Irregularity of Post Mining Deformations As Indicator Revealing Effects of Processes of Unknown Origin in Area of Bochnia

DOI 10.4467/21995923GP.20.008.13073 GEOINFORMATICA POLONICA 19: 2020

Zbigniew Szczerbowski ORCID: 0000-0002-2398-559X

IRREGULARITY OF POST MINING DEFORMATIONS AS INDICATOR REVEALING EFFECTS OF PROCESSES OF UNKNOWN ORIGIN IN AREA OF BOCHNIA

AGH University of Science and Technology, Faculty of Mining Surveying and Environmental Engineering, Krakow, Poland [email protected]

Keywords: neotectonics, salt deposit, salt mining, vertical displacements, Chebyshev polynomials Abstract The presented work deals with the problem of terrain surface and rock mass deformation in the area of the Bochnia Salt Mine. The deformations are related to natural causes (mainly the tectonic stress of the Carpathian orogen) as well as anthropogenic ones related to the past mining activity conducted directly under the buildings of the town of Bochnia. The discussed characteristics of land surface deformation are important from the point of view of threats to surface features and contribute to spatial development. Particularly anomalous zones of observed subsidence basins are examined as places of second order deformation effects. The author presents a method of determinations of these anomalous areas and he discusses their origins.

NIEREGULARNOŚĆ ODKSZTAŁCEŃ POGÓRNICZYCH JAKO WSKAŹNIK UJAWNIAJĄCY EFEKTY PROCESÓW O NIEZNANYCH PRZYCZYNACH W REJONIE BOCHNI

Słowa kluczowe: neotektonika, złoża solne, górnictwo soli, przemieszczenia pionowe, wielomiany Czebyszewa

Abstrakt Przestawiona praca dotyczy problematyki deformacji powierzchni i górotworu w rejonie Kopalni Soli Bochnia. Deformacje te związane są zarówno z przyczynami naturalnymi (głównie nacisk tektoniczny orogenu karpackiego), jak i antropogenicznymi związanymi z minioną aktywnością górniczą prowadzoną bezpośrednio pod zabudową miejską Bochni. Omówione charak- terystyki deformacji powierzchni terenu są istotne z punktu widzenia zagrożeń dla obiektów powierzchni oraz są elementem planowania przestrzennego. Szczególnie przeanalizowane zostały strefy anomalne niecki obniżeniowej jako efekty drugiego rzędu deformacji. Autor przedstawił sposób ich wyznaczania oraz omówił genezę ich powstania.

1. INTRODUCTION history but impressing geological setting too. The Boch- nia salt deposit is situated at the front of the Carpathian Bochnia is best known for its historic salt mine, overthrust. The very geological image of the deposit stirs which dates back to 12thcentury. The Bochnia Salt Mine the imagination and gives an idea of the collision of great was established probably in 1247, what makes it one of tectonic units, where the role of the ram was played by the oldest companies in the world. However, the mine a salt deposit, tectonically deformed in an extreme way. ceased producing salt in 1990, it is still active as a tourist Mining operations carried out in this complicated geo- attraction. The object is outstanding due to its mining logical environment had to face technical problems as 82 ZBIGNIEW SZCZERBOWSKI large tensions activating convergence of underground boundary of two geological units: the Outer Carpathi- passages and chambers. This process was the reason ans and the Carpathian Foredeep. of terrain surface deformations and still observed sub- The geology of the salt deposit in Bochnia is well rec- sidence is a remnant of old mining activity in Bochnia. ognized due to long-time mining activity. It was widely Long time surveying measurements provided distribu- discussed in numerous papers (Poborski, 1952; Poborski tion of vertical displacements, which form subsidence and Skoczylas-Ciszewska, 1963; Garlicki, 1968; Garlic- basin. However spatial distribution of the displacements ki, 1979; Wiewiórka et al., 2006; Wiewiórka et al., 2008; has not been varying much in many years, the decrease Wiewiórka et al., 2009). The most significant feature of their annual rates is noticeable. The distinctive feature of the area is complicated tectonics, whose recent tec- of temporal vertical displacement distribution is certain tonic activity was already discussed by Liszkowski irregularity of the subsidence basin geometry. So, vertical (1982) or Toboła and Bezkorowajny (2006). displacements demonstrated by benchmarks of the mine The Bochnia salt deposit is just situated in a narrow leveling network were analyzed. The aim was to deter- belt of folded Miocene strata, called the allochthonous mine zones of anomalous subsidence, which probably unit, which spreads along the northern boundary of the reveal combination of mining and other source influenc- Carpathians (Fig. 1). es. Analytical tools for separation of mining and natural Uplift of the deposit was related to overthrust (geological) influences are proposed by the author. movements of the Flysch Carpathians over the strata of the Carpathian Foredeep. Due to these movements, the 2. GEOENVIRONMENT salt series were thickened and uplifted towards to the surface (see: Poborski, 1952; Poborski and Skoczy- The area of the study is situated on the river Raba, las-Ciszewska, 1963; Garlicki, 1968; Garlicki, 1979). in the Babica stream valley, at the boundary of the Investigations on recent tectonic movements of the Carpathian Foothills and Sandomierz Basin and at the Outer Carpathians have been ongoing for several de-

S Bochnia N

Campi B4 B1 1 3 B3 Bocia

czwartorzęd Quarternary utwory fliszowe flysch deposits Chodenice Bochnia BADEN BADENIAN B3, B4, B1,1, 3 - drill holes utwory spągowe serii solnej seria solna deposits at the bottom of the salt series salt series jednostka autochtoniczna jednostka allochtoniczna autochthonous unit allochthonous unit warstwy chodenickie warstwy grabowieckie utwory stropowe serii solnej Chodenice Beds Grabowiec Beds top deposits of the salt series Fig. 1. Bochnia. Geological cross-section through the salt deposit (after Garlicki, 1968) Ryc. 1. Bochnia. Przekrój geologiczny przez złoże soli (wg Garlicki, 1968) IRREGULARITY OF POST MINING DEFORMATIONS AS INDICATOR REVEALING EFFECTS... 83 cades, involving successive generations of research- mations and the observed by geodetic methods move- ers. According to Zuchiewicz there are several uplifted ments of the rock mass have 3 sources (Poborski 1982): tectonic zones, with similar uplift intensities, rates and – tectonic – tectonic stress of the Carpathians, durations in different parts of the orogen (Zuchiewicz, – mining – the effect of plastic (most often) conver- 2001). These zones are aligned subparallel to the Car- gence of underground excavations, pathian belt, and the Bochnia area is one of them. – halotectonic (pushing salt masses upwards). Tectonic setting reflects actions of geological forces in the past and probable recent stress distribution that Tectonic activity of the area has been a subject of has probably been preserved from the Miocene to the widespread interest of successive generations of scien- present day. Furthermore, they may be the forces that tists. According to Liszkowski (1982) effects of geo- currently manifest in the form of movements of the rock logical processes observed nowadays: as suffusion, mass and the terrain surface or more precisely: they dis- land mass movements (as landslides) observed at the turb the characteristics of the deformations caused by front of the Carpathians are manifestations of their ne- old mining operations. The noticeable tectonic defor- otectonic activity. There are numerous landslides in a)

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20.4 20.405 20.41 20.415 20.42 20.425 20.43 20.435 20.44 20.445 Fig. 2. Bochnia. Situational map of the area with locations of benchmarks and mining shafts: a – aerial view with topographic contour lines; b – base maps from Google Maps (September, 2020). Horizontal coordinates: latitude, longitude Ryc. 2. Bochnia. Mapa sytuacyjna terenu z lokalizacją reperów i szybów górniczych: a – widok z lotu ptaka wraz z warstwicami; b – na podkładzie mapy pozyskanej z portalu Google Maps (wrzesień, 2020). Współrzędne horyzontalne: szerokość i długość geograficzna 84 ZBIGNIEW SZCZERBOWSKI

Bochnia (active, periodically active, inactive) and ar- Geodetic monitoring of historical excavations was eas exposed to landslides. The landslides in Bochnia involved in efforts to preserve the Bochnia mine as ob- cover quite large areas: in total, approximately 26.8 ha ject of outstanding universal value, hence it was en- of urban area are within the range of active and peri- tered on World Heritage List. It “illustrates the historic odically active landslides (Bereś and Olbromska-Matu- stages of the development of mining techniques in Eu- siak, 2020). Geomorphologic conditions, characterized rope from the 13th to the 20th centuries: both mines have by steep slope gradients favor the landslide hazard in hundreds of kilometers of galleries with works of art, Bochnia (Fig. 2). underground chapels and statues sculpted in the salt, Some more geological manifestations of tecton- making a fascinating pilgrimage into the past” (accord- ic stress in underground, within the salt deposit after ing to https://whc.unesco.org/en/list/32). its final formation are discussed in (Toboła and Bez- Mine surveying in the Bochnia Salt Mine has a long korowajny, 2006). Underground galleries and passages history, addressing geological, mining, networking (car- of the Bochnia Salt Mine are usually N-S oriented i.e., tographic) matters. The historical documents devoted to in a direction perpendicular to the strike of the salt de- mine surveying survived through the ages, but the geo- posit and parallel both to the general movement of the detic infrastructure itself (control points, benchmarks) Carpathians and to the orientation of the stress field, as well, so they are still of use today. It is essential to as estimated by Jarosiński (1998). Observations in the monitor still existing deformations caused by compres- Bochnia mine show differences in the convergences sion of old excavations as a response of surrounding of mining excavations in some areas of the rock mass rocks to loads. Fortunately, plasticity of rock salt is the according to their orientations to the deposit’s strike main “damper” in the cave-in process (Jeremic, 1994), and to the margin of the Carpathians (Toboła and Bez- so the old excavations in the Bochnia Salt Mine are still korowajny, 2006). maintained. Orientation of the historical excavations reflects The mine's surface leveling network consists of both stress field in underground: being oriented in that way wall and ground benchmarks (only about 25% of to- they are usually well preserved and they are considered tal number of control points), and the network itself is to be stable in the long term (Toboła and Bezkorowajny, mainly dispersed. The exception is the group of bench- 2006; Szczerbowski et al., 2016). This existing stress marks forming the B-B line (ground benchmarks), and its northward orientation may be evidence of recent which passes through the area latitudinally (Fig. 2). movements of the Carpathians. The spread of benchmarks is quite uneven and Results of some geodetic measurements show also many, unfortunately, lack them. However, taking into effects of tectonic stress (Szczerbowski et al., 2016). account the relatively small differentiation of the dis- Outline of the terrain surface deformations shows ef- tribution of vertical displacements and the stability of fects that are not related to observation errors or bench- their changes over time, it can be concluded that their marks instability, as they are observed in certain zones. number is sufficient for determination of subsidence The method of their determination, their localization, basin. Unfortunately, a gradual decrease in the number and an attempt to explain their origin are discussed in of these benchmarks is noticeable. They are damaged or the further part of the work. destroyed mostly due to renovation works of buildings in Bochnia. 3. SURVEYS Leveling measurements carried out over the years in the mining area of the Bochnia Salt Mine covered Geodetic underground measurements are usually area of 7.6 km2 (approximately 5 × 1.5 km) maximally devoted to practical problems in mining or tunnel engi- (Fig. 2). However, the most of the benchmarks are neering. Mine surveying methods are also carried out in placed in the area of 3.5 × 1.5 km (approx. 5 km2). Al- the Bochnia mine for engineering purposes as determi- though the first benchmarks were established in 1952 nation of displacements of control points. Detailed ex- (about 20), and the next ones in 1972 (about 40), the amination of the data was performed by the author to de- first useful information about the movements of the tect additional effects induced by geological processes. city's terrain surface was obtained only in the 1980s. IRREGULARITY OF POST MINING DEFORMATIONS AS INDICATOR REVEALING EFFECTS... 85

years 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 0.000

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Fig. 3. Vertical displacements of Rp56 and Rp114 benchmarks from 1972 to 2015 Ryc. 3. Przemieszczenia pionowe reperów Rp56 i Rp114 w latach 1972–2015

In that time, an observation network with a satisfactory in the further analysis just the annual rates of vertical number of points was established. Therefore, heights of displacements of the benchmarks are analyzed and their benchmarks determined by measurements carried out distribution in the area of Bochnia. Then the next figure in 1980 were assumed as reference in the next analy- shows average annual velocities of vertical displace- sis. Then the number of benchmarks was 135 and they ment of the Rp56 and Rp114 benchmarks between 1980 covered a large part of the studied area. Thus, tempo- and 2015 (Fig. 4). rary vertical displacements from particular years were As it shown the annual rates have been decreasing analyzed in relation to 1980, and vertical displacements successively, although the decrease has been getting for the period 1980-2015 were assumed here as total slower and slower. It outlines a process observed in vertical displacements. the area: the clear majority of benchmarks show de- Temporal vertical displacements observed in the crease of subsidence rates. However, there is a group area by years are outlined by plot on Fig. 3. There are of benchmarks whose characteristics of subsidence are height changes of benchmarks Rp 56 and Rp114 located out of this trend. They show uplift or increased values in the central part of the subsidence basins (Fig. 2). Pre- of subsidence. It is possible that in the case of such sented displacement performance in successive year is points there are measurement errors or local effects, e.g. typical and temporal changes demonstrated by the other of landslide origin. Anomalous vertical displacements benchmarks are similar. of a larger group of benchmarks may have geological Deformations and their changes in time can be ex- (e.g. drainage) or mining causes (impact of a group of pressed by another parameter – annual velocity of verti- shallow workings of the old mining operation). Identifi- cal displacements. This is much comparable for vertical cation of such anomalous regions may be possible based displacements evaluated in different time intervals. So, on the appropriate analysis, which is presented below. 86 ZBIGNIEW SZCZERBOWSKI

years 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 0,000

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Fig. 4. Annual rates of vertical displacements (with linear trends) of Rp56 and Rp114 benchmarks between 1972 and 2015 Ryc. 4. Roczne prędkości przemieszczeń pionowych (z trendem liniowym) reperów Rp56 i Rp114 w latach 1972–2015

3. NUMERICAL ANALYSIS scattered data – annual rates of vertical displacements OF SPATIAL DISTRIBUTIONS evaluated by leveling surveys of benchmarks of the OF VERTICAL DISPLACEMENTS mine’s network in Bochnia. This theoretical model is a smoothed surface, which geometry can be described by The main goal of the study is separation of deforma- polynomials approximating acceptably close influence tions caused by old salt mining in Bochnia and the other function based on Gaussian distribution of deformations effects, mainly resulted from geological factors such as (vertical displacements) induced by mining (Szczer- drainage, subrosion etc. bowski, 2001). In practice, the 6th degree polynomial sat- In mining practice, theories of mining influences isfactorily approximates the subsidence basin, which is are based usually on the Gaussian distribution of min- geometrical distribution of subsidence data, or precisely: ing influences, which are expressed in the form of so the Budryk-Knothe function that describes it (Szczer- called influence function with empirically determined bowski, 2001). In order to obtain the most reliable results parameter values. In Poland the most popular approach of this modeling, the following steps were performed: in modelling and calculating ground movement, how- – geometric analysis of distributions for different ever basically applied for coal mining areas, is the influ- periods – modeled and observed values, ence-function method by Knothe (Knothe, 1959; Kno- – approximation with the use of Chebyshev poly- the, 1969; Knothe, 1970, Knothe, 1984). nomials: 3rd, 4th, 6th and 10th degrees – the polyno- In the analyzed case the Gaussian distribution of mials were assumed as sufficient to approximate the effects of salt mining is assumed but the parameters subsidence distribution, of influence function are unknown. The determination – comparative analysis of modeled subsidence (re- of “theoretical” model of subsidence basin is based on sulted from polynomial approximation) and de- IRREGULARITY OF POST MINING DEFORMATIONS AS INDICATOR REVEALING EFFECTS... 87

termined discrepancies between the theoretical benchmark – 0.018 m/year. This benchmark, together and the vertical displacements determined by with a fairly large group of benchmarks is concentrated measurements (residuals of the approximation in a small area of approx. 500 m2 which is situated in by polynomials), the center of the subsidence basin. It is approx. 300– – estimation of differences between observed and –400 m southeast of the Campi shaft. All of the above the modeled values of subsidence were residual benchmarks showed average annual subsidence of over values. They formed zones of negative or positive 0.015 m/year. deviations (residues), The first obvious observation was certain variabil- – interpretation of evaluated zones of anomalous ity of geometry of particular basins. It is a paradoxical vertical displacements. fact, considering that the temporal distributions of vertical displacements of individual benchmarks presented It was assumed that subsidence that should be re- before are characterized by high stability. However, as vealed on terrain surface is a result of summation of already mentioned, the high variability of the number mining effects (caused by compression of underground of benchmarks involved in levelling measurements in workings), which can be approximated by Chebyshev particular years, as well as their loss combined with the polynomials and the others, which interference the di- reestablishment of new points is the main cause of vary- rect effect of mining. This approximation of spatial dis- ing in time geometry of the determined contour lines tribution of vertical displacement distribution allows (isolines) outlining vertical displacements. a determination of disturbances in spatial data – zones Variability in the time-spatial distribution of vertical of anomalous vertical displacements. displacements of terrain surface in Bochnia does not Assuming these disturbances resulted from effects affect clear regularities: of natural processes taking place in the rock mass (not related to mining), the presented approach identifies – the center of the subsidence basin is located in areas, where their effects occur. This is important for a narrow strip roughly between the Campi and separation mining, i.e., primary and secondary effects, Sutoris shafts, especially in a case, where influence of mining work- – the subsidence basin is stretched latitudinally, ings on terrain surface is impossible to be modeled (as which is justified in the mining situation, in the case of the Bochnia Salt Mine). – moreover, the subsidence basin is characterized The method was applied before for vertical displace- by an outstanding lack of symmetry and local ments observed in Inowrocław, another already histor- variations, including temporary uplifts. ical salt mining area in Poland (Szczerbowski, 2005). The general picture of temporary vertical displace- So, in the first stage of the displacement analysis, ments of the terrain surface also includes local distur- distributions of subsidence were determined for the pe- bances in the geometry of individual subsidence basins. riods: 1980–1984, 1980–1987, 1980–1993, 1980–1997, They take the form of local subsidence basins, surpris- 1980–2003, 1980–2007, 1980–2011, 1980–2015. These ing sudden changes in the course of the isolines, which displacements formed temporary subsidence basins, i.e. is not justified in the mining situation due to the con- which were formed between particular years in the peri- siderable depth of mine workings. This irregularity in od 1980-2015. (Fig. 5) presents vertical displacements the image of individual subsidence basins was just the in Bochnia evaluated in chosen periods in the form of reason for presented application of polynomial approx- contour maps and spatial maps for selected periods, re- imation of height change distributions. spectively. The distributions of mentioned above temporary As it is shown the subsidence basin has an oval subsidence of time intervals of 1980–2011 and 1980– shape and it is latitudinally extended, what corresponds –2015 were approximated by Chebyshev polynomial to the orientation of post mining excavations. Another with two variables of: 3rd degree, 4th degree, 6th degree, distinct feature is it asymmetry: northern and eastern 10th degree (Fig. 6 and Fig. 7). Two time intervals and parts of the basin are more inclined than their oppo- the significant number of applied polynomials were site sides. In the period 1980–2015, the highest rate chosen to outline differences in obtained results. As it is of vertical displacements was demonstrated by Rp133 shown in various time intervals distribution of areas of 88 ZBIGNIEW SZCZERBOWSKI

Fig. 5. Bochnia. Temporary vertical displacements [mm] in time intervals. Local coordinate frame Ryc. 5. Bochnia. Okresowe przemieszczenia pionowe [mm] w latach. Lokalny układ współrzędnych positive and negative residues don’t differ very much. approximation) but mentioned features are maintained, Fig. 6 and Fig. 7 present modeled distribution of sub- especially in case of approximation of higher degree sidence as well: contour lines are more smoothed (more polynomials. It’s worth remarking that the residues or less dependably on degree of polynomial applied for occurred more or less closely in the same areas in all IRREGULARITY OF POST MINING DEFORMATIONS AS INDICATOR REVEALING EFFECTS... 89

Fig. 6. Approximation of annual rates of vertical displacements in the period of 1980–2011. Modeled rates (yellow contour lines) and their residues (color map; negative values in blue, positive values in red) based on approximation by Chebyshev polynomials of: A – 3rd degree, B – 4th degree, C – 6th degree, D – 10th degree. Horizontal coordinates: latitude, longitude Ryc. 6. Aproksymacja rocznych przemieszczeń pionowych w latach 1980–2011. Modelowane wartości (zaznaczone żółtymi liniami) i ich rezydua (mapa kolorów; wartości ujemne w kolorze niebieskim, wartości dodatnie w kolorze czerwonym) na podstawie aproksymacji wielomianami Czebyszewa: A – 3. stopnia, B – 4. stopnia, C – 6. stopnia, D – 10. stopnia. Współrzędne poziome: szerokość i długość geograficzna 90 ZBIGNIEW SZCZERBOWSKI

Fig. 7. Approximation of annual rates of vertical displacements in the period of 1980–2015. Modeled rates (yellow contour lines) and their residues (color map; negative values in blue, positive values in red) based on of approximation by Chebyshev polynomials of: A – 3rd degree, B – 4th degree, C – 6th degree, D – 10th degree. Horizontal coordinates: latitude, longitude Ryc. 7. Aproksymacja rocznych przemieszczeń pionowych w latach 1980–2015. Modelowane wartości (zaznaczone żółtymi liniami) i ich rezydua (mapa kolorów; wartości ujemne w kolorze niebieskim, wartości dodatnie w kolorze czerwonym) na podstawie aproksymacji wielomianami Czebyszewa: A – 3. stopnia, B – 4. stopnia, C – 6. stopnia, D – 10. stopnia. Współrzędne poziome: szerokość i długość geograficzna IRREGULARITY OF POST MINING DEFORMATIONS AS INDICATOR REVEALING EFFECTS... 91 analyzed time intervals and in a particular polynomi- anomalous zones could be considered as resulted from al approximation. This means that the irregularity was inadequacy of the 4th degree polynomial fit into the ge- somewhat “inscribed in” the distribution of vertical dis- ometry of an atypical geometry of subsidence basin, placements and it resulted from non-mining reasons. formed also by shallow, abandoned and not document- And locations of certain zones of anomalous vertical ed old galleries. In the case of 3rd degree polynomial displacement rates do not seem to be accidental. fitting values maximal/minimal residues (several mm) Due to the use of various polynomials – more or less is about 40% of maximal/minimal value of subsidence precisely fitting into the distributions of the analyzed rate, in the case of 4th degree polynomial fitting – about vertical displacements, anomalous zones are obtained 30%, in the case of 6th degree polynomial fitting – about with different area size. So: fitting with ath 4 degree 20% and in the case of 10th degree polynomial fitting polynomial results in residuals appearing in larger ar- the value of maximal residues is about 5% of maximal/ eas. They could be called 1st degree residuals (and the minimal value of subsidence rate. corresponding anomalous zones – 1st degree zones). For As it was mentioned Chebyshev’s polynomial of 6th a 6th and 10th degree polynomials these are respective- degree was accepted as sufficient to approximate the ly 2nd degree residuals (zones) and 3rd degree residuals distribution of subsidence (or rather Budryk-Knothe’s (zones). 10th degree polynomial very good fits into the function describing it). So, differences between values vertical displacement distribution and areas of anoma- determined by measurements and values modeled on lous zones is wide spread but values of residue is not the base of polynomial fitting (residues) should be min- significant. The zones in this case are not very useful imal and their distribution should be random. Otherwise for investigation of additional effects in outline of de- the obtained residues convey information about a phe- formations. nomenon causing additional vertical displacements The obtained residuals could be random but con- distorting deformations caused by mining. The higher sidering their replicability in successive periods that degree polynomials produce filtered information; how- seems pretty unlikely. On the other hand, the 1st order ever it still can be significant and useful.

Fig. 8. Bochnia. Zones of anomalous vertical displacements observed in the period of 1980–2015 determined on the base of 6th Chebyshev approximation (areas of negative rates in blue and areas of the positive rates in red). Base maps from Google Maps (September, 2020). Horizontal coordinates: latitude, longitude Ryc. 8. Bochnia. Strefy anomalnych przemieszczeń pionowych obserwowanych w latach 1980–2015 wyznaczone na podstawie aproksymacji wielomianów Czebyszewa 6. stopnia (obszary współczynników ujemnych w kolorze niebieskim i obszary współczynników dodatnich w kolorze czerwonym). Na podkładzie mapy pozyskanej z portalu Google Maps (wrzesień, 2020). Współrzędne poziome: szerokość i długość geograficzna 92 ZBIGNIEW SZCZERBOWSKI

The significant anomalous zones are exposed by cal geometry of temporary subsidence basins. Specific overlaying on situational base map for better identifi- variability of the course of isoclines (lines of constant cation of their locations. Fig. 8 presents the zones de- vertical displacement rate) depicting subsidence sug- termined on the base of 6th Chebyshev approximation of gests that the deformation processes are under addition- subsidence of terrain surface in Bochnia between 1980 al influence (not related to effect of convergence of old and 2015. They are presented on Fig. 7C as well. In this mining galleries and chambers). Polynomial approxi- outline the contour lines are removed. As it is shown mation of subsidence basin was proposed here to de- there are 5 zones of “smaller values” of subsidence termine the area of anomalous vertical displacements. rates than modeled values, i.e., they are areas where The author assumed 6th degree polynomial as sufficient subsidence is affected by other sources than mining. for approximation of influence function and he applied They increased the subsidence rates – as it was men- it as a tool for numerical separation of deformation tioned – about 20%. The south western zone is situated caused by mining and the other sources. The residues on steep hillside of the Carpathians and the probable between observed and modeled values were presumed reason of anomalous vertical displacements is downhill as anomaly in deformations, which amounted maximal- creep. Another zone of the negative values of residues is ly to 20% of maximal influence of convergence caused in the eastern part of the area. Its western part is affected by documented excavations of the Bochnia Salt Mine. by documented landslides. The next one, situated cen- Values of the residues are of negative and positive char- tral part of the city is extended along the Babica stream. acter, which in practice means too low (decreased) or Geometry of this zone of negative residue values and its too high (increased) subsidence. placement suggests influence of the stream. However, The zones of negative values of anomalies are usu- this zone is situated between the Campi and the Sutoris ally situated on a steep hillside and between the main shafts and it may be resulted from the specific effects of shafts of the mine, where mining operations were con- old shallow, abandoned and not documented workings centrated since 13th century and many old shallow of the mine. Another zone of the negative values is lo- workings were situated. Currently, they are abandoned, cated on hill in the north western part of the city. The collapsed and not documented. This zone is surround- probable reason of anomalous vertical displacements ed by the area of subsidence of anomalously decreased there is downhill creep. values (zones of positive residues). Their origin is to be There are 3 zones of “too high values”. So, annual investigated by other methods. rates of vertical displacements (subsidence) are much Although the presented analysis is based on numeri- smaller than modeled values there. Their area size is cal method of approximation spatial distribution of data rather small on this model of residues determined on the (subsidence values), it is not a quantitative analysis. base of approximation of 6th degree polynomials. But It should be considered as a proposal to determine are- they occur in the other models as a significant area size as of atypical deformations that should be investigated of the city. There is no credible explanation of the zones further with application or it provides initial identifica- of positive residue values. They could be a numerical tion the causes of the phenomenon (anomalous vertical effect of polynomial fitting (result of asymmetric dis- displacements). tribution of subsidence values). The only physical explanation of the reason of decreased subsidence values REFERENCES is an uplift factor. The only one in the area is halotec- 1. Bereś A. and Olbromska-Matusiak A. (eds). 2020. Study tonic movement of salt structure towards the surface. of the Conditions and Directions of Spatial Development This problem should be explained with the use of other for Municipality of the City of Bochnia. Electronic docu- methods. ment available online at: https://bip.malopolska.pl/api/files/ 2305230 (access 30.09.2020). 2. Garlicki A. 1968. Autochthonous salt series in the Miocene of 4. CONCLUSIONS the sub-Carpathian area between Skawina and Tarnow. Biul. Inst. Geol., 215, pp. 5–78 (in Polish). In the area of Bochnia, subsidence as an effect of 3. Garlicki A. 1979. Sedimentation of Miocene salts in Poland. old mining is still being observed. Distributions of the Prace Geologiczne PAN, 119, pp. 1–67 (in Polish, English long-term vertical displacements demonstrated atypi- summary). IRREGULARITY OF POST MINING DEFORMATIONS AS INDICATOR REVEALING EFFECTS... 93

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