Jökull - 01.12.1977, Page 89

fluid surface allowed to recover to the equi-
librium position. Using equations (28) and (15),
we find on the basis of (23) that the position
of the fluid surface duing the recovery period
is given by
h (S,t) =
-(v„/27rgC) [(l/rSQ. (wto)) - (l/rgQ,t)], (36)
where t > t0 and
rSQ’ (t-t0) =
[(x-x')2 + (y-y')2 + (a(t—t0)+d)2]V4.
The initial rate of recovery at S0 vertically
above the sink is
r (So>lo+) = d*1 (S0>to+)/^t
= (v0/27Tg(/)d2) [1—d2/(at0-f d)2]. (38)
As indicated in the introduction, the above
results have been obtained on the assumption
of an incompressible aquifer. In other words,
the elastic capacitivity or storage capacity of the
fluid-rock system has been neglected (see for
example De Wiest, 1965). The rationale for this
assumption is that in most practical cases the
time scale of the elastic effects is much shorter
than that of the free surface effect. The elastic
response of the aquifer to an impressed loading
will be mostly completed before a noticeable
free surface effects appears. Moreover, the in-
clusion of the elastic effects in the theory leads
to a considerably more complex mathematical
analysis. An elementary investigation which will
not be discussed here indicates that the results
developed above will be essentially valid for
sinks and/or sources at depths up to a few
kilometers. The interaction of the elastic and
free surface effects will become important when
the sources or sinks are located at greater depths.
ACKNOWLEDGMENT
This research was supported by the U. S. Geo-
logical Survey Extramural Geothermal Research
Program under Grant No. 14—08—0001—G—398.
REFERENCES
De Wiest, R. J. M. 1965. Geohydrology. John
Wiley and Sons, New York, 366 pp.
Duff, G. F. D. and D. Naylor. 1966. Differential
Equations of Applied Mathematics. John
Wiley and Sons, New York, 423 pp.
ÁGRIP
Reikningslegar athuganir á grunnvatnsstreymi
með óbundnu yfirborði eru yfirleitt erfiðar.
Grundvallarjöfnur slíkra líkana eru jafnan
ólínulegar. Við athuganir hagnýts eðlis, einkum
á jarðhitasvæðum, má þó oft gera ráð fyrir til-
tölulega litlum hreyfingum vatnsyfirborðsins.
Þá má beita línulegum nálgunaraðferðum, en
þær eru alkunnar í eðlisfræði. Sýnt er fram á
hvernig nota megi slíkar aðferðir við grunn-
vatnsrannsóknir. Niðurstöður þær, sem lagðar
eru fram, má einkum nota á jarðhitasvæðum, en
þar eru borholur yfirleitt svo djúpar, að um-
rædd nálgun nær ágætum árangri.
JÖKULL 27. ÁR 87