The Statistical Fingerprint of Fluid-Injection Operations on Microseismic Activity at the Val d’Agri Oil Field (Southern Italy)

Abstract

In this paper, we examined the dynamical properties of the fluid-injection microseismicity at the Val d’Agri oil field (southern Italy) by applying different statistical methods to find correlations and common periodicities with injection parameters, such as injected volumes and injection pressure. Two periods of observation were analyzed: (1) from 2006 to 2015 (the first 10 years after the beginning of injection operations), the seismicity was recorded by the seismic network of the ENI company that manages the exploitation of the oilfield; (2) from 2016 to 2018, the seismicity was recorded by a denser seismic network capable of significantly reducing the completeness magnitude. If a significant correlation between seismicity and fluid-injection variables was found in the first period, in the second period, the seismic activity and injection variables were characterized by common periodicities after the reservoir acidification and for injection rates above 1900 m³/day. Finally, we applied and compared two different approaches proposed in the literature to forecast the maximum expected magnitude. The results showed that one of the approaches yielded an estimated maximum magnitude of M_max = 1.7 ± 0.4, which is consistent with the maximum observed magnitude.

1. Introduction

It has been widely acknowledged for several decades that the exploitation of energy resources through underground fluid injection or withdrawal may cause seismicity [1,2,3]. Although microearthquake activity is typically observed at the majority of injection sites, when pore fluid pressures or pre-existing stress conditions reach a significant level over a wide fault area, the probability of larger earthquakes increases [4]. Examples of large earthquakes induced by fluid injections are the 1967 Mw 4.8 earthquake that occurred in Rocky Mountain Arsenal, Colorado [1], and the 2011 Mw 5.7 and 2016 Mw 5.8 earthquakes in Oklahoma [5].

In some cases, the onset of seismicity can occur within days or weeks after injection [6,7,8], while in others, seismicity increases only after months or years of active injection [9,10]. Furthermore, the occurrence of natural seismicity coincidentally near an injection well or any other human activity, and in contrast, the occurrence of induced earthquakes in areas that have experienced natural earthquakes in the past, highlights the actual difficulty in identifying whether a particular earthquake occurred naturally or was promoted by anthropogenic activities.

The challenge of discerning whether human activity caused earthquakes has been addressed by several researchers in recent years. Some of them focused on providing qualitative commonly accepted discrimination criteria (e.g., [11]), while others proposed different quantitative probabilistic [12,13] or physics-based [5] forecasting approaches.

Generally, induced seismicity poses a range of issues due to its strong socioeconomic impact; thus, most of the research projects in this field are funded by national and international institutions or companies to develop guidelines and operational strategies to manage and mitigate the risks associated with induced seismicity [14]. On the other hand, induced events offer a unique opportunity to study the fault processes at time scales ranging from hours to years and to understand how a small known perturbation (i.e., the anthropogenic perturbation) may affect the stability of faults over time. Some of these processes can be seen from features of spatiotemporal dynamics of the induced microseismicity [15,16]. The increase in recent years of well-designed microseismic monitoring networks and the development of more efficient and robust tools [17,18,19] and automated procedures [20,21] for processing increasingly large data volumes has allowed the investigation of the statistical properties of earthquakes due to the availability of huge datasets of weak events, even of negative magnitudes.

In this paper, we investigate the statistical fingerprint on seismicity induced by fluid-injection operations at the Costa Molina 2 well in the Val d’Agri oil field in southern Italy. We applied different statistical analyses: (1) to find correlations and common periodicities between seismicity and fluid-injection parameters (injected volumes and injection pressures), (2) to quantitatively estimate the probability of changes in seismicity rates after the beginning of injection (2 June 2006) and the acidification treatment of the reservoir (17 September 2017), (3) to obtain information regarding the mechanical state of rocks and the physical properties of the reservoir, and (4) to estimate of the expected maximum magnitude of injection-induced earthquakes. The results obtained by these statistical analyses can also be used as a valuable tool for managing injection operations not only in the Val d’Agri oil field but worldwide.

2. Materials and Methods

2.1. Study Area, Fluid-Injection Operations, and Seismicity Data

The study area is situated in the southeast portion of the High Agri Valley (hereafter referred to as HAV), a Quaternary intermontane basin of the Southern Apennines in southern Italy that trends NW–SE (Figure 1a). The HAV accommodates the Val d’Agri oil field, which is the largest onshore oil field in western Europe, producing an average of roughly 3.6 × 10⁹ kg of oil and 9.6 × 10⁸ m³ of gas per year [8]. On 2 June 2006, the wastewater (saline formation water) coproduced during oil and gas field exploitation began to be disposed by injection through the Costa Molina 2 (CM2) well drilled in the southern marginal zone of the hydrocarbon reservoir. The disposal operations have been conducted with non-uniform injection rates and well-head pressures [8,22,23,24], including three stops after 2016 (Figure 1b).

To monitor the seismic activity in the valley, in July 2001, a local seismic network consisting of 13 stations (yellow triangles in Figure 1a) was established in the area by Eni S.p.A. company, which operates the oilfield. On 25 October 2011, two additional stations (FORE and GRUE) were installed by the Eni company. At the end of 2016, a dense seismic network of 8 shallow borehole broadband stations (INSIEME network [25,26]) was installed in the HAV for scientific purposed during the SIR-MIUR INSIEME project, with the primary objective of analyzing with greater detail the anthropogenic seismicity clusters linked to the exploitation of local georesources (Figure 1a).

On these grounds, the present research study focuses on the identification of the statistical fingerprint of fluid-injection operations on microseismic activity observed close to the CM2 injection well by applying several statistical methodologies, described in detail in the following sub-sections, on two different seismic datasets:

• Seismic dataset obtained from data acquired by the ENI local seismic network from 2006 to 2015 (green circles in Figure 1c; dataset1.csv file in the Supplementary Materials);
• Seismic dataset obtained from data acquired by the INSIEME seismic network from 2016 to 2018 (red circles in Figure 1c; dataset2.csv file in the Supplementary Materials).

Both the datasets report absolute locations of events belonging to the CM2 seismicity cluster using the 3-D Vp and Vs velocity models of the study area [27], but without stressing on the application of high-accuracy location methodologies since high-precision earthquake locations are not necessary for the objectives of this work. Local magnitudes Ml of events have been obtained using the magnitude scale proposed by [28] for the Southern Apennines, then the moment magnitude Mw has been estimated from local magnitude using the relationship proposed by [29]. Finally, the seismic moment Mo has been estimated from Mw using the classical equation from [30].

2.2. Probability of a Change in Seismicity Rate Greater Than a Given Ratio r

Quantitative measures of changes in seismicity rates become particularly important when attempting to detect specific patterns likely linked to variation in stress due to fluid-injection operations. While microseismic events may not pose a significant seismic hazard, their occurrence provides valuable insights into the state of the Earth’s crust at seismogenic depths. Considering seismic catalogs with magnitudes computed in a consistent way and using only events with magnitude above the completeness magnitude Mc, it is possible to estimate the probability of a change in seismicity rate greater than a ratio r after the occurrence of a crucial event, such as the starting or stopping of injection operations, the acidification treatment of the reservoir, or the increase in injection rates and/or pressures over given threshold values. Thus, denoting with λ_b the rate N_b/∆t_b of N_b earthquakes occurring in a time interval ∆t_b before the crucial event and with λ_a the rate N_a/∆t_a of N_a earthquakes occurring in a time interval ∆t_a after that event (subscripts a and b indicate after and before, respectively), such probability can be computed using the following equation [31,32]:

$$P\left(\frac{{\lambda }_a}{{\lambda }_b}>r\right)=1-\frac{1}{N_a!N_b!}{\int }_0^{\infty }{e}^{-x} x^{N_b}\mathsf{\Gamma }\left(N_a+1, rx\frac{\mathsf{\Delta }{t}_a}{∆t_b}\right)dx,$$

(1)

where $\mathsf{\Gamma }\left(n,x\right)={\int }_0^x{e}^{-t}{t}^{n-1}dt$ is the incomplete Gamma function.

2.3. The Lomb Periodogram

The Lomb periodogram is the estimate of the power spectrum of time series that are sampled with an uneven sampling time, like those with gaps [33]. The Lomb periodogram of a series {(t_k, x_k), for k = 1, …, N} is defined by the following equations:

$$P_{LS}(f)=\frac{1}{2{\sigma }^2}\left\{\frac{{\left[{\sum }_{k=1}^N\left(x_k-\overline{x}\right)\mathit{cos}\left(2\pi f\left(t_k-\tau \right)\right)\right]}^2}{{\sum }_{k=1}^N{\mathit{cos}}^2\left(2\pi f\left(t_k-\tau \right)\right)}+\frac{{\left[{\sum }_{k=1}^N\left(x_k-\overline{x}\right)\mathit{sin}\left(2\pi f\left(t_k-\tau \right)\right)\right]}^2}{{\sum }_{k=1}^N{\mathit{sin}}^2\left(2\pi f\left(t_k-\tau \right)\right)}\right\},$$

(2)

where

$$\overline{x}=\frac{1}{N}\sum _{k=1}^N{x}_k$$

and

$${\sigma }^2=\frac{1}{N-1}\sum _{k=1}^N{\left(x_k-\overline{x}\right)}^2$$

are, respectively, the mean and variance of x_k.

The time offset τ is chosen as

$$\mathit{tan}\left(4\pi f\tau \right)=\frac{{\sum }_{k=1}^N\mathit{sin}\left(4\pi f\tau \right)}{{\sum }_{k=1}^N\mathit{cos}\left(4\pi f\tau \right)}$$

The peak in the Lomb periodogram occurs at the same frequency which minimizes the sum of squares of the residuals of the fit of a sine wave to the data [34]. Since the injection variables (monthly mean pressure and monthly injection energy) are affected by gaps, we used the Lomb periodogram for calculating their power spectrum (we used the Matlab built-in function plomb, https://it.mathworks.com/help/signal/ref/plomb.html (accessed on 5 May 2023)).

2.4. The Schuster’s Spectrum

The Schuster’s spectrum is a method to identify significant frequencies or periodicities in a point process. If the probability of the times of occurrence of the earthquakes varies sinusoidally with the period T, for each time of occurrence t_k, we can define a phase θ_k = (2πt_k)/T, and thus the series of N times of occurrence can be converted in a unit-length step 2-dimensional walk changing its direction with θ_k. If D is the distance between the two end-points of this walk, the probability p that a distance larger than or equal to D can be reached by a uniformly distributed random 2-dimensional walk is the probability that the times of occurrence t_k are randomly drawn by a uniform seismicity rate. This probability is called Schuster’s p-value and is given by:

$$p=e^{-\frac{D^2}{N}}.$$

(3)

The probability of a periodicity at period T increases with the decrease in the Schuster’s p-value. Indicating as T_min and T_max the smallest and the largest period to be tested, the number M of Schuster’s tests is given by [35]:

$$M=\frac{t}{\epsilon }\left(\frac{1}{T_{min}}-\frac{1}{T_{max}}\right)$$

where, usually, ε = 1. As demonstrated in [35], a periodicity T is not obtained by chance if its Schuster’s p-value is significantly lower than T/t.

2.5. The Seismogenic Index

The seismogenic index ∑ serves as a valuable measure of potential seismicity caused by fluid injections, which reflects how rocks respond to the injection of fluids within a specific location [36]. The parameter was first introduced by Shapiro et al. [37] and is derived from poroelasticity assuming a model of independent point-source earthquakes activated by an increase in pore-fluid pressure over time (while considering non-decreasing fluid-injection rates). As the index grows larger, the likelihood of significant magnitudes increases. Due to several unknown parameters, the theoretical calculation of ∑ can be challenging. However, it can be estimated from the injected cumulative volume Q_c(t) at time t, the expected number N_≥M of events with magnitudes greater than M, and the b-value of the Gutenberg–Richter law, as expressed in the following equation ([38] and references therein):

$$\Sigma =\log N_{\ge M}-\log Q_c\left(t\right)+bM,$$

(4)

where log ≡ log₁₀ everywhere in this paper.

2.6. Expected Maximum Magnitude of Injection-Induced Earthquakes

Different methods have been suggested to predict the potential maximum magnitude of an earthquake caused by fluid injection in a specific region [39]. Some of them (e.g., [40]) encompass a geometric method that takes into account the dimension of the stimulated volume, but the accurate estimation of the volume needs very accurate locations with significantly smaller location errors compared to the estimated dimensions of the volume. Here, we investigate the capability of estimating the maximum plausible magnitude by two methods that do not require any information of the stimulated volume.

The first one is the simple formula developed by McGarr [41] that expresses the maximum expected seismic moment M_O(max) in terms of the shear modulus of the medium μ (typically assumed to be about 30 GPa) and the net injected fluid volume (ΔV ≡ Q_c) as follows:

M_O(max) = μ ΔV,

(5)

The second one is the equation derived by van der Elst et al. [42] for the most probable maximum magnitude for injection-induced seismicity:

$$M_{max}=\frac{1}{b}\left(\Sigma +\log Q_c\left(t\right)\right),$$

(6)

where ∑ is the seismogenic index, b is the b-value, and Q_c(t) is the injected cumulative volume at time t.

3. Results

3.1. Completeness Magnitude and b-Value Estimate for the 2006–2015 and the 2016–2018 Fluid-Induced Seismicity at CM2

For both the seismic datasets (2006–2015 and 2016–2018) we first built the cumulative and noncumulative frequency-magnitude distributions by considering equal bins of size 0.1 magnitude units. We estimated the completeness magnitude Mc for each dataset using the maximum curvature method [43] on the noncumulative distribution; then, we estimated the b-value and its standard error using the maximum likelihood method [44]. We estimated Mc and b for both local magnitude Ml and moment magnitude Mw distributions. The results are reported in

Table 1. Estimated completeness magnitude Mc and b-value for the two investigated periods.

Period	Using Ml		Using Mw
	Mc	b-Value	Mc	b-Value
2006–2015	1.0 ± 0.1	1.38 ± 0.13	1.3 ± 0.1	1.70 ± 0.11
2016–2018	−0.5 ± 0.1	1.33 ± 0.11	0.1 ± 0.1	1.34 ± 0.08

.

3.2. Statistical Results for the 2006–2015 Seismicity

The first question to be answered is whether the area close to the CM2 injection well really experienced an increase in seismicity rate after the beginning of injection operations. This can be estimated by computing the probability of a change in seismicity rate greater than a ratio r using Equation (1).

Table 2. List of earthquakes recorded by the ENI seismic network before injection with epicenters located within 7 km from the CM2 injection well.

Date	Time	Lat °N	Lon °E	Z (km)	Ml	Mw
6 February 2002	04:14:53.48	40.3457	15.9292	5.84	1.10	1.47
1 March 2003	02:13:43.17	40.2855	15.9518	9.81	1.40	1.70
27 June 2003	12:37:16.30	40.3073	16.0318	5.18	1.30	1.62
29 June 2003	05:17:41.69	40.3045	16.0327	5.42	0.40 *	0.96 *
30 September 2003	07:44:36.06	40.3412	15.9307	10.97	1.20	1.55
30 September 2003	09:20:11.16	40.3445	15.9277	11.14	1.60	1.84
13 February 2004	21:10:34.47	40.3265	16.0033	11.97	1.70	1.92
16 February 2004	01:47:01.38	40.3275	15.9982	11.30	0.80 *	1.25 *
2 July 2004	04:44:30.78	40.3237	16.0195	4.10	1.20	1.55
18 March 2006	00:45:44.91	40.2947	16.0050	8.53	0.80 *	1.25 *
2 June 2006	05:42:43.04	40.2630	15.9885	7.66	1.00	1.40

* Magnitudes below the correspondent completeness magnitudes reported in Table 1.

compiles all the seismic events recorded by the ENI seismic network prior to injection, starting from 2002, with epicenters within 7 km distance from the CM2 injection well. Independently of using Ml or Mw, the number of events in Table 2 with a magnitude above the completeness magnitude was eight; then, we compared the earthquake rates before and after the injection and evaluated the probabilities for an increase in seismicity rate after 1 week, 1 month, 3 months, 1 year, and 6.5 years. We obtained a probability of nearly 100% for a change in seismicity rate greater than 100 until one year after the start of injection. Furthermore, the probabilities that 6.5 years after the injection the rate of earthquakes is at least three, five, and six times greater than the rate of earthquakes before are 99%, 83%, and 66%, respectively.

In light of the varying injection rates and well-head pressures observed during disposal operations (Figure 1b), especially between 2006 and 2015, we focused on identifying any recurring patterns between the time series of seismic activity (monthly counts of events N_eqk and monthly cumulative seismic moment M_Ocum) and fluid-injection parameters (monthly cumulative injected volume V_cum, monthly maximum injected volume V_max, monthly average injected pressure P_ave, and monthly maximum injected pressure P_max). Since the fluid-injection parameters were unevenly recorded, we applied the Lomb periodogram (Equation (2)), to compute the power spectrum of all the investigated time series. The comparison between the log–log Lomb periodograms of the four injection parameters (V_cum, V_max, P_ave, and P_max) with that of the monthly counts of events N_eqk is displayed in Figure 2, while with that of the monthly cumulative seismic moment M_Ocum is displayed in Figure 3.

Common periodicities between the monthly counts and the injection parameters, especially M_Ocum and V_cum, are rather clearly visible; however, to quantitatively assess the overall similarity among the spectra, we calculated the correlation coefficient between the Lomb spectra of N_eqk and M_Ocum and each one of the four injection parameters. The results are reported in

Table 3. Correlation coefficients between the Lomb spectra of seismic activity variables and the Lomb spectra of injection parameters from 2006 to 2015.

Period 2006–2015	Vcum	Vmax	Pave	Pmax
Neqk	0.55	0.56	0.49	0.51
MOcum	0.67	0.67	0.62	0.56

. Notably, there is a higher correlation between the spectrum of the volumes and that of both the number of events and the cumulative seismic moment during the period of 2006–2015.

The non-decreasing rate on average of fluid injections at least until the end of 2012 (cyan line in Figure 1b) allowed us to confidently estimate the seismogenic index ∑ from 2006 to 2012 using Equation (4). The obtained estimate is ∑ = −1.9 ± 0.4. We will quantitatively compare the obtained result with the estimates of the seismogenic index for other worldwide fluid-injection case studies in Section 4 along with its use for the computation of the expected maximum magnitude.

3.3. Statistical Results for the 2016–2018 Seismicity

The second period of observation started after the stop of injections operated from 1 April 2016 to 21 August 2016. In this period, only one event had a local magnitude Ml above 1.0 (see Figure 1b), which is the completeness magnitude for the first dataset. Fortunately, the second dataset benefited from the continuous data recordings from the INSIEME seismic network [26], allowing the seismic catalog to be complete for Ml ≥ −0.5 (Mw ≥ 0.1, see Table 1). The decrease in Mc of more the one point of magnitude allowed us to obtain a seismic dataset (red circles in Figure 1c) large enough to perform statistical analyses also for the 2016–2018 dataset. We used this enriched dataset to evaluate the effects of acidification treatment carried out on 17 September 2017 [22] on earthquake production. Therefore, we applied again Equation (1) to estimate the probability of a change in seismicity rate greater than a given ratio r after the acidification treatment with respect to the one observed before in the 2016–2018 dataset. The probabilities of 99%, 90%, and 68% are obtained for an increase in the seismicity rate greater than 3, 10, and 23, respectively, one day after the reservoir acidification and greater than 13, 20, and 28, respectively, one week after the reservoir acidification. Furthermore, we still obtained a 96% probability of a change in seismicity rate greater than four one year after the acidification treatment.

Also, for the period 2006–2015, we computed the Lomb periodograms of the monthly counts of events N_eqk, the monthly cumulative seismic moment M_Ocum, and the four fluid-injection parameters (V_cum, V_max, P_ave, and P_max). The comparison between the log–log Lomb periodograms are displayed in Figure 4 and Figure 5, then we assessed the overall similarity among spectra by calculating the correlation coefficient. The results are reported in

Table 4. Correlation coefficients between the Lomb spectra of seismic activity variables and the Lomb spectra of injection parameters from 2016 to 2018.

Period 2016–2018	Vcum	Vmax	Pave	Pmax
Neqk	0.22	0.35	0.24	0.45
MOcum	0.17	0.41	0.21	0.49

.

Although the correlation between the Lomb periodograms of seismicity variables and injection parameters is very low, probably due to the increased stability of fluid injections after 2016 (daily injected volumes and injection pressures, Figure 1c), Stabile et al. [22] showed that the seismicity rate and the daily cumulative seismic moment significantly increase for injection rates above 1900 m³/day. Thus, we investigated if earthquake occurrences and injection rates greater than a given threshold value might have been characterized by common periodicities. To this purpose, we applied the Schuster’s spectrum analysis to the series of the earthquake occurrence times and to the series of the occurrence days where the rate of the injected volume is above 1900 m³/day, 2000 m³/day, and 2100 m³/day. For each of the four temporal point processes, we estimated the significant periodicities (at 99% confidence level) through the Schuster’s p-value given by Equation (3).

Finally, we compared the Schuster’s spectrum of the earthquake temporal occurrence (Figure 6a) with that computed for the temporal occurrence of days with injection rates exceeding 1900 m³/day (Figure 6b), 2000 m³/day (Figure 6c), and 2100 m³/day (Figure 6c). Considering the periodicities above 40 days, and assuming that two periodicities of different datasets are mutually consistent for an offset of less than 5 days, we observe that seismicity and injected volumes are characterized by common periodicities.

Table 5. Significant periodicities (days) above 40 days of the earthquake temporal occurrence and of the days where injection rates are greater than 1900 m³/day, 2000 m³/day, and 2100 m³/day. Common periodicities (offset of less than 5 days) are highlighted in bold.

Seismicity	Vinj > 1900 m3/day	Vinj > 2000 m3/day	Vinj > 2100 m3/day
56	-	73	41
84	-	94	54
96	-	109	82
113	135	131	-
169	169	164	-
225	225	219	-
337	-	328	-

reports the significant periodicities found for the four series. In particular, we observe that the lower periodicities in seismicity (56 days and 84 days) are consistent with those of days where injected volumes are above the threshold of 2100 m³/day (54 days and 82 days); the intermediate periodicities (96 days and 113 days) are consistent with those with a threshold of 2000 m³/day (94 days and 109 days); and the higher ones (169 days and 225 days) are consistent with those with a threshold of 1900 m³/day (169 days and 225 days).

4. Discussion and Conclusions

In this paper, we investigated the statistical fingerprint of fluid-injection operations on microseismic activity at the Val d’Agri oil field in southern Italy by applying different statistical methods. We considered two periods of observations. The first one is based on earthquakes recorded by the ENI local seismic network from the beginning of injection in June 2006 to the end of 2015. The second one benefited from continuous data recordings from the denser INSIEME seismic network installed in 2016 [26].

In the period 2006–2015, the seismic network acquired only triggered data; therefore, data cannot be reprocessed to decrease the completeness magnitude (which is 1.0 using Ml and 1.3 using Mw, see Table 1). In any case, the catalog contains a sufficient number of events above the completeness magnitude to investigate how fluid-injection operations at CM2 well affected the seismicity rate with respect to the period before injections (1 January, 2 June 2002, 2006; see Table 2) and how injection parameters are correlated with observed seismicity. We find that the start of injection operations significantly affected the seismicity rate with a probability of nearly 100% for a change in seismicity rate greater than 100 until one year after the start of injection, and still a 99% of probability of a change in seismicity rate greater than three until 6.5 years later. Also, the correlations between the monthly time-series of the seismic activity and of the injection parameters are generally high. Indeed, correlation coefficients between the Lomb periodograms of the seismic activity (monthly counts of events N_eqk and monthly cumulative seismic moment M_Ocum) and of the fluid-injection parameters (monthly cumulative injected volume V_cum, monthly maximum injected volume V_max, monthly average injected pressure P_ave, and monthly maximum injected pressure P_max) are generally above 0.5 (see Table 3). The highest correlations are found between M_Ocum and injection volumes (either V_cum or V_max), confirming that the changes in injection rates over time observed in the period 2006–2015 significantly affect not only the earthquake production close to the CM2 injection well but also their magnitudes. The phenomenon can be attributed to pore pressure diffusion, resulting in a reduction in the effective normal stress on fractures within the reservoir as the pressure increases, consequently promoting their failure.

However, due to the relatively high Mc compared to the magnitudes of recorded microearthquakes (Figure 1c), it is not possible to further investigate temporal patterns of seismicity and changes in the b-value in shorter periods of time. This limitation applies particularly between the first swarm activity that occurred shortly after the beginning of injection operations and the second swarm activity that occurred after September 2010, during which the daily injected volumes reached values up to 3000 m³/day (Figure 1b). From a physical point of view, these injection volumes likely contributed to the occurrence of the largest event (26 October 2010, at 15:54:09 UTC time, Ml = 2.0, Mo = 2.04× 10¹²) in the CM2 seismicity cluster, but we cannot statistically assess this hypothesis as we did for the acidification treatment carried out in September 2017.

The non-decreasing rate on average of fluid injections at least until the end of 2012 (cyan line in Figure 1b) allowed a reliable estimate of the seismogenic index obtaining ∑ = −1.9 ± 0.4. Figure 7, adapted from [38], illustrates a comparison of the seismogenic index calculated at multiple borehole injection sites, including CM2 (violet line n.1 in the figure). In each case, the time periods of the injections align with non-decreasing fluid rates. Figure 7 also shows a reasonable stability of the seismogenic index values at the CM2 injection site as they do not fluctuate as a function of time.

As already discussed in [38], generally, the largest index is obtained for geothermal sites (Cooper Basin, Basel, and Soultz), whereas the lowest index is obtained for shale gas reservoirs in Cotton Valley and Barnett. It is worth noting that for reservoir locations like Soultz and the KTB site, where multiple fluid injections have been conducted, the estimated seismogenic index can vary. This variation can be attributed to the fact that the fluid was injected in different wells and/or at different depths within the reservoir [38]; consequently, the differences observed in the seismogenic index may indicate variations in the characteristics of the fracture systems. Figure 7 shows that the Cotton Valley reservoir also exhibits a significant range of ∑ values across different injection stages. Notably, the highest index is observed during stage B (blue line n. 14 in Figure 7), which can be attributed to the intersection and subsequent opening of natural fractures [38,45]. The same situation may have occurred at the CM2 site, where the high estimated index, comparable to Soultz and the KTB sites (see Figure 7), can be attributed to the activation of the NE-dipping fault mapped by various authors from accurate earthquake locations [8,22,23,24,46,47].

Using Equation (6) derived by van der Elst et al. [42], we estimated the most probable maximum magnitude at the CM2 site, obtaining M_max = 1.7 ± 0.4. This result is consistent with the maximum magnitude observed at the CM2 site, which is Ml = 2.0 (Mw = 2.1). For comparison, we also estimated the maximum expected seismic moment and the corresponding moment magnitude by applying the simple McGarr’s formula given in Equation (5). The predicted magnitudes using the McGarr’s formula are as follows: M_max = 3.2 one week after the start of injections, M_max = 3.6 one month later, M_max = 4.5 one year later, and M_max = 5.3 after 6.5 years. While the McGarr’s formula can be a valuable tool for overseeing the maximum expected magnitude and setting an upper limit for total injected volume before operations begin, it is based on simple assumptions and may yield unrealistic results if any of those assumptions are not met. This is the case at Costa Molina 2, where fluids are injected into the same hydrocarbon reservoir to partially balance the pressure reduction caused by extractions. As a result, the CM2 site is hydraulically connected to the production area, and the net injected volume (ΔV) cannot correspond to the total cumulative injected fluid volume (Q_c). Nonetheless, the McGarr’s formula can still provide an estimation of the maximum expected magnitude if fluid injections were carried out in a different reservoir not hydraulically connected to the Val d’Agri oil field.

The second period of observation, from 2016 to 2018, is characterized by a significant reduction in the seismicity rate and event magnitude (Figure 1c) due to several reasons:

• The NE-dipping fault at the CM2 site has likely released most of the accumulated tectonic stress;
• Fluid-injection operations have been going on for over 10 years, thus the triggering front of seismicity (i.e., the relaxation zone of the pore pressure) has already diffused throughout the poroelastic medium;
• Both the average injection rates (blue line in Figure 1b) and the average injection pressure (yellow line in Figure 1b) are stable or decreasing;
• The disposal operations are carried out with less varying daily injected volumes (blue dots in Figure 1b) and daily injection pressures (yellow dots in Figure 1b) with respect to the precedent period.

If during this period there were only earthquake data from the ENI seismic network, we would not be able to perform a statistical analysis due to the lack of a sufficient number of earthquake observations. By utilizing the enriched dataset published in [22], we were able to overcome this potential issue and conduct statistical analyses for the period 2016–2018 as well.

We obtained a very low correlation among the Lomb periodograms of seismicity variables and injection parameters (Table 4), confirming the increased stability of fluid injections both in terms of daily injected volumes and injection pressures. However, we found significant common periodicities between the microearthquake occurrence and the temporal occurrence of days when the injection rates were greater than 1900 m³/day through the application of the Schuster’s spectrum (Figure 6). More specifically, as the injection threshold increases, the duration of each injected volume dataset becomes shorter due to a lower number of days exceeding the higher thresholds. Consequently, we observe lower periodicities (higher frequencies) in the Schuster’s spectrum for V_inj > 2100 m³/day (Figure 6b) compared to V_inj > 2000 m³/day (Figure 6c), which, in turn, are lower compared to V_inj > 1900 m³/day (Figure 6d). These periodicities are also significant in the Schuster’s spectrum computed for the temporal occurrence of earthquakes (Figure 6a). Given that the periodicities of seismicity decrease as the injection rate threshold increases (Table 5), we can assert that the increase in daily injection rate significantly affects microearthquake production by increasing the seismicity rate and temporal clustering of events.

Considering that on 17 September 2017, the Eni company carried out the acidification treatment of the reservoir, we also estimated the probability of a change in seismicity rate greater than a given ratio r after this operation. We obtained a probability of 99% that the seismicity rate increases three times the day after the reservoir acidification and 13 times after one week. A 96% probability of a change in seismicity rate greater than four is still estimated after one year. This result combined with those from the Schuster’s spectrum provide a robust statistical confirmation of the hypothesis given in [22] that the 2016–2018 fluid-induced microseismicity is mainly activated after acidification operations and for injection rates above 1900 m³/day.

Concluding, this work demonstrates how statistical analyses conducted on sufficiently rich datasets enable the investigation of the impact of fluid-injection operations on microseismic activity at a specific site. They also provide insights into the underlying physical mechanisms governing induced seismicity and assist operators in effectively managing injection operations from their early stages.