Electrical resistivity tomography imaging of the near-surface structure of the Solfatara crater, Campi Flegrei (Naples, Italy)

Abstract

We describe the results from an electrical resistivity tomography (ERT) survey performed inside the Solfatara crater, located in the central part of the Campi Flegrei (CF) composite caldera. The Solfatara volcano represents the most active zone within the CF area, in terms of hydrothermal manifestations and local seismicity. Eight dipole-dipole ERT lines have been measured with the aim of deducing a 3D resistivity model for the upper 80 m beneath the Solfatara. The results have allowed classification of the shallow structure below the crater into a low-resistivity (LR) class, up to about 4 Ωm, an intermediate resistivity (IR) class, from 5 Ωm up to 50 Ωm, and a high-resistivity (HR) class, from 60 Ωm onward. In order to solve the ambiguities arising in the interpretation of the nature of these bodies, a comparison has been done between the 3D ERT model and the CO₂ flux, soil temperature, and gravity maps over the same area. By combining all of these parameters, the whole LR body has been ascribed to a water-dominated geothermal basin and the HR body to a steam/gas-dominated reservoir. Finally, the IR class has been interpreted as a widespread background situation with intermediate character, where volatiles and condensates can coexist in the same volumes at variable percentages, coherently with the resistivity variation within this class. Since fluid dynamics in the Solfatara crater change rapidly, ERT surveys repeated in the future are expected to be of great help in monitoring possible pre-eruptive changes, as well as in better following evolution of the local geothermal system.

Appendix

Outline of the PERTI method

The 3D PERTI method was proposed by Mauriello and Patella (2009) in the framework of the probability tomography theory, which is now briefly outlined in order to better introduce the basic principle underlying the inversion algorithm.

Probability tomography was at first suggested for the self-potential method to identify the places underground, where higher is the occurrence probability of the sources that cause the anomalies detected on the ground (Patella 1997a, b). In geoelectrics, a similar approach was formulated to image the most probable location of the resistivity anomaly source bodies, consisting in plotting the occurrence probability function $\eta \left({P}_q\right)$, calculated at a grid of points P _q (q = 1,2,…,Q) below the ground surface by the formula (Mauriello and Patella 1999)

$$ \eta \left({\mathrm{P}}_q\right)={\mathrm{C}}_q{\displaystyle {\sum}_{k=1}^K{\displaystyle {\sum}_{j_k=1}^{J_k}\left[{\rho}_a\left({\mathrm{P}}_{jk}\right)-\widehat{\rho}\right]}}\psi \left({\mathrm{P}}_{j_k},{\mathrm{P}}_{\mathrm{q}}\right) $$

(A1)

In Eq. A1, ${\rho}_a\left({P}_{j_k}\right)$ is the measured apparent resistivity at ${P}_{j_k}$, i.e., the j _k -th nodal datum point of the k-th profile (j _k  = 1,2,…,J _k ; k = 1,2,…,K), $\widehat{\rho}$ is the resistivity of a homogeneous, isotropic half-space assumed as reference, or starting model, C _q is the positive-definite non-null normalization factor, given by

$$ {C}_q={\left\{{\displaystyle {\sum}_{k=1}^K{\displaystyle {\sum}_{j_k=1}^{J_k}{\left[{\rho}_a\left({\mathrm{P}}_{j_k}\right)-\widehat{\rho}\right]}^2\cdot {\displaystyle {\sum}_{k=1}^K{\displaystyle {\sum}_{j_k=1}^{J_k}{\psi}^2\left({\mathrm{P}}_{j_k},{\mathrm{P}}_q\right)}}}}\right\}}^{-1/2} $$

(A2)

and $\psi \left({\mathrm{P}}_{j_k},{\mathrm{P}}_q\right)$ is the j _k -th Frechet derivative referred to the reference model, also known as the sensitivity function of the array. It physically describes the effect generated at ${\mathrm{P}}_{j_k}$ by a small perturbation of the reference resistivity at P _q , under Born approximation (Loke and Barker 1995, 1996; Mauriello and Patella 1999).

Including topography, the sensitivity function for the DD array is calculated as follows. Taking a rectangular coordinate system with the xy-plane at mean sea level and the z-axis upwards, and indicating with $\left({x}_{j_k}^{\mathrm{A}},{y}_{j_k}^{\mathrm{A}},{z}_{j_k}^{\mathrm{A}}\right)$, $\left({x}_{j_k}^{\mathrm{B}},{y}_{j_k}^{\mathrm{B}},{z}_{j_k}^{\mathrm{B}}\right)$, and $\left({x}_{j_k}^{\mathrm{M}},{y}_{j_k}^{\mathrm{M}},{z}_{j_k}^{\mathrm{M}}\right)$, $\left({x}_{j_k}^{\mathrm{N}},{y}_{j_k}^{\mathrm{N}},{z}_{j_k}^{\mathrm{N}}\right)$ the coordinates of the current electrodes A and B and potential electrodes M and N, respectively, and with (x ^P _q , y ^P _q , z ^P _q ) the coordinates of the model point P _q , $\psi \left({\mathrm{P}}_{j_k},{\mathrm{P}}_q\right)$ is explicated asFor (8), the authors may emphasize in the manuscript that the authors interpret the results of gravitational survey assuming that the sources are located almost at same locations although this assumption should be examined.

$$ \psi \left({\mathrm{P}}_{j_k},{\mathrm{P}}_q\right)=\frac{G_{j_k}}{4{\pi}^2}\cdot \left({L}_{q,{j}_k}^{\mathrm{AM}}-{L}_{q,{j}_k}^{\mathrm{AN}}-{L}_{q,{j}_k}^{\mathrm{BM}}+{L}_{q,{j}_k}^{\mathrm{BN}}\right), $$

(A3)

where ${G}_{j_k}$ is the geometrical factor of the DD array and

$$ {L}_{q,{j}_k}^{\mathrm{A}\mathrm{M}}=\frac{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^A\right)\left({x}_q^P-{x}_{j_k}^M\right)+\left({y}_q^P-{y}_{j_k}^A\right)\left({y}_q^P-{y}_{j_k}^M\right)+\left({z}_q^{\mathrm{P}}-{z}_{j_k}^A\right)\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{M}}\right)}{{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^A\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{A}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{A}}\right)}^2\right]}^{3/2}{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{M}}\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{M}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{M}}\right)}^2\right]}^{3/2}} $$

(A4a)

$$ {L}_{q,{j}_k}^{\mathrm{A}\mathrm{N}}=\frac{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{A}}\right)\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{N}}\right)+\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{A}}\right)\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{N}}\right)+\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{A}}\right)\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{N}}\right)}{{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{A}}\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{A}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{A}}\right)}^2\right]}^{3/2}{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{N}}\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{N}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{N}}\right)}^2\right]}^{3/2}} $$

(A4b)

$$ {L}_{q,{j}_k}^{\mathrm{B}\mathrm{M}}=\frac{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{B}}\right)\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{M}}\right)+\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{B}}\right)\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{M}}\right)+\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{B}}\right)\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{M}}\right)}{{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{B}}\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{B}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{B}}\right)}^2\right]}^{3/2}{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{M}}\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{M}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{M}}\right)}^2\right]}^{3/2}} $$

(A4c)

$$ {L}_{q,{j}_k}^{\mathrm{B}\mathrm{N}}=\frac{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{B}}\right)\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{N}}\right)+\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{B}}\right)\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{N}}\right)+\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{B}}\right)\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{N}}\right)}{{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{B}}\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{B}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{B}}\right)}^2\right]}^{3/2}{\left[{\left({x}_q^{\mathrm{P}}-{x}_{j_k}^{\mathrm{N}}\right)}^2+{\left({y}_q^{\mathrm{P}}-{y}_{j_k}^{\mathrm{N}}\right)}^2+{\left({z}_q^{\mathrm{P}}-{z}_{j_k}^{\mathrm{N}}\right)}^2\right]}^{3/2}} $$

(A4d)

In practice, the average apparent resistivity is assumed as reference uniform resistivity $\widehat{\rho}$. Hence, η(P _q ) which is a number between −1 and +1, is interpreted as an occurrence probability measure of a resistivity deviation from $\widehat{\rho}$ at P _q Positive or negative values Of η(P _q ) give the occurrence probability of an increase or a decrease of resistivity, respectively.

Many field cases were dealt with using this approach, including the Italian volcanic areas of Mt. Etna and Mt. Vesuvius (Mauriello et al. 2004; Mauriello and Patella 2008a, b). In all cases, the mapping of η(P _q ) proved to be a reliable tool for outlining geometry and location of the source bodies, compatibly with the available data set.

Using Eq. A1, no information can, however, be deducted as to the real resistivity values of the structures, geometrically defined by the analysis of the probability index η(P _q ). Just to find a solution to this last problem that the PERTI method has been proposed. The basic principle for the PERTI method is that the reference resistivity $\widehat{\rho}$ must not be pre-assigned, but assumed to be the unknown true resistivity value ρ _q at P _q . With such an assumption, η(P _q ) given in Eq.A1 can be rewritten as

$$ \eta \left({\mathrm{P}}_q\right)={\mathrm{C}}_q{\displaystyle {\sum}_{\mathrm{k}=1}^K{\displaystyle {\sum}_{j_k=1}^{J_k}\left[{\rho}_a\left({\mathrm{P}}_{jk}\right)-{\rho}_q\right]\psi \left({\mathrm{P}}_{jk},{\rho}_q\right)}} $$

(A5)

The rationale for the PERTI approach is that if η(P _q ) = 0 resulted at P _q , then the most probable resistivity would be there exactly ρ _q . Since it is always C _q  ≠ 0, the η(P _q ) = 0 condition allows the following inversion formula to be derived (Mauriello and Patella 2009)

$$ {\rho}_q=\frac{{\displaystyle {\sum}_{\mathrm{k}=1}^K{\displaystyle {\sum}_{j_k=1}^{J_k}{\rho}_a\left({\mathrm{P}}_{j_k}\right)\psi \left({\mathrm{P}}_{j_k},{\mathrm{P}}_q\right)}}}{{\displaystyle {\sum}_{\mathrm{k}=1}^K{\displaystyle {\sum}_{j_k=1}^{J_k}\psi \left({\mathrm{P}}_{j_k},{\mathrm{P}}_q\right)}}} $$

(A6)

The most probable real resistivity ρ _q at P _q , compatibly with data accuracy and density and within the assumed first order Born approximation, is simply derived as the weighted average of the apparent resistivity values, using as weights the sensitivity function of the array. Thus, the PERTI formula of Eq. A3 can easily be converted into a user-friendly algorithm, quite apt to combine a great multiplicity of large datasets.

The main features of the PERTI method, derived from many simulations and field tests (Mauriello and Patella 2009; Cozzolino et al. 2012, 2014), are: (i) independence from a priori information; (ii) absence of iterative processes; (iii) drastic reduction of computing time with respect to standard deterministic inversion tools, like RES3DINV and ERTlab, which may require extremely long time of several hours, compared with the few ten seconds of the PERTI software, to elaborate a set of several thousands data points on a conventional 1 GB RAM PC (Cozzolino et al. 2014); (iv) independence from data acquisition techniques and spatial regularity, unlike the above mentioned commercial softwares, which are designed to invert data collected with a rectangular grid of electrodes.

A direct consequence of not requiring a priori information and iterative processes is, for the PERTI method, the uselessness of the computation of the RMS error between measured and modelled apparent resistivity values. The RMS error, whatever is, cannot be lowered in any way within the PERTI theory. Nonetheless, the same tests have shown PERTI modelling results quite comparable with those from the mentioned commercial softwares (Mauriello and Patella 2009; Cozzolino et al. 2012, 2014).