EXPRESS ANALYSIS OF TRANSIENT ELECTROMAGNETIC DATA ACQUIRED ON THE WASTE RESERVOIR DAM IN STEBNYK

Abstract

Electro­mag­ne­tic (EM) met­hods of ge­ophysics al­low to ima­ge the sub­sur­fa­ce con­duc­ti­vity distri­bu­ti­on by analyzing da­ta me­asu­red on the Earth sur­fa­ce. The tran­si­ent electro­mag­ne­tic (TEM) so­un­ding met­hod is a ti­me-do­ma­in control­led so­ur­ce one which uti­li­ze a non-sta­ti­onary tran­si­ent pro­cess of the EM fi­eld de­ca­ying in the con­duc­ti­ve me­di­um due to the step cur­rent ex­ci­ta­ti­on which is descri­bed by the He­avi­si­de functi­on. The mat­he­ma­ti­cal and al­go­rithmic to­ols for express analysis of such ex­pe­ri­men­tal da­ta ac­qui­red for the TEM met­hod are pre­sen­ted in this ar­tic­le, the prac­ti­cal appli­ca­ti­on of which is so­me­ti­mes im­por­tant for ex­pe­ri­men­tal in fi­eld me­asu­re­ments, sin­ce it al­lows as to ma­ke im­me­di­ate de­ci­si­ons on op­ti­mi­za­ti­on of ex­pe­ri­men­tal fi­eld work as well as to qua­li­ta­ti­vely es­ti­ma­te the sta­te of the ob­ject un­der study. The pro­po­sed express analysis al­go­rithm is de­ve­lo­ped on the ba­sis of a wi­dely used transfor­ma­ti­on of the ex­pe­ri­men­tal TEM cur­ve, al­so known as the S-in­ver­si­on, which in turn is ba­sed on the appro­xi­ma­ti­on of a con­duc­ti­ve half-spa­ce by a thin she­et which is im­mer­sing in­to a non-con­duc­ti­ve half-spa­ce with the de­ca­ying of tran­si­ent pro­cess in the EM fi­eld. To re­du­ce the influ­en­ce of no­ise in­to the me­asu­red da­ta, we carrying out the appro­xi­ma­ti­on of the ex­pe­ri­men­tal so­un­ding cur­ves ac­co­un­ting se­ve­ral as­pects: the so­lu­ti­ons of eq­ua­ti­ons which descri­be the pe­net­ra­ti­on of EM fi­eld in­to a con­duc­ting me­di­um; the functi­on of the cu­bic spli­ne; and ele­ments of mat­he­ma­ti­cal analysis of con­tin­uo­us functi­ons. Ac­cor­ding to pro­fi­le me­asu­re­ments, one di­men­si­onal mo­dels of re­sis­ti­vity distri­bu­ti­on we­re ob­ta­ined using the cre­ated express analysis to­ols and a pseu­do two di­men­si­onal mo­del of the geoelectric cross-sec­ti­on of the was­te re­ser­vo­ir dam which is next to the Stebnyk town was construc­ted on the­ir ba­sis. The analysis of the ob­ta­ined mo­dels al­lo­wed us to de­tect two are­as whe­re it is de­si­rab­le to carry out ad­di­ti­onal stu­di­es to cla­rify the ge­olo­gi­cal sit­ua­ti­on. Of co­ur­se, al­go­rithms for in­ver­si­on of ex­pe­ri­men­tal da­ta, both as from a mat­he­ma­ti­cal po­int of vi­ew as well as from the po­int of vi­ew of al­go­rithm imple­men­ta­ti­on, are much mo­re compli­ca­ted. Ho­we­ver, if one imple­ments a fast and ef­fi­ci­ent one-di­men­si­onal in­ver­si­on al­go­rithm for the TEM da­ta inste­ad of the transfor­ma­ti­on men­ti­oned abo­ve, it will be pos­sib­le to sig­ni­fi­cantly impro­ve the re­li­abi­lity of the re­sult.