeling, where the gravity field inside the masses needs to be modeled. This is quite challenging because no one can measure gravity inside the topography at a desired resolution (only a very limited number of borehole gravity measurements are available in the whole world). Therefore, topographic mass modeling is usually treated either by the residual terrain modeling (RTM) or by the Helmert’s 2<sup>nd</sup> condensation among other alternative reduction schemes. All of these topographic reductions need intense computation efforts for the integration of topographic mass induced gravity effects. Currently, the most popular tool for topographic mass modeling is the ‘tc’ program available in the GRAVSOFT package. In this program, the mass elements provided by a digital terrain model (DTM) are treated as rectangular prisms which cannot directly take the Earth curvature into account and suffer from geometrical shape change due to meridian convergence. In this study, the tesseroids which are naturally obtained from a DTM are employed and their gravity effects are precisely evaluated by numerical integrations. Four topographic mass integration schemes are proposed and programmed in FORTRAN. Their computational performances in computing the RTM effect, terrain correction, and total topographic effect with and without using parallelizing technique are tested in the Colorado area. Then they are applied to local geoid modeling to see the geoid model differences among these various integration schemes in the RTM case. The numerical findings reveal that: (1) The application of parallelization techniques can greatly reduce the computation time without the loss of any computation accuracy; (2) Among the four integration schemes, the maximum absolute difference of RTM effect, terrain correction, and total topographic effect is about 3 mm, 6 cm, and 7.5 cm for the height anomaly, and 4 mGal, 3 mGal, and 40 mGal for the gravity anomaly; (3) In the RTM case, the geoid model difference can reach a maximum of 1 cm in the target area, and a larger difference should be expected in areas with rougher terrain; (4) The effects on geoid models from mass density anomalies is bigger than the counterparts from DTM errors.</p>

Application of deformation–induced topographic effect in interpretation of 2013–2016 spatiotemporal gravity changes at Laguna del Maule (Chile)

<p>The accurate deformation-induced topographic effect (DITE) should be used to account for the gravitational effect of surface deformation when analyzing residual spatiotemporal (time-lapse) gravity changes in volcano gravimetric or 4D micro-gravimetric studies, in general. Numerical realization of DITE requires the deformation field available in grid form. We compute the accurate DITE correction for gravity changes observed at the Laguna del Maule volcanic field in Chile over three nearly annual periods spanning 2013–2016 and compare it numerically with the previously used free-air effect (FAE) correction. We assess the impact of replacing the FAE by DITE on the model source parameters of analytic inversion solutions and apply a new inversion approach based on model exploration and growing source bodies. The new inversion results based on the DITE correction shift the position of the mass intrusion upwards by a few hundred meters and lower the total mass of the migrated fluids to roughly a half, compared to the inversion results based on the local-FAE correction. Our new Growth inversion results indicate that vertical dip-slip faults beneath the lake, as well as the Troncoso fault play active roles in hosting migrating liquid. We also show that for the study period, the DITE at Laguna del Maule can be accurately evaluated by the planar Bouguer approximation, which only requires the availability of elevation changes at gravity network benchmarks. We hypothesize that this finding may be generalized to all volcanic areas with flatter or less rugged terrain and may alter interpretations based on the commonly used FAE corrections.</p>

Establishment of a seismic topographic effect prediction model in the Lushan Ms 7.0 earthquake area

SUMMARY The seismic topographic effect is one of the debated research topics in seismology and earthquake engineering. This debate is due to the discrepancy between the observed amplification and the amplification underestimation in numerical simulations. Although the numerical simulation of ground motion, which began in the 1970s, has been an important and effective way to study topographic effects, the quantitative mathematical model of topographic amplification is urgent. The actual influences on ground motion due to the topography depends on multiple topographic features, such as the topographic slope, topographic geometrical scale. To date, no definite conclusions regarding the main influencing factors and how to express the influencing factors have been made. In this paper, by introducing the back-propagation (BP) neural network technique, a set of mathematical parameters are determined to establish a quantitative topographic effect prediction model. These parameters are the elevation, the first gradient of the elevation and the higher order gradient in two orthogonal directions. Theoretically, the set of mathematical parameters is directly related to the simple topographic features, such as the elevation, topographic slope and height-to-width ratio. Furthermore, their combinations indirectly denote the complex topographic geometrical features, such as the different topographic geometrical scales, designated by the elevation (large-scale variable), the first gradient (middle-scale variable), the second-order gradient (small-scale variable) and so on (smaller scale variable), and the hill ridges that correspond to the sites with the first gradient of the elevation equal to zero and an elevation larger than its surrounding. In 2013, an earthquake of Ms 7.0 occurred in the Lushan area of Sichuan Province in Western China, where the topography sharply fluctuates. At station 51BXD, an acceleration was recorded close to 1.0 g, while at station 51BXM (14 km away from station 51BXD), the acceleration was recorded at only 0.2–0.3 g. In this paper, the spectral element method (SEM) is used to simulate the ground motion in the Lushan Ms 7.0 earthquake area. Then, the topographic amplification ratio of the simulated ground motion is calculated. Furthermore, a BP topographic amplification prediction model is established and compared based on different parameters. A rms of less than or close to 10 per cent between the BP model prediction results and topographic amplification ratio calculated using the simulated ground motion suggests that the parameters of the topographic elevation, the first gradient of the elevation and the second-order gradient in two orthogonal directions are enough to provide the acceptable topographic effect model in the Lushan area. Finally, using the prediction model, the topographic spectral ratio at stations 51BXD and 51BXM is predicted, and the topography amplification due to the scattering of seismic waves by the irregular topography at 51BXD is found to be 1.5–2 times that of 51BXM. The most important highlights of this paper identify the main factors of the topographic effect for the first time and provide an effective method for establishing a quantitative topographic effect prediction model.