Enhanced three-dimensional stochastic adjustment for combined volcano geodetic networks

Volcano geodesy is unquestionably a necessary technique in studies of physical volcanology and for eruption early warning systems. However, as every volcano geodesist knows, obtaining measurements of the required resolution using traditional campaigns and techniques is time consuming and requires a large manpower. Moreover, most volcano geodetic networks worldwide use a combination of data from traditional techniques; levelling, electronic distance measurements (EDM), triangulation and Global Navigation Satellite Systems (GNSS) but, in most cases, these data are surveyed, analysed and adjusted independently. This then leaves it to the authors’ criteria to decide which technique renders the most realistic results in each case. Herein we present a way of solving the problem of inter-methodology data integration in a cost-effective manner following a methodology were all the geodetic data of a redundant, combined network (e.g. surveyed by GNSS, levelling, distance, angular data, INSAR, extensometers, etc.) is adjusted stochastically within a single three-dimensional referential frame. The adjustment methodology is based on the least mean square method and links the data with its geometrical component providing combined, precise, three-dimensional, displacement vectors, relative to external reference points as well as stochastically-quantified, benchmark-specific, uncertainty ellipsoids. Three steps in the adjustment allow identifying, and hence dismissing, flagrant measurement errors (antenna height, atmospheric effects, etc.), checking the consistency of external reference points and a final adjustment of the data. Moreover, since the statistical indicators can be obtained from expected uncertainties in the measurements of the different geodetic techniques used (i.e. independent of the measured data), it is possible to run a priori simulations of a geodetic network in order to constrain its resolution, and reduce logistics, before the network is even built. In this work we present a first effort to apply this technique to a new volcano geodetic network on Arenal volcano in Costa Rica, using triangulation, EDM and GNSS data from four campaigns. An a priori simulation, later confirmed by field measurements, of the movement detection capacity of different benchmarks within the network, shows how the network design is optimised to detect smaller displacement at the points where these are expected. Data from the four campaigns also proves the repeatability and consistency of the statistical indicators. A preliminary interpretation of the geodetic data relative to Arenal’s volcanic activity could indicate a correlation between displacement velocity and direction with the location and thickness of the recent lava flow field. This then suggests that a deflation caused by the weight of the lava field could be obscuring the effects of possible deep magmatic sources. Although this study is specific to Arenal volcano and its regional tectonic setting, we suggest that the cost-effective, high-quality results we present, prove the methodology’s potential to be incorporated into the design and analysis of volcano geodetic networks worldwide.