Understanding caldera structure and development: An overview of analogue models compared to natural calderas

The karst environment is one of the most challenging in terms of groundwater, engineering and environmental issues. Geophysical methods can provide useful subsurface information in karst regions concerning , for instance, hazard estimation or groundwater exploration and vulnerability assessment. However, a karst area remains a very difficult environment for any geophysical exploration; selection of the best-suited geophysical method is not always straightforward, due to the highly variable and unpredictable target characteristics. The state of the art is presented, in terms of the contributions made by geophysical methods to karst-system exploration, based on extensive analysis of the published scientific results. This report is an overview and should be used as a preliminary meth-odological approach, rather than a guideline.

Contribution of geophysical methods to karst-system exploration: an overview

Space and time spectra of stationary stochastic waves, with special reference to microtremors

The information provided by different geophysical data sets (gravimetric, magnetic, seismic, etc.) can be used, together with petrophysical and geostatistical information, to estimate the major lithological properties of the rocks within the studied volume. The formalization of this inverse problem requires a joint representation and parameterization of the different media properties in the model. The information relating rock properties together couples the inversion of the plural geophysical data sets and allows one to relate the observations with the lithological parameters of the model. The representation by probability density functions (pdfs) of the different types of information entering the problem is also required and provides the mathematical framework to formulate their combination. The resulting joint posterior pdf is composed of two factors: the joint likelihood function, which is the product of independent likelihood functions associated with each geophysical data set, and the joint prior pdf. The latter decomposes, following a partition of the model parameter space in a primary (lithological) subspace and secondary (physical) subspace, as a marginal pdf over the primary model parameter space and a conditional pdf over the secondary model parameter space. A Markov-chain Monte Carlo method was adapted to sample joint models from the posterior pdf: (1) the method starts with a Markov-chain sampling primary models from the marginal prior pdf, (2) the chain is extended to the joint model space, by sampling from the conditional pdf of the secondary parameters with respect to the primary parameters, and (3) it is modified to sample from the posterior pdf, by applying the Metropolis rule, which uses the evaluation of the joint likelihood function to accept or reject model transitions in the sampling chain. Finally, posterior marginal or posterior conditional pdfs for the model parameters or the model properties can be straightforwardly calculated from the set of joint models sampled by the chain.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JB900014

Lithologic tomography: From plural geophysical data to lithology estimation

Combining Electrical Resistivity Tomography and Ground Penetrating Radar to study geological structuring of karst Unsaturated Zone

This paper presents a gravity inversion method for determining the volumes of bodies with pre‐established density contrasts. The method works step‐by‐step on a prismatic partition of the subsurface volume, expanding the anomalous bodies to fit the observed gravity values in a systematic exploration of model possibilities. The process is treated in a 3-D context; at the same time, it can determine a simple regional trend. Moreover, positive and negative density contrasts are simultaneously accepted. The solution is obtained by a double condition: (1) the &#x1d4c1;2-fitness to the observed gravity data (model fitness) and (2) the minimization of the total (weighted) anomalous mass (model smoothness). A positive parameter is used to balance the two minimization terms. The method is applied to a simulated example and also to a real example: the volcanic island of Gran Canaria (Canary Islands, Spain). In both cases, the results obtained show the possibilities of the method.

/pdf/gravity-inversion-by-means-of-growing-bodies-2d9zqshqtv.pdf

Gravity inversion by means of growing bodies

Internal structure of Tenerife (Canary Islands) based on gravity, aeromagnetic and volcanological data

A 3-D gravity inversion tool based on exploration of model possibilities

The use of genetic algorithms in geophysical inverse problems is a relatively recent development and offers many advantages in dealing with the non-linearity inherent in such applications. We have implemented a genetic algorithm to efficiently invert a set of gravity data. Employing several fixed density contrasts, this algorithm determines the geometry of the sources of the anomaly gravity field in a 3-D context. The genetic algorithms, based on Darwin’s theory of evolution, seek the optimum solution from an initial population of models, working with a set of parameters by means of modifications in successive iterations or generations. This searching method traditionally consists of three operators (selection, crossover and mutation) acting on each generation, but we have added a further one, which smoothes the obtained models. In this way, we have designed an efficient inversion gravity method, confirmed by both a synthetic example and a real data set from the island of Fuerteventura. In the latter case, we identify crustal structures related to the origin and evolution of the island. The results show a clear correlation between the sources of gravity field in the model and the three volcanic complexes recognized in Fuerteventura by other geological studies.

/pdf/using-a-genetic-algorithm-for-3-d-inversion-of-gravity-data-2fv2z187ah.pdf

Using a genetic algorithm for 3-D inversion of gravity data in Fuerteventura (Canary Islands)

Gravimetric studies are becoming more and more widely acknowledged as a useful tool for studying and modeling the distributions of subsurface masses that are associated with volcanic activity. In this paper, new gravimetric data for the volcanic island of Sao Miguel (Azores) were analyzed and interpreted by a stabilized linear inversion methodology. An inversion model of higher resolution was calculated for the Caldera of Furnas, which has a larger density of data. In order to filter out the noncorrelatable anomalies, least squares prediction was used, resulting in a correlated gravimetric signal model with an accuracy of the order of 0.9 mGal. The gravimetric inversion technique is based on the adjustment of a three-dimensional (3-D) model of cubes of unknown density that represents the island's subsurface. The problem of non-uniqueness is solved by minimization with appropriate covariance matrices of the data (resulting from the least squares prediction) and of the unknowns. We also propose a criterion for choosing a balance between the data fit (which in this case corresponds to residues with rms of the order of 0.6 mGal) and the smoothness of the solution. The global model of the island includes a low-density zone in a WNW-ESE direction and a depth of the order of 20 km, associated with the Terceira rift spreading center. The minimums located at a depth of 4 km may be associated with shallow magmatic chambers beneath the main volcanoes of the island. The main high-density area is related to the Nordeste basaltic shield. With regard to the Caldera Furnas, in addition to the minimum that can be associated with a magmatic chamber, there are other shallow minimums that correspond to eruptive processes.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/96JB03667

Fuensanta González Montesinos

Papers

Gravity inversion by means of growing bodies

Internal structure of Tenerife (Canary Islands) based on gravity, aeromagnetic and volcanological data

A 3-D gravity inversion tool based on exploration of model possibilities

Using a genetic algorithm for 3-D inversion of gravity data in Fuerteventura (Canary Islands)

A three-dimensional gravity inversion applied to São Miguel Island (Azores)