The gravity anomaly of a complicated two‐dimensional (2-D) source having arbitrary surfaces and density varying in either horizontal or vertical direction is calculated using a combination of closed form solutions and numerical integration. The surfaces and density can be defined by continuous or piecewise continuous two‐dimensional functions in the integration interval. For example, the anomalies for intrusions or folded sedimentary units, having an arbitrary density in the horizontal direction and a polynomial density distribution in the vertical direction, can be calculated using surfaces represented by functions of the horizontal dimension. When modeling dipping layered intrusions or sedimentary beds the surfaces are represented by functions of the vertical dimension in which case the density can be an arbitrary function of depth and a polynome function of horizontal coordinate. The accuracy of the method is defined by the user. The method gives simple and general equations to calculate anomalies of complicated sources which have no closed form solution, thus reducing the number of algorithms needed in interpretation programs.

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In bedlock covered by continental ice, the depth to electrically conductive saline waters enriched below permafrost can be defined by electromagnetic measurements. Thus, if the ice thickness is also measured we obtain estimates of permafrost thickness variations in the survey area. Moreover, using the relation between ice and permafrost thicknesses and approximations of the melting temperature of saline waters combined with the average annual temperature at the surface, we can estimate temperature variations within both the bedrock and the ice. These can further be used for estimating the temperature values at the ice base. The method was developed for interpreting two geophysical field profiles measured on continental ice in western Dronning Maud Land, Antarctica. Gravity, magnetic and electromagnetic profiles were measured between the nunataks Basen and Plogen (≈22 km) and Basen and Fossilryggen (≈38km). In the Basen–Fossilryggen profile the electromagnetic soundings revealed good conductors in the bedrock beneath the ice. The significant correlation between the ice thickness and the depth of the conductor in the bedrock strongly suggests that the conductors are not sedimentary rock layers but rather saline groundwater in which salinity has been enhanced by permafrost processes. From the regression curve we can conclude that the temperature vs depth curve in the ice can be represented by a first-degree line and that the “warm” ice base of about −2° C is expected to occur at depths of about 650 m, the base of permafrost in outcropping bedrock being at about 1 km. The mean temperature gradients in the ice and in the bedrock can be estimated as being about 20°Ckm−1 and 13°C km−1 respectively. In the Basen–Plogen profile, conductors were detected only in the beginning of the profile, where ice thickness was below 650m. In the main part of the profile where the ice thickness exceeds 650 m, no conductors were observed. In those areas our interpretation is that the icebase is “warm” and no saline waters enriched by permafrost are present.

ABSTRACT. In bed roc k covered by co ntin e nta l ice, the d e pth to elec trica ll y co nduct i\'C sa lin e wate rs e nri c h e d be low p er m a fr os t ca n b e d e fin ed by ele c trom ag n e ti c meas urem e nts. Thus, if th e ice t hi ckness is a lso m eas ured we o bt a in es tim ates o fp crm ali'ost thickn ess \'a ri ations in th e sun'ey a rea. iVlo reO\'er, using th e rel ati on betwee n ice a nd permafrost thicknesses a nd a pprox im ati o ns of th e mel ting tempe rature of sa lin e wa ters combin ed w ith the m'C rage a nnu a l tempe ra ture a t t he sur facc, wc can es tim a te temperal ure \'ari a ti ons within bo th th e bedrock a nd th e ice. Th ese ca n furth er be use d fo r estima ting th e te m pe ra ture \'alues a t th e ice base.Th e m e th od was de \'e lo p ed fo r in terp re ting two geophys ica l fi e ld profil es m eas ured on co ntin ent a l ice in wes tern Dro n n ing Ma ud La nd , Anta rctica. G rav ity, mag neti c a nd e lectromagne tic pro files \\'e re m eas ured betwee n th e nun ata ks Base n a nd Ploge n (~22 km ) a nd Base n a nd Fossilrygge n (~38 km ). In th e B ase n~Fossi l rygge n profi le the e lect rom agneti c so und i ngs 1'C \'Ca led good co nductors in t h e bed roc k ben ea th the ice. Th e sig n i fi ca nt cor rela ti o n be t ween th e ice thi c kn ess a nd th e d epth o f th e co nductor in th e b e droc k st ro ng ly suggests t hat th e co nd uctors a rc no t sedimen ta r y roc k laye rs but ra th e r salin e groun dwa ter in which salinit y has bee n enh a nced by perm a fr os t processes. Fro m the reg ress io n cu n T wc ca n co nclud e t hat th e te mperat ure \'s de pth C lln T in the ice ca n be re presrn ted b y a first-deg ree lin e and th at th e "wa rm" ice base o f a b o ut 2 C is ex pected to occ ur a t d e pth s o f abo ut 650 m , the base o f p e rm a fr os t in o utcropping bedroc k b e ing a t abo ut I km . Th e mea n temper a t ure g rad ie nts in th e ice a nd in th e bed rock ca n b e estimated as b e ing abo ut 20 C km I a nd 13 c: km I, respeCl i\·ely.In th e Base n Pl oge n p ro fi le, conducto rs were d etected o n I)' in the begi nn i ng o f' t he profile, w he re ice th ic kness \\'as below 650 m . I n the ma in part o f t he profile w h ere th e ice th ickn ess exceeds 650 m , no conductors we re o bse l'\'Cd. In th ose a reas our int e rpre tati on is th a t t he ice base is "wa rm" a nd no sa l i ne waters enriched b y perm a fr os t a re prese nt.

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