The study area of the northwestern (NW) Dinarides lies at the northeastern (NE) corner of the Adriatic microplate and is bounded by the Southern Alps to the north, the Pannonian basin to the east, and the Adriatic foreland to the west, thus representing an important junction between these units (Fig. 1). The evolution of the Dinarides is tied to the ongoing collision between the Eurasian plate (Eurasia) and the Adriatic microplate (Adria), which began in the late Cretaceous (Tari, 2002; Handy et al., 2010; Ustaszewski et al., 2010; Handy et al., 2015).

The first 3-D compressional (P) wave velocity model in this area was obtained with local earthquake tomography (LET) study done by Michelini et al. (1998). It revealed two areas of distinct high and low velocities in western and eastern Slovenia, which were interpreted as the upper-crustal expression of the ongoing convergence between the Adria and the Eurasia. The authors also proposed a relocation study using the 3-D velocity model to map active faults and trends in seismicity. This was partly realized by a study that focused on the Idrija fault system in western Slovenia (Vičič et al., 2019). Its authors were able to constrain the geometry of each fault by relocating seismicity with the regional 3-D shear (S)-wave velocity model of Guidarelli el al. (2017) and a constant P-wave to S-wave velocity ratio (vP/vS). The model of Guidarelli et al. (2017) was obtained with ambient seismic noise tomography and shows distinct lateral change in the crustal structure under western Slovenia. This was interpreted as a transformation from a uniform to a more variable crustal structure across the bounding strike-slip Idrija fault, indicating the transition between the Dinarides and Pannonian basin units. Recently, Kapuralić et al. (2019) computed a 3-D P-wave velocity model from LET and used these results to constrain the relationship between the crust and uppermost mantle at the junction between the Dinarides and the Pannonian basin. Their findings show significant changes in the crustal structure at the transition zone between the NW Dinarides and the Pannonian basin and map several zones of higher seismic velocity in the NW Dinarides crust. As opposed to the model of Guidarelli et al. (2017), this 3-D velocity model shows no obvious crustal signature of the dividing Idrija fault. The 3-D velocity models of Bressan et al. (2012) provided insights into the upper-crustal structure of NE Italy and cover the NW corner of our study area. The models show strong variations in P-wave velocity and vP/vS related to lithological heterogeneities and variable degree of fracturing caused by several different tectonic phases. The surface wave dispersion study in Slovenia by Živčić et al. (2000) showed a 4–6 km thick layer with S-wave velocities between 2.75 and 3.00 km s-1 above a 7–9 km thick layer with S-wave velocities between 3.00 and 3.30 km s-1. The velocity of the underlying layer was found to be lower in eastern Slovenia. Their results also suggest comparatively high velocities in deeper parts of the upper crust in western Slovenia. The most recent 3-D model of the region was constructed by Magrin and Rossi (2020) by critically selecting and integrating all available information on the depth of the primary interfaces and the physical properties of the crust. Using this model, they were able to tie the spatial distribution of the seismicity in the northern part of the Adria to the sharp changes in various physical parameters in the crust. Active seismic investigations of Brückl et al. (2007) and Šumanovac et al. (2009) provided important insights into the crustal structure along profiles crossing the Alps and Dinarides, constraining P-wave velocities and the depth of the Mohorovičić discontinuity (Moho). Direct comparison between P- and S-wave velocity models should be done with care due to the highly variable average vP/vS values in the region (Behm, 2009; Stipčević et al., 2020). The latest receiver functions study applied to the Dinarides and the surrounding area (Stipčević et al., 2020) showed the transition from the thick Dinaric crust to the thinner Pannonian crust and indicated that the earthquake depths generally follow the crustal thickness.

Despite the numerous investigations that completely or partially covered the study area, the details of the upper-crustal structure remained unresolved. Moreover, the 3-D velocity models covering the study area show markedly different and rapid lateral velocity variations in the upper crust. For these reasons, there is still a need for a detailed, small-scale study focusing mainly on the upper, brittle part of the crust. Therefore, our goal is to investigate the velocity structure of the crust using the concept of a minimum one-dimensional (1-D) velocity model. The minimum 1-D velocity model is computed by simultaneous inversion for hypocenter and velocity parameters (coupled hypocenter–velocity problem) and represents the best fit to the observed travel time data in the least-squares sense. This iterative approach is necessary because of the strong coupling between hypocenter and velocity parameters (Kissling, 1988; Kissling et al., 1994). If obtained properly, the minimum 1-D velocity model can be used to calculate accurate earthquake locations (e.g., Husen et al., 1999) and detect systematic errors in travel time data (e.g., Maurer et al., 2010), especially when computed at a smaller scale (Husen et al., 2011). Station delays computed as part of the minimum 1-D velocity model allow identification of major geological and tectonic features or trends. The minimum 1-D velocity model is also essential for 3-D velocity modeling in LET, where it is commonly used as an initial model in inversion (e.g., Kissling, 1988; Kissling et al., 1994; Haslinger et al., 1999; Diehl et al., 2009). Using a minimum 1-D velocity model as the initial model in LET can greatly reduce inversion artifacts in a final 3-D velocity model and improve error estimates (Kissling et al., 1994).

Most of the seismicity in the study area has been located with the synthetic 1-D velocity model (routinely used 1-D velocity model, R1D from now on) aggregated mainly from the results of Michelini et al. (1998) and Živčić et al. (2000). Compared to today's situation, the results of these studies were obtained with a relatively small amount of data. Seismic station coverage in the area improved significantly with the gradual modernization of the Seismic network of the Republic of Slovenia (SNRS) between 2001 and 2008 (Vidrih et al., 2006; Jesenko and Živčić, 2018) and the deployment of additional seismic stations in Croatia within the VELEBIT project (2015–2019), and during 2015 and 2016 as part of the AlpArray project (Molinari et al., 2016). With better station coverage and smaller epicentral distances, we are now able to sample the upper-crustal structure more densely, and therefore we can calculate more accurate upper-crustal velocity models. Furthermore, studying spatial distribution of the relocated seismicity allows us to put additional constraints on the crustal structure and the processes driving the seismicity itself.

The tectonic evolution of the study area is closely related to the dynamics of the Adria (e.g., Anderson and Jackson, 1987). The subduction processes associated with the closure of the Neotethys ocean started in the Jurassic (Pamić et al., 1998; Tari, 2002; Schmid et al., 2008) and led to the continental collision between Adria, which at that time detached from the African plate (Schmid et al., 2008), and Eurasia in the late Cretaceous (Tari, 2002; Handy et al., 2010; Ustaszewski et al., 2010; Handy et al., 2015). The collisional processes that occurred along the northern (e.g., Kissling et al., 2006) and western (e.g., Vignaroli et al., 2008) margins of the Adria gave rise to the Alps and the Apennines, respectively. Along the eastern margin, the collisional process started after the oceanic part of the Adria was consumed in the subduction, leading to the formation of the thrust sheets and the ophiolitic units of the Neotethys (Schmid et al., 2008). The subduction ceased in the early Paleogene (Pamić et al., 1998; Schmid et al., 2008), and the deformation front began to migrate southwestward (Tari, 2002; Korbar, 2009; Ustaszewski et al., 2010; Handy et al., 2015). The peak of still-ongoing deformation lasted until the early Oligocene and was expressed by the foreland-directed thrusting (Pamić et al., 1998; Tari, 2002; Schmid et al., 2008; Placer et al., 2010), which strongly deformed the upper parts of the Adria crust (Schmid et al., 2008; Korbar, 2009). At the same time, the continental part of the Adria began to underthrust the Dinarides (Tari, 2002; Placer et al., 2010). In addition, the movement of the Adria was responsible for the late Oligocene–Miocene south-verging thrusting in the Southern Alps (Schmid et al., 2004; Handy et al., 2010, 2015) and the lateral extrusion of the Eastern Alps along the ENE–WSW-striking Periadriatic fault, which separates the Southern Alps from the Eastern Alps (Fodor et al., 1998). An important factor in the process of lateral extrusion of the Eastern Alps was the extension of the area behind the retreating subduction zone in the Carpathians (Ratschbacher, 1991a, b; Horváth and Cloetingh, 1996), which led to rifting and subsidence, resulting in the formation of the Pannonian basin (Fodor et al., 1998). In the late Miocene to early Pliocene (Márton et al., 2003; Márton, 2006), a sustained counterclockwise rotation of the Adria began (Anderson and Jackson, 1987; Battaglia et al., 2004; Grenerczy et al., 2005; Weber et al., 2010), and the end of subduction in the Carpathians (Horváth and Cloetingh, 1996) led to transpressive reactivation of the former extensional structures in the Pannonian basin (Horváth and Cloetingh, 1996; Fodor et al., 1998, 1999; Tari, 2002; Grenerczy et al., 2005; Ustaszewski et al., 2010) and to transpressive to purely strike-slip deformation along the zone of steep, NW–SE-striking faults in the Dinarides and the Southern Alps (Picha, 2002; Placer et al., 2010; Vičič et al., 2019). Currently, shortening in the area is more strongly absorbed on the southern front of the Eastern Alps in the area of the Sava fault, with movement increasingly turning eastwards towards the Pannonian basin (Métois et al., 2015).

Crustal thickness in the NW Dinarides has recently been constrained by many different studies (Brückl et al., 2007; Behm et al., 2007; Šumanovac et al., 2009; Stipčević et al., 2011; Guidarelli et al., 2017; Kapuralić et al., 2019; Stipčević et al., 2020). It varies from about 38 to 45 km under the External Dinarides, slightly thickening towards the Alps and thinning to about 30 km in the Adriatic foreland and 25 km in the Pannonian basin. A similar pattern was observed for the lithosphere thickness in the same area (Belinić et al., 2018). The underthrusting of the Adria resulted in two-layered thickened crust in the External Dinarides. The thinner crust in the Adriatic foreland is associated with the undeformed parts of the Adria. The extension in the late Oligocene and early Miocene, which caused crustal thinning in the Pannonian basin, is most likely responsible for relatively low P-wave seismic velocities in the upper and middle crust under the transition zone from the Southern Alps and the Dinarides to the Pannonian basin. The thinned crust in contact with the Adria in this transition zone belongs to the Pannonian fragment. The junction between these two units appears as a 10 km jump in Moho depth, probably as a result of the crustal thinning (Brückl et al., 2007, 2010).

Throughout the study area the seismicity is mostly constrained to the upper crust (Herak et al., 1996; Gosar et al., 2021). Several strong historical and instrumentally recorded earthquakes occurred in this region. The strongest historical earthquake with estimated magnitude of about Mw=6.8 and a maximum estimated intensity of X European macroseismic scale (EMS-98) occurred in 1511 CE on the Idrija fault in western Slovenia (Vidrih and Ribičič, 2004; Fitzko et al., 2005; Cecić and Jocif, 2011). The Rijeka region was hit by four damaging earthquakes between 1750 and 1904 CE with maximum intensity estimates from VI to VIII Medvedev–Sponheuer–Karnik (MSK) scale (Herak et al., 2017, 2018). The strongest historical earthquake near Zagreb occurred in 1880 CE with a maximum intensity of VIII Mercalli–Cancani–Sieberg (MCS) scale (Herak et al., 1996). Shortly after, two destructive earthquakes occurred in Slovenia. In 1895 CE, an earthquake near Ljubljana (central Slovenia) occurred with Mw 6.0 (VIII–IX EMS-98) (Lapajne, 1989; Tiberi et al., 2018), and in 1917 CE an earthquake with Mw 5.6 (VIII EMS-98) struck the Krško basin (Lapajne, 1989; Cecić et al., 2018). Recently, two strong earthquakes occurred on the Ravne fault in northwestern Slovenia. The first one was in 1998 CE with Mw 5.6 and a maximum intensity of VII–VIII EMS-98 (Zupančič et al., 2001) and was followed by an earthquake with Mw 5.2 (VII EMS-98) on 12 July 2004 (Vidrih and Ribičič, 2004). A review of the seismological, geological, and seismotectonic studies related to both earthquakes was given by Gosar (2019a, b). A detailed LET study with aftershock sequences of these two main events was performed by Bressan et al. (2009), linking the physical properties of the crust along the Ravne fault with the spatial seismicity distribution and different types of focal mechanisms. The most recent damaging events in this area occurred in Croatia near Zagreb (Mw 5.4; Atalić et al., 2021) and Petrinja (Mw 6.4; Tondi et al., 2021) in 2020.

The seismological bulletin of the Slovenian Environment Agency (ARSO), consisting of 7733 local earthquakes with ML of at least 1.0 that occurred between 2004 and 2018 CE, served as a starting point for this study. The earthquakes are routinely analyzed by ARSO and cover the entire territory of Slovenia and its surroundings. Their locations were determined with the HYPOCENTER program (Lienert and Havskov, 1995) using P- and S-arrival times and the routine 1-D velocity model. Mining blasts are removed from the main catalogue and are used as an independent dataset for testing. The arrival time picks (arrivals) in the seismological bulletin were grouped into six uncertainty classes based on the uncertainty intervals subjectively determined by the analysts, as shown in Table S1. In our dataset, the best-estimated first arrivals (classes 0, 1, 2) dominate, and only a small number of arrivals belong to uncertainty classes of 3 and 4. For our study, we only considered the arrivals that belong to uncertainty classes of 0, 1, and 2.

Most earthquakes in the study area are confined to depths between 1.1 and 18.3 km (5th and 95th percentiles). The earthquake with ML 4.9 (Mw 5.2) that occurred on 12 July 2004 (Vidrih and Ribičič, 2004) is the strongest earthquake in our dataset and one of the few that exceeded ML 4.0. Earthquakes of the lowest magnitude considered (ML 1.0) had on average 9 P and 8 S arrivals, which is sufficient for a good location estimate. Moreover, the arrival times of these smaller earthquakes were still reliably picked (uncertainty class ≤2) at maximum average epicentral distance of about 84 km.

The study area is densely populated with seismic stations (Fig. 1). The arrival times were picked mainly at seismic stations of the Seismic Network of the Republic of Slovenia (Slovenian Environment Agency, 2001) together with seismic stations belonging to other seismic networks and temporary seismic arrays in the region (Zentralanstalt für Meteorologie und Geodynamik, 1987; MedNet Project Partner Institutions, 1990; University of Zagreb, 2001; OGS, 2002; INGV Seismological Data Centre, 2006; AlpArray Seismic Network, 2015; OGS, 2016). The Seismic Network of the Republic of Slovenia (SNRS) was gradually modernized between 2001 and 2008 and currently consists of 26 permanent stations (Vidrih et al., 2006; Jesenko and Živčić, 2018). During the last 16 years, many temporary stations have also been in operation in Slovenia. In recent years, some additional seismic stations have been installed as part of the VELEBIT and AlpArray projects (Molinari et al., 2016), filling the gaps between the permanent stations of the Croatian Seismic Network (CR). Some seismic stations located in Austria and Italy were also used to cover the periphery of our study area. The seismic network operating in northeastern Italy is managed by the Italian National Institute of Oceanography and Applied Geophysics (OGS) and is described in detail in Bragato et al. (2021).

Observations of seismic phase arrival times can be used to investigate seismic velocity structure of Earth's interior. Arrival time of a wave (Tij) generated by an earthquake (i) and observed at a station (j) is a nonlinear function of station coordinates (sj), hypocenter parameters (hi), and velocity model parameters (m). This function can be approximated with a Taylor series expansion about the points in a hypocenter and a velocity model solution space (hi0, m0). By only keeping linear terms, we obtain its linearized form 1Tij=Tij0+∑k=14∂Tij∂hkihi0,m0Δhki+∑k=1p∂Tij∂mkhi0,m0Δmk+e, which relates small changes in arrival time to small changes in the hypocenter and the velocity model parameters. The third term is summed over the total number of velocity model parameters (p). The error term (e) contains arrival time errors caused by the approximation and errors in calculated and observed arrival times.

By estimating (predicting) hypocenter and velocity model parameters, we can calculate arrival time (Tij0) of an earthquake phase, and all partial derivatives in Eq. (1). We do this numerically by tracing rays for predicted hypocenter parameters through predicted velocity structure (e.g., Crosson, 1976; Kissling, 1988). The difference between the calculated and observed arrival time can be expressed as an arrival or travel time residual, which is related to the perturbations (corrections) in the hypocenter and velocity model parameters, Δhki and Δmk, respectively. For I earthquakes, all observed at J stations, we obtain a system of N=I×J linear equations, which we solve by minimizing the misfit (residual) to the data with the damped least-squares approach (e.g., Crosson, 1976; Aki et al., 1977; Kissling, 1988). Because we are solving for hypocenter and velocity parameters simultaneously, this inverse problem is known as the coupled hypocenter–velocity problem. Since the system of equations that we are solving is not a true linear system, the hypocenter and velocity model perturbations must be small. Therefore, an initial estimate of the unknown parameters must be sufficiently close to the correct solution and the inversion performed iteratively by adjusting hypocenter and velocity model parameters in each step (Crosson, 1976).

The result of the coupled hypocenter–velocity problem described above is the velocity model (velocities and possibly station delays) and the revised hypocenter parameters. The resulting model minimizes the travel time residuals and is referred to as the minimum 1-D velocity model in the case of the 1-D parameterization. The layer velocities of a 1-D velocity model approximate the average velocity of a 3-D velocity model in the same depth interval. The construction of a minimum 1-D model is a trial-and-error process that requires careful selection of only high-quality data and rigorous evaluation of the results (Kissling et al., 1994).

Throughout the modeling process, many 1-D velocity models were obtained from various initial 1-D velocity models and inversion parameters. We note that in the P-only inversion, the velocity models obtained from the initial models with low and high velocities only partially converged towards the solution obtained with the three initial models derived from the independent studies (R1D; Brückl et al., 2007; Šumanovac et al., 2009) and performed comparatively poorly in the tests. This suggests that it is very difficult to obtain a stable solution when the starting point in the parameter space is relatively far from the true model. For this reason, we used the two best performing models computed in the P-only inversion (MP1, MP2) as initial models for the S-only inversion by multiplying the velocity values by a constant vP/vS value of 1.73. The performance of the computed models was evaluated using the rms residuals, stability tests, and relocations. We also selected the two best-performing models of the S-only inversion (MS1, MS2) and used them, together with the MP1 and MP2 models, as initial models for the combined P and S inversion. For all inversions, the damping value for the velocity parameters was set to 10.0 in the second run, as we obtained better convergence and slightly lower rms residuals. In practice, however, no large difference was observed in well-sampled layers when the value was set to 1.0. Since the velocity of the surface layer in the S-only inversion rapidly dropped to unrealistically low values, we individually damped the velocity in this layer by setting the damping to 10.0 and 50.0. We then decided to use the former value, which still allowed some velocity perturbations in the surface layer. This damping value for the S velocity of the surface layer was also kept in the initial models for the combined P and S inversion. We constructed four initial P and S models. Two where we used the same damping value (10.0) for the P velocity of the surface layer as well and two where the P velocity of the surface layer was left undamped. Since the P- and S-only inversions served as intermediate steps for the combined P and S inversion, we only discuss the results of the latter. Nonetheless, the results of P- and S-only inversions serve as another indicator of how well the velocity is constrained in each layer. The best-performing models of P- (MP1, MP2) and S-only (MS1, MS2) inversions are shown in Fig. S1, along with the final models of the combined P and S inversion and their median velocities.

Using the four initial P and S velocity models, 80 velocity models (final models; Fig. S1) were obtained with different total numbers of iterations in the combined P and S inversion. The P velocities of the final models show very good convergence and are well constrained for layers between 8 and 26 km depth, with a maximum difference between the 15th and 85th percentiles (hereafter referred to as the percentile difference) of 0.10 km s-1 (Figs. 5 and S1, Table S2 in the Supplement). Layers between 0 and 8 km depth show worse convergence, with percentile differences between 0.12 and 0.15 km s-1. At greater depths, between 26 and 34 km, the P velocities diverge the most, with percentile differences of 0.18 and 0.20 km s-1. The S velocities are well constrained for layers between 4 and 26 km depth, with percentile differences of less than 0.09 km s-1 (Figs. 5 and S1, Table S3). In layers between 0 and 2 km and between 30 and 34 km depth, the S velocities converged to a similar extent, with the percentile differences ranging from 0.10 to 0.12 km s-1. Despite some relatively small percentile difference values, we estimate that the P and S velocities are poorly constrained at depths below 34 km because only 9–618 rays sampled the corresponding layers. The final rms residuals for the combined P and S inversion dataset are mostly (85th percentile) below 0.323 s, with the lowest value of about 0.288 s (Fig. S2), and generally show a reduction of up to 13 %–22 % compared to the first iteration. Based on the rms residuals, stability tests, and relocations, we selected a (minimum) 1-D P- and S-velocity model for which we show the detailed results.

One of the goals of this study was to complement the results of previous studies and to expand our knowledge of crustal structure in the region. The seismic ray distribution (Fig. 6) shows that the upper crust is adequately sampled. This was made possible by the modernization of the SNRS (Vidrih et al., 2006; Jesenko and Živčić, 2018) and the deployment of additional seismic stations in Croatia within the VELEBIT and AlpArray projects (Molinari et al., 2016). Considering the results of the stability tests and the convergence of the final regional models (Fig. 5), we estimate that a good solution was obtained for depths between 0 and 26 km. The fact that the layers below 26 km were sampled by a comparatively small number of subvertical rays (Fig. 6), ranging from 9 to 1163 rays, limits the ability of the inversion to resolve the velocity structure of the lower crust in more detail. Nevertheless, the presence of at least 618 rays, the convergence of the final regional models, and the simple velocity structure suggest that at least the average velocity has been resolved for depths between 26 and 38 km.

Several features are observed in the computed regional velocity model. Rather prominent P velocity jumps appear at 8 and below 23 km depth (Fig. 5). Large velocity jumps are observed in the lower crust at the interfaces between 23 and 34 km depth, where the P velocity starts to increase more rapidly. As expected, we do not observe a single sharp increase in velocity that would indicate a clear depth of the Moho discontinuity. Rather, the depth interval of the rapid increase in P velocity suggests a change in crustal structure or highly variable Moho topography. The apparent increase in velocity gradient with depth at interfaces between 23 and 30 km could therefore indicate the transition from upper to lower crust, in agreement with the results of Magrin and Rossi (2020) for the northern Adria, including the NW Dinarides. The transition was interpreted to occur at a P-wave velocity of about 6.4 km s-1. The last and largest jump in P velocity at 34 km depth coincides with the only prominent jump in S velocities below 4 km depth. This is the only feature of the MPS model that could indicate an average Moho depth in the study area and would place it roughly between 34 and 38 km, consistent with previous studies (e.g., Stipčević et al., 2020). The velocity jumps are unlikely to be as pronounced as in reality, as the velocity in each layer approaches the average of the 3-D velocity variations sampled by the rays. Large lateral variations may therefore mask large vertical velocity discontinuities, meaning that some of them were probably not resolved by this method.

P velocities in the E subregion between 0 and 8 km depth are much lower compared to the other two subregions (Fig. 13, Tables S4, S5, and S6) and are related to the presence of deep sedimentary basins at the periphery of the Pannonian basin such as the Krško basin. The reason for the higher P velocities in the NW and SW subregions is most likely the thick cover of carbonate rocks. In the depth range from 8 to 23 km, the P velocities are very similar in all subregions and close to the regional model. The main difference among the subregions in this part of the crust is found between 12 and 18 km, where the SW subregion shows 0.04–0.12 km s-1 higher P velocities. The S velocities of the selected subregional models (Fig. 14, Tables S4, S5, and S6) are very similar in the layers above 6 km depth and diverge considerably below this depth. The E subregion shows the lowest S velocity for the layer starting at 0 km depth and consistently higher S velocities for all other well-resolved layers. The higher S velocities in the E subregion indicate a more compact material, while the lower S velocities in the NW and SW subregions can probably be associated with highly fractured rocks. Furthermore, this also suggests denser volcanic crust in the E subregion, the origin of which can be attributed to the rifting in the Pannonian basin (e.g., Fodor et al., 1998), and less dense thickened crust of continental origin in the NW and SW subregions that formed as a result of the underthrusting of the Adria (e.g., Tari, 2002; Brückl et al., 2010). The largest jump in S velocity occurs at 4 km depth in all subregional models and is also consistent with the regional model. This shallow jump in S velocity indicates a transition from the overlying layers being more saturated with fluids than the underlying layers. A less pronounced, but still significant, jump in S velocity that is apparent in the model for the E subregion at 2 km depth likely indicates a transition from loose to more compacted sediments. In all subregional models, depth intervals of slow velocity increase are observed, ranging from 8 to 10 km. Such features could result from thick homogeneous layers where seismic velocity is mainly controlled by pressure and temperature gradient. The vP/vS values calculated from the P and S velocities of the MPS model and the subregional models (Fig. 15, Tables S4, S5, and S6) are consistently high in the upper 4 km depth. Below this depth, vP/vS values are relatively high until a depth of 16 km, where they begin to decrease for all subregions. Below 4 km depth, vP/vS of the regional model is consistently close to 1.73 and shows no significant variation.

In terms of absolute P velocities, the obtained velocity models show significantly higher velocities above 30 km depth compared to the R1D model (Fig. 16). Only the P velocities of the layer between 2 and 4 km depth obtained for the E subregion are lower compared to the routine model. In comparison with the S velocities of the R1D model, the S velocities computed in this study are lower in the upper 4 km depth and mostly higher in the deeper layers (Fig. 17). We see large differences in velocities between our results and the R1D model, except when compared to the S velocities of the NW and SW subregions. The velocities computed for the subregions in the well-constrained layers between 0 and 23 km depth can also be compared with some other velocity models obtained in previous studies. As already observed by Michelini et al. (1998), we see that P velocities in the upper 6 km differ significantly between western and eastern Slovenia. We also obtained similar P-velocity values in the first 6 km of the crust. The velocities of the deeper crust in the west at 13 and 20 km obtained by Michelini et al. (1998) also agree well with our results, but on the other hand we obtained higher P velocities for the E subregion. The P velocities in the deeper parts of the E subregion seem to be more in agreement with the velocity values determined by Kapuralić et al. (2019). The P velocities extracted from the 3-D model of Magrin and Rossi (2020) at the point near the reference station for our regional inversion (NAC2, 45.83∘ N, 14.86∘ E) agree well with the P velocities of the MPS model in the upper 34 km depth, with some relatively large differences in the depth intervals 4–8 and 18–23 km. The S velocities show large differences in the upper 12 km depth and a very good agreement between 12 and 38 km depth. Compared to the velocities of Magrin and Rossi (2020) at another point of their model (NAC2, 46.05∘ N, 14.28∘ E), we obtained slightly lower P velocities for the NW subregion between 0 and 23 km depth, while the S velocities between 4 and 23 km depth are in very good agreement with their results. In the depth interval between 6 and 23 km depth, the P velocities of the NW subregion are also lower than those obtained by Brückl et al. (2007; ALP01 460 and 520 km), which was expected since this model was also one of the models used for the construction of the NAC2 model (Magrin and Rossi, 2020). The model of Magrin and Rossi (2020, NAC2, 45.51∘ N, 14.35∘ E) also agrees well with the P velocities of the SW subregion in the depth range from 4 to 18 km. The largest differences are above 4 km and between 18 and 23 km depth. This model fits well with our S velocities of the SW subregion between 4 and 14 km depth and shows much higher velocities in other layers up to 23 km depth. The velocities extracted at 300 km along the ALP02 profile of Brückl et al. (2007) do not fit our P velocities for the E subregion very well. Only the depth interval between 6 and 18 km depth shows moderate agreement with our values. The discrepancy above 6 km depth seems to be due to the fact that the velocities were extracted at a single point along the ALP02 profile, which shows large lateral velocity variations in these layers. The same is true for the other two subregions. The S velocities determined by Živčić et al. (2000) agree well with the velocities between 16 and 23 km depth for the E subregion, between 12 and 23 km for the NW subregion, and between 12 and 23 km depth for the SW subregion. However, the relatively high S velocities of the E subregion compared to the NW subregion are not consistent with their results. The model of Šumanovac et al. (2009) shows large discrepancies with our results, with higher P velocities in the depth intervals 18–23 and 16–23 km for the E and SW subregions, respectively.

The pattern of computed P-wave station delays (Fig. 7) agrees very well with the map of sediment delay times compiled by Behm (2009). The only station delays that do not agree with the sediment delay times belong to the seismic stations on the Istra peninsula. These positive station delays could be related to the relatively low velocities at shallow depths observed in the velocity models of Guidarelli et al. (2017) and Kapuralić et al. (2019) or to large-scale variations in the crust due to the limited azimuthal coverage of the observations. The travel times calculated for the southernmost three stations correspond mostly to the rays refracted at 40 km depth and above (Fig. 6). According to Stipčević et al. (2020), the Moho is deeper in this region, which means that the observed travel times are larger than the calculated ones due to longer refracted ray paths, resulting in positive station delays. According to the computed rays, the positive station delays in the east are mainly due to the rays that sampled the shallower crust with lower velocities. For the two easternmost stations, we see the opposite effect of what was described earlier. Since some computed rays were refracted below 30 km and the Moho is shallower in this region (Stipčević et al., 2020), the observed travel times are smaller than the calculated ones. The computed station delays are probably smaller but are still significantly positive due to a small number of these rays. A relatively small positive station delay of the easternmost station (MOSL) could also be due to the rays that pass through the high-density body under the Sava basin (Šumanovac et al., 2009; Šumanovac, 2010).

In the western part of the study area, the seismicity relocated with the MPS model (Fig. 11) is confined to depths between 0 and 20 km, which corresponds to the depths determined by Vičič et al. (2019) for western Slovenia. Towards the eastern part of the study area, the earthquake hypocenters become shallower and mostly occur below 15 km depth. The shallowing of the earthquake hypocenters is consistent with the shallowing of the Moho depth, as already suggested by Stipčević et al. (2020). Moreover, most of the seismicity in the region seems to be confined to the depths above the depth interval of the rapid P-velocity increase and to the depths with relatively higher vP/vS values. Therefore, the lower vP/vS values and the increase in velocity gradient in the lower crust indicate a change in physical properties that prevents the occurrence of deeper earthquakes. A similar observation has already been made in several studies (Bressan et al., 2009, 2012; Magrin and Rossi, 2020) that related the spatial distribution of seismicity in the northern part of the Adria to the changes in various physical parameters in the crust. A look at the depth distribution of the relocated seismicity shows that about 2 % of the earthquakes were relocated to depths between 0 and 1 km. These earthquakes occurred mostly at the periphery of our study area (Fig. S4). Relocation using the velocity model for the corresponding subregion mitigated this problem only in the area of the SW subregion, where one event remained at a depth above 1 km and even this one directly at a quarry. Since other events in this region could not be attributed to quarries and were relocated to greater depths with the subregional model, this suggests that the shallow structure was more accurately resolved with inversion at a smaller scale, as also previously shown by Husen et al. (2011). Thus, despite a relatively poor performance in the stability tests compared to the other two subregions, the model for the SW subregion still provides reliable earthquake locations.

Earthquake hypocenters in the northwest that remain at depths above 1 km after the relocation with the velocity model for the NW subregion are probably still accurate due to the high topography in this area. Such hypocenters in the east could be biased toward the surface because a 1-D velocity model cannot fully account for the local effects of deep sedimentary basins. Since 16 more earthquakes in the east were relocated above 1 km depth using the velocity model for the E subregion, two large P-velocity jumps in this model computed for the unconstrained layers below 23 km depth (Figs. 13 and 16) may also bias the earthquakes with readings from distant stations. In addition, only about 3.5 % of earthquakes in the E subregion were relocated to depths above 1 km, and most of them with depths above 0.5 km had high rms residuals ranging from 0.37 to 0.97 s. For this reason, unconstrained depths could also result from some potentially inaccurate readings with high residuals. Due to their proximity to quarries, five of these events most likely resulted from explosions. Lower rms residuals obtained for the subregions also indicate a better fit of the obtained velocities and better-resolved station delays, as there are relatively few differences between the structure below the reference station and all other stations. The gap in seismicity above about 7 km depth in some parts in the west can be observed in both the relocated and routinely located seismicity. In the east, the earthquakes are in some parts already absent below about 10 km depth. Since earthquakes have occurred at comparable depths in the other parts of the study area, the apparent absence of earthquakes could be due to the relatively short time span of our dataset. If there are structural reasons for this type of depth distribution of earthquakes, we expect to find them with the computation of a 3-D velocity model.

With this study, we evaluated in detail the performance of 1-D velocity inversion, which has been shown many times to be essential for the results of LET (e.g., Kissling et al., 1994). The obtained regional and local 1-D velocity models provide reliable hypocenters of local events using first P- and S-arrival times. Based on the results for the subregions, the study area cannot be considered uniform in terms of seismic velocity and seismicity. This means that using only one model to locate earthquakes at the regional level may bias the hypocenters, even with the computed station delays. As can be seen from our study, the station delays cannot always account for the full effect that lateral velocity variations in the shallow crust have on travel times, especially in the case of deep sedimentary basins. Further work is needed in the study area to obtain a more reliable 1-D P- and S-velocity model for the Dinarides further south, where the data selection process is more challenging due to the smaller number of seismic stations. Based on the results of this and other studies (Stipčević et al., 2020) showing a highly variable vP/vS in the study area, the P and S velocity models resulting from the combined P and S inversion provide an improvement for the relocation of the seismicity compared to the constant vP/vS often used in studies in this region. The results of this study will also be used to compute a high-resolution 3-D velocity model that has the potential to resolve tectonic structures in the upper crust in greater detail and link tectonics to seismicity. The division into subregions allows us to further investigate the ray sampling and seismicity distribution of each subregion, which in turn allows better preparation for a 3-D tomography.