ABSTRACT

THE THERMOMETRICAL METHODS OFSTUDYING GROUND WATER

N.M. FROLOVAil-Union Research Institute of Hydrogeology

and Engineering Geology, Moscow, USSR

ORIGINAL (not corrected)

Ground water is characterized by a high heat capacity and mobility. When groundwater moves through rock pores and fractures, it transports a lot of heat energycreating negative thermal anomalies in some places and positive ones in others. Thetime when the heat equilibrium occurs in the rock-water system depends mainly onthe velocity of ground water movement. If ground water does not move, its temperatureis equal to that of the enclosing rocks, and when it moves the difference between therock and water temperatures increases with increase in the velocity of ground water.Considering the above and measuring the temperatures of ground water and enclosingrocks, different problems (of ground water generation may be studied. These aredetermination of the intensity of water exchange and the thickness of hydrodynamiczones, study of the surface and ground waters interaction in discharge and rechargeareas, etc.

The earth's thermal regime is being generated under the influence of two groups ofenergy sources—endogenous and exogenous. The first group mainly comprises theheat from radioactive decay of uranium, thorium and potassium contained in rocks,and the principal external source is the heat of the sun. The earth's outer shell fromwhere heat flows off and where the influence of exogenous factors is manifested to anydegree and in any form within the geological time scale is related by the author to theheliothcrmozone. The inner part where heat is accumulated during geologic time isrelated to the geo-thermozone.

Surface temperature amplitudes due to rock heat conductivity penetrate intodepth attenuating exponentially (/JaXHOB, /JbKKOHOB, 1952):

where At is the temperature amplitude at depth x;Ato is the temperature amplitude atground surface; a is rock temperature conductivity; T is the period of temperaturefluctuations.

Using this expression it is possible to determine the depth of temperature amplitudeattenuation:

\nAt0 — In Atx

nax

It mainly increases with increase in the duration of temperature fluctuations (table I).In this connection, six principal geothermal layers are distinguished (<ï>po^OB, 1964,1966): the layer of daily temperature fluctuations, the layer of seasonal temperaturefluctuations, the layer of annual temperature fluctuations, the layer of long-termtemperature fluctuations, the layer of secular temperature fluctuations and the layer ofgeologic time temperature fluctuations.

It is known, however, that the upper parts of the earth's crust are saturated every-where by ground water which due to its extraordinarily high heat capacity and mobility

269

TABLE tDepth of Influence of Surface Temperature Fluctuations on Earth's Thermal Regime due to Heat Conductivity

to© Geothermal Climatic cycles, Temperature conduc-

laycrs years tivity, em'/sec

At0 =•• 1 0 ° C At0 = 30 °C

Atx = 0.1 °C x -= 0.01 °C u = 0.\°C tx = 0.0l°C

Annual

Longtcrm

Secular

Geologic time

11

35

100

4.5.103

275.103

150.106

250.106

0.0010.0100.0200.0010.0100.020

0.0010.0100.020

0.0010.0100.020

0.001

0.010

0.0200.0010.0100.0200.0010.0100.020

0.0010.0100.020

metres4.614.620.615.348.468.5

27.386.4122.0

46146206

310

980km1.4

2.47.710.8

56179253

73231327

6.921.931.023.070.6102.7

41.0130.0183.0

69219310

465

1.5

2.1

3.611.516.2

85269380

109346490

5.718.125.619.060.084.8

33.8107.0151.0

57181256

384kilometres

1.2

1.7

3.09.513.4

70221314

90286404

8.025.435.926.684.2119.1

47.5150.0212.0

80254359

539

1.7

2.4

4.213.318.8

98311440

127401568

transports great amounts of heat that considerably complicates the thermal regime ofthe stratisphere. Superior convection processes are added to conduction processes. Inthis connection, the thickness of the geothermal layers distinguished substantiallyincreases and must be correlated with the position of corressponding drainage baselevels. The layers themselves should be more correctly called hydrogeothermal.Substituting the convection parameter a = Kh/fi into expression (2), we obtain anexpression for determining the depth of the influence of surface temperature fluctuationsintensified by convection processes within aquifers:

In Ato-\nAtxX =

Khx

(3)

where fi is rock porosity; K is the coefficient of permeability; h is the thickness of theaquifer.

In this case, as calculations show, the depth of the influence of surface temperaturefluctuations mainly depends on rock permeability (table II).

TABLE II

The value of

\nAto-\nAtx

ŒTV Khx

at h = 100 m

Coefficient ofpermeability,

cm/sec

0.1.10"5

0.1.10"4

0.1 10 " 3

0.1.10"2

0.010.1

1.0

10.0

Daily (At0

At = 0.1 °C

0.82.47.6

24.0

76240

760km2.4

Length of temperature wave (T)

= 10 °C)

At = 0.01 °C

metres

1.13.6

11.436.1

114361

km1.1

3.6

Annual (Ato =

At = 0.1 °C At

21.356.5

213565

30 °C)

= 0.01 °C

25.080.3

250803

kilometres

2.15.6

21

56

2.58.0

25

80

Note: The table value is further divided by a specific value of \Z/u, and if it is neces-sary to determine the depth approximately (instead of the distance from the rechargearea) the table value is also multiplied by the sine of the aquifer dip angle.

271

On the basis of the peculiarities of the geological-hydrogeological structure of differ- ,.ent regions, the author distinguishes three main types of hydrogcothermal zonation: 'closed type, open type and combined type (fig. 1).

M M n si u T y y ÙI 'c '(b) Ce) (b) (c) <bj ce)

Cejo"ni>ie rugoôùie CeJOhtMae rogûôbie Cewifee fjgoôo/e

ia ?o o eo to lo o eo to la o ?o a>

(i) 50

- © -

©•

©

O " © ®

Fig. 1 — Types of hydrogeothermal zonation:(a) Temperature amplitudes in °C;(b) Seasonal;(c) Annual;(d) Depth in metres;© Closed type;© Combined type;® Open type;© Impervious rocks;© Pervious rocks.

The closed type of hydrogcothermal zonation should be observed in the areas com-posed of thick strata of impervious rocks with very poor erosional ruggedness. In thiscase, annual temperature waves penetrating from the earth's surface by conductivityattenuate at an average depth of as low as 22-25 m (see table I). Below the rock tem-perature remains constant (±0.01 °C) during the year.

The open type of hydrogeothermal zonation occurs in the areas composed, in theupper part of the section, of pervious and well-drained rocks over 30-50 m thick. Inthis case, even the thickness of the layer of seasonal temperature fluctuations exceedsthe depth to the "neutral layer" and depends on the thickness of pervious rocks andthe depth of the erosional cut.

272

The combined type of hydrothermal zonation is characteristic of drained areascomposed of alternating impervious and pervious rocks with a dense impervious bedover 30 m thick in the upper part of the section. In this case, annual temperatureamplitudes initially attenuate as in the closed type of hydrothermal zonation, but than(in contrast to the closed type) they are recorded at the level of aquifers.

The thermometrical methods of studying ground water are based on the peculiaritiesof the processes of mass and heat exchange in the rock-water system (l). At rest,ground water saturating rocks gets their temperature, but when ground water movesthis process has no time to come to an end. The difference between the temperatures ofrocks and water increases with increase in rock permeability. In general, the hydro-geothermal regime is determined by a complex of geological-hydrogeological andphysiographical factors. Knowing the regularities of the hydrogeothermal regime andspecific features of the influence of different factors on the formation of the hydrogeo-thermal regime, and studying the temperature of rocks and water it is possible todecipher certain factors.

Taking into account the foregoing, the areas characterized by the closed type ofzonation are without prospects as to application of hydrogeothermal methods. Theproblems that can be solved by using hydrogeothermal methods in the areas of openand combined types of zonation are very diverse, and though in each case studies arespecific these methods are based on two general conditions:

(1) Temperature measurements should be made along all the borehole (from mouth tobottom) irrespective of the filling material (water, air, clay mud);

(2) The accuracy of the measurements must be no less than ±0.01 CC and, therefore,point measurements are recommended instead of continuous recording. The inter-vals between the records may range from 0.5-1.0 m to 5-25 m.

The hydrogeothermal methods are grouped as follows:

(1) Methods of single temperature measurements;(2) Regime methods.

At present, simpler methods based on single measurements are usually usedthough most interesting prospects are connected with studying the temperature regimeat different depths. The author has developed techniques for studying the temperatureregime along the borehole as well as techniques for treatment and interpretation of thesedata and suggested a graph where, in addition to thermograms, to the right of thegeological column the temperature amplitude is shown for a certain period anddepth (fig. 2).

The extensive network of regime hydrogeological stations of the Ministry forGeology of the USSR (85 stations at the end of 1965) having thousands of wells andcovering all important geological-hydrogeological and physiographical zones of thecountry allows, if thermometrical studies are organized properly, a number of specialscientific and practical problems to be solved. These data are also of value to relatedsciences. Based on short- and long-term observations of the ground water temperatureregime, the following problems may be solved:(1) Determination of the thickness and regularities of areal occurrence of hydrodynamic

zones (separation of the geological-hydrogeological section according to rockpermeability(2);

(1) The science of the thermal regime of the earth's crust, the role of ground waterin the formation of this regime, and the methods of its investigation is suggested to bebe called hydrogeothcrmometry.

(2) It is also of pure practical significance. So, the lower hydrogeothermal zonewith a stable temperature regime (long-term and secular cycles) may be regarded as apromising zone for oil and gas while beds with annual temperature fluctuations promisefresh ground water needed for water supply and irrigation.

273

> —,̂

\

J

1I i

1'••

/

-.

r

c '

c •• o

n •f-, o

.9'

o

•

• — - — J

r• • !

' r 1 '

Fig. 2 — Temperature regime in Well 308, Alma-Ata (open type of hydrogeothermalzonation in case of spray percolation of surface water):(a) Depth in metres;(6) Temperature in °C (-tO.lcC);(c) Amplitude in °C (±0.02 °C);1. Daily temperature variations in °C;2. Decade temperature variations in °C;3. Monthly temperature variations in °C;4. Screen;5. Temperature amplitude measurement point;6. Static water level and head line;7. Rubbly-gravelly-pebbly sediments with sand.

(2) Establishment of the thickness and intensity of development of karst;

(3) Study (determination of location, delineation, etc.) of "obscure" (under detritaldeposits and at the bottom of surface water reservoirs) centres of ground waterdischarge as well as conditions of interaction of ground and surface waters atdischarge and recharge sites (conditions of mixing deep water with free groundwater in the zone dispersion, etc.);

274

(4) Solving hydrodynamic problems (conditions of movement, recharge, leakage,prediction of the development of cones of depression at water intakes, etc.);

(5) Estimatiom of the quantity of heat transported by ground water from the earth'sinterior;

(6) Study of the general regularities of the ground water temperature regime to solveproblems of ground water generation as well as practical use (as heat source incase of thermal waters, for irrigation, water supply, etc.).

Interrelation between the intensity of water exchange and the hydrogeothermalregime is the basis of hydrogeothermal methods (Table III).

TABLE III

Zone Periods of recording temperature Intensity of water exchangenumber amplitudes with accuracy of (hydrodynamic zones)

±0.01 °C (hydrogeothermal layers)

I daily very intensiveII seasonal intensiveIII annual slowIV long-term very slowV secular at relative standstill

The dynamics of ground water influences the temperature regime of the aquifer asvigorously as it does the chemical composition of its water. It is well known that as theintensity of water exchange (or the role of convection) decreases ground water salinityincreases, and in this way the geothcrmal gradient, temperature and record period Atincrease, and the value of At decreases.

In nature, hydrogeothermal zonation represents a complicated system of alternatinghydrogeothermal layers that is determined by a complex of geostructural, lithological-facial and hydrodynamical factors. Due to different pecularitics of rocks the value andrecord period At, for exemple, vary with depth even at the level of visually homogeneousrocks which is well examplified by piedmont detrital cones (see fig. 2).

The lower boundary of hydrodynamic zones (and corresponding hydrogeothermallayers) is traced along the base of the last layer with corresponding temperaturefluctuations. The number of hydrodynamic zones distinguished from hydrogeothermaldata depends on the depth of the well and the observation period.

Hydrodynamic zones have the greatest thickness in mountain-fold areas and karstregions. (The thickness of the karst zone is established both by separation of the sectionaccording to the value and record period At, and from the results of single temperaturemeasurements. The karst zone is almost isothermal and at its base the temperaturecurve bends.) Short periods of water exchange and large ground water yields in theseregions also produce anomalies, mostly negative ones. (Negative anomalies in karstregions are being formed not as a result of heat transport by ground water, but alsounder the action of fiowing-in of atmospheric air in winter, if funnels exist. In case ofrecharge of karst water by stream water, positive thermal anomalies are observed.)

The criterion of estimating the anomaly sign is the temperature of the "neutrallayer" the depth to which, if convection is absent (the closed type of zonation), is equalto 25 m (a = 0.010 cm2/scc). For the area of the USSR a map of geoisotherms at adepth of 25 m, using the author's data of long-term investigations and data of theHydrometeorological Service, has been compiled (fig. 3). These data have shown that

275

the temperature of the "neutral layer" is approximately equal to the average long-termtemperatureof the soil in the rangeof 1.6-3.2 m (±0.1 °C). It was found that the "neutrallayer" temperature changes with altitude and latitude in keeping with the laws whichgovern the variation of the mean annual temperature of air and soil; the value of the/hypsogeothermal gradient^) coincides with that of the aerothermal one, in this con-jnection the temperature of the "neutral layer" was determined using the formula'/(/JpoflOB, 1964, 1966): j

tn.i. = ts ±0.006 A (4)

where tn.i. is the temperature of the "neutral layer" in °C; /„is the average long-termtemperature of soil in °C; h is the difference between the altitudes of the meteorologicalpost and the investigation poijit in metres. (The correction is adopted with a plus, ifthe meteorological post is higher and vice versa.)

Fig. 3 — Hydrogcothermal map of the USSR compiled by N.M. Frolov andV.l. Pogulyaev:1. Geoisotherms at a depth of 25 m ("neutral layer", convection is absent);2. Isotherms reduced to sea level using the hypsogeothermal gradient of 0.6 C/100m;3. Permafrost boundary;4. The convection component of heat flow from the upper hydrodynamic zone

(less than 10"7 cal/cm2sec);5. Ditto, from 10"7 to 10"6 cal/cm2 sec;6. Ditto, about 10"6 cal/cm2sec;7. Ditto, from 10"6 to lO"5 ca)/cm2sec;8. Ditto, about 10~5 cal/cm2 sec.

If this regularity is neglected, the anomaly sign may sometimes be determinedincorrectly. J. F. Mink (1964) explained the high value of the ground water temperaturein the centre of discharge in Oahu Island, Hawaii by conversion of water potentialenergy into heat and by heat contribution from return irrigation water. R. Schneider(1965) adds the heat transported in a vertical direction by upward deep ground water

(l) The hypsogeothermal gradient is the change of the temperature of the rocks ofthe "neutral layer" per altitude unit: °C/1 m, °C/100 m, etc.

276

flow. However, from the data presented in Mink's paper it is clear that the watertemperature in the centre of discharge (21.0-22.2 °C) is lower than the background one(23.9 °C). (This temperature is calculated from observations in Honolulu at a depthof 0.9 m, the hypsogeothermal gradient for Oahu Island in the altitude range of216-350 m is equal to 0.67 "C/100 m.). In the light of the mentioned regularities thelower temperature of ground water as compared to the background one indicates ahigh specific rate of ground water flow. The ground water having in the recharge area atthe elevation of 490 to 610 m temperatures of 19.5 to 18.0 °C, respectively, have no timeto get the temperature of the enclosing rocks at sea level; furthermore, they cool theserocks within their range of influence. The temperature difference in the centre of dis-charge indicates the complexity of seepage routes. So, lower temperature may beindicative both of the high hypsometric position of the recharge site and higher rate offlow recharging such a spring.

The difference between the ground water temperature and background one may bedue to exposure of the recharge area and ground water circulation, conditions of mix-ing ground and surface waters, etc. Thus in the southern slope of Kungei Alatau theground water temperature is higher than the background one by 2.5 °C, and in thenorthern slope of Zailiiskii Alatau it is lower by 1.5 °C.

The "obscure" (under detrital deposits) centers of discharge of deep ground waterwere studied by means of thermometry probably for the first time by A.N. Ogilvy(OfHJTbBH, 1932) in Kislovodsk mineral springs. Later he drew a diagram of thermo-isoclines for a discharge site in Matsesta. The complex studies of temperature and levelregimes carried out in 1992 (dppOJIOB, 1966) have shown that upward thermal waterflow in the zone of crush is crossed by thick flow of cold water from the Akhun karstmass; in this connection two centres of discharge were formed.

The thermometrical investigations in a bay at the village of Cholpon-Ata nearLake Issyk-Kul allowed us to delineate the areas of cold ground water discharge at thebottom of the lake and distinguish active sinks among inactive ones. The measurementsof water temperature made in July 1964 in sinks showed that the temperature ofwater at their bottoms (10.8 to 13.7 "C) was lower than the background temperature ofthe lake above the sinks by 7.8-10.7 °C. In the sites of dissipated discharge, this differenceis less (3.0 to 3.5 °C) due to more intensive mixing of water in the lake, and outsidethe zone of discharge the water temperature in the lake from surface to bottom (4 to 6 m)is uniform (±0.1 °C). The efficiency of thermemotrical studies raises when the differencebetween the temperatures of ground and surface waters (on this basis it is necessary toselect a season that will be favourable to studies) and discharge increases, and whenwater storage, waves and movement decrease in a surface reservoir. The efficiency ofthe method is drastically lowered when surface waters move. Thus in case of "LowerPulsing" geyser located in Pauzhetka, Kamchatka, discharging into a spring with aflow rate of 5 1/sec, the temperature of the water under the very gryphon dropped aslow as 35 °C, the temperature of the water and air being 21 °C and 25 °C, respectively.The measurements of the temperatures in the silt at the bottom of the spring showed adistinct anomaly of temperatures similar to the water temperature in the centre of thegeyser.

The regularities of ground water recharge by surface streams were studied by theauthor at the site of wells 220 and 221 located side by side in Alma-Ata where thetemperature of the ground water at depths of 23-40 m increased during a period of twomonths (14.7.66-14.9.66) from 10.5 to 14.5 "C in accordance with the increase in thewater temperature of the M. Almatinka River flowing near the well. In September,when the water temperature in the river stopped rising and then gradually began drop-ping, the temperature in the well at first began stabilizing and later began decreasingslowly. The nature of the thermograms in the zone of aeration and also the value of A tindicate that the upper interval of 5 to 15 m at the well site is composed of semi-

277

pervious rocks (fig. 4). This suggests that inflow of stream water takes place at somedistance from the well through "hydrogeological openings". The lag of the variation jof the ground water temperature as compared to the surface water temperature is Iindicative of this fact. ,/

Fig. 4 — Open type of hydrogeothermal zonation in case of recharge through;"hydrogeological openings" (Wells 220 and 221, Alma-Ata, 1966):

(a) Depth in metres;(b) Temperature in °C (±0.1 °C)(c) Temperature amplitude in °C ( ± 0.02 °C);1. Daily temperature variations in °C

a) minimum, at the stage of stabilization;b) maximum, in the period of water breakthrough in annular space);

2. Temperature variations (max), bi-weekly;3. Ditto, monthly;4. Ditto, bi-monthly;5. Temperature amplitude measurement point;6. The place of installation of the screen;7. Sandy clay yellowish-gray with pebble;8. Boulders with pebble and gravel, the filler is clay;9. Ditto, the filler is sand inequigranular, clayey;

10. Pebble with inclusions of boulders, filler is sand;11. Sandy clay yellowish-gray, dense;12. Pebble with boulders, filler is sand inequigranualr, clayey;13. Ditto, filler is sand with sandy clay interbeds;14. Static water level with head line.

The materials of the observations of the temperature regime also permit us, as afirst approximation, to have an idea of percolation conditions in local recharge areas;in this connection, spray recharge, recharge through the "hydrogeological openings"and recharge by dissipated percolation are distinguished. Peculiar temperature regimegraphs are characteristic of these types of recharge. When water percolates slowly anduniformly through the zone of aeration composed, for instance, of fine, uniform as togranulometric composition sands, the temperature amplitudes for different periodsdecrease regularly with depth (fig. 5). In fractured or gravel-pebble rocks due to com-plexity of seepage ways and due to the occasional nature of this recharge, the zone ofaeration is characterized both in the thcrmogram and the regime diagram by largevalues of At and the variability of values ofAt and / with depth (see fig. 2). The maxi-mum values of At are usually observed not only in the upper part of the section, butalso near the water table, i.e. in the zone of mixing of ground water and percolatingwaters. In these cases, during a month the value of At may exceed 5 °C. If rechargeoccurs through the "openings", in the thermograms inpervious beds are noted for

278

smaller values of temperature and At, and below the impervious beds temperature andAt vary in time much more rapidly.

j^pp^^r^^rr^y^r]^^

Fig. 5 — Open type of hydrogeothermal zonation under the conditions of dissipatedpercolation of surface water (Well 74, the village of Shchemilovo, Moscow Region):

(a) Temperature amplitudes in °C;1. Daily temperature variations in °C;2. Monthly temperature variations in °C;3. Seasonal (three-monthly) temperature variations in °C;4. Temperature amplitude measurement point;5. Vegetative layer;6. Fine sand;7. Water-bearing sand;8. Quicksand with inclusions of pebble.

Interesting thermometrical investigations while studying ground water recharge inthe zone of seasonal freezing have been carried out by Robert Schneider in 1961. Thecorrelation of curves obtained from automatic recording data of ground water leveland mean daily air temperature has shown that the ground water level lowers as airtemperature drops below 0 °C, i.e. in winter when the upper layer is frozen and perco-lation water flow through the zone of aeration stops. When air temperature rises abovezero, the water table at first rises slowly at the expense of thawing rocks from below.After full defreezing the ground water level curve sharply rises.

The knowledge of the general regularities of the hydrogeothermal regime is ofprime importance in studying thermal waters as, at first, it is the basis in the generalestimation of the prospects of the area as to thermal waters and then in preparing theinitial data for commercial deposits. The temperature within the stratisphcre at anydepth is determined from the initial increment of the temperature at ground surfacedepending on the latitudinal and altitudinal position of the investigation point (seefig. 3) and the temperature increment with depth that in turn depends on the gcothermalgradient characteristic of the given point. In general, the gradient increases from the

279

sites composed of dense old rocks to regions of recent orogenic movements composedof loose sediments with a high heat resistance. It also increases from areas of rechargeto the central parts of artesian basins, from the zone of active water exchange to zones ;of slow water exchange. On the average, the geothermal stage varies from 100 m/°C •'(crystalline shields) and 50 m/°C (areas with Pre-Cambrian folding) to 40 m/"C (areaswith Mesozoic folding) and 30 m/°C in areas with Cenozoic folding.

Based on the regularities revealed, maximum temperatures should be observed indeep troughs noted for high gradients and presence of aquifers of development value.Therefore, at the first stage, the problem of search of thermal water is reduced todistinguishing the central parts of artesian bassins on hydrogeothermal maps. Withincrystalline rock masses, volcanic regions and centres of deep ground water discharge,thermal anamolies are distinguished.

At the second stage, detailed hydrogeothermal maps are constructed for mostpromising aquifers. Along the base of the aquifer, isolines of temperature, specificyield, head, chemical composition and the minimum depth to thermal water are given(fig. 6).

Fig. 6 — Sketch map of the relief of isothermal surface + 20°C for the area of theUSSR compiled by N.M. Frolov and V.N. Shkatunkin:

1. Depth to the isothermal surface +20°C ranges from 50 to 250 m;2. Ditto, from 250 to 550 m;3. Ditto, from 500 to 1,000 m;4. Ditto, from 1,000 to 1,500 m;5. Ditto, over 1,500 m;6. Boundaries of shields and mountain-fold areas;7. Permafrost boundary;8. Positive thermal anomalies.

Thermometrical studies are also of great importance in studying ground waterwith the aim of development (determination of inflow sites, annular circulation andground water drainage in wells and in the annular space), these problems arc discussedby Dakhnov and Dyakonov (flaXHOB, flbMKOHOB, 1952). Leakage takes placeboth under natural conditions through semi-confining beds and under artificial

280

(disturbed) conditions (in the annular space). The author has noted in observationhydrogeological wells occasional "pulse" leakage of ground water (in the annularspace) into the lower artesian aquifer separated by a semi-confining bed 20 m thickand from this aquifer. The temperature épures show that water breakthrough occursoccasionally in 12-40 hours (fig. 7). Sometimes water breakthrough continues forseveral hours and then stabilization continues for several days. At the breakthroughtime, the ground water level drops, the temperature in the upper part of the confiningbed sharply increases, and below decreases.

In conclusion, let us make a calculation of heat transport by ground water from theearth's interior. Heat is transported on to ground surface by molecular heat conductionof rocks (?.), in the process of volcanic eruptions and also by ground water. At present,the first value is determined from the formula:

< ? = / • — • 5)oh

Volcanic regions cover a relatively small area of the earth's surface, ground wateris spread everywhere and, therefore, the convection component can not be neglected.The convection component can be determined if the quantity of water that dischargesper unit area at ground surface and water enthalpy are known. The first value ischaracterized by the modulus of ground water flow (m), and the second value is deter-mined from the product of the specific heat capacity (C) and excessive temperature (T).As r almost cannot be practically determined, it may be substituted (with a small error)by the average temperature of the rocks where discharging waters circulate:

T = 0 . 5 / 1 — (6)oh

where r is excessive temperature in CC; h is the thickness of the layer in cm; dtldh is thevertical gradient in "C/cm.

The total heat flow is determined using the following expression (<I>poflOl>, 1964,1966):

q = X?L+ 0.5 hmC—. (7)oh dh

As heat is transported not only from the upper hydrodynamic zone, in accurateinvestigations it is necessary to take into account the convection component for twolower zones as well, but due to a sharp decrease of the flow modulus with depth, thevalue of the convection component for lower zones is highly insignificant.

For different regions of the USSR, the convection component for the zone of inten-sive water exchange ranges from 0.5 • 10~8 cal/cm2 sec in platform areas with a poorlydissected relief to 3.5 • 10~4 cal/cm2 sec in mountain-fold areas with manifestations ofmodern and recent volcanism (see fig. 3). For all the area of the USSR ground waterflow to streams amounts to 880 km3 per year, and for the earth's land surface 12,000 km3

per year, the average modulus of ground water flow is equal to 1.3 and 2.5 1/secperkm2,respectively. The average thickness of the upper hydrodynamic zone of intensive waterexchange ranges from 50-100 m in plains to 500-1,000 m in mountain regions, and800 m for land surface on the average. If the excessive temperature of dischargingwater is assumed to be equal to the temperature gained in the middle of this zone, evenat the geothermal stage of 40 m/°C the temperature will be equal to 10 °C that leads tothe average value of the convection component for the area of the USSR equalling1.3 • 10~6 cal/cm2 sec and for the earth approximately 2.5 • 10~6 cal/cm2 sec.

281

oo

Fig. 7 — Temperature regime in Wells 220 and 221, Alma-Ata, at level of confining bed:(a) Depth in metres.

To estimate the convection component qc in the well for a separate aquifer, thefollowing formula is recommended:

qc = KhICy ^ (8)o;

where I is the flow gradient; y is the water density; ol/ôz is the aquifer temperaturegradient.

REFERENCES

Mink, J.F. Groundwater temperatures in a tropical island environment,J. Geophys. Res., Vol. 69, Ns 24, pp. 5225-5230, 1964.

Schneider, R. Discussion of paper by J.F. Mink « Groundwater tempera-tures in a tropical island environment », J. Geophys. Res., Vol. 70,JST» 16, pp. 4073-4074, 1965.

.ZJaXHOB B. H., .HbHKOHOB fl. H. TepMHTCCKHe HCCJieflOBaHHH CKBaJKHH.M., rocTonTexH3flaT, 1952.

OrmibBH A. H. TepMOMerpHH KEIK MCTOÄ rHAporeojiorH^ecKHXBaHHH. M., reoJioropa3BeflH3flaT, 1932.

4>poJioB H. M. H «p. MeTOflHiecKHe yKa3a«HH no myieHHioBOfl B cKBaHcimax. M., Heflpa, 1964.

«t>pojioB H. M. TeMnepaTypHbiö peHCHM reJiH0TepM030Hbr. M., Heflpa, 1966.

283