Spectra of poloidal aperiodic MHD ballooning eigenperturbations in the Earth's inner magnetosphere are studied with taking into account the finity of ionospheric conductivity and dipolar geometry of the geomagnetic field. We demonstrate that the same set of parameters can yield solutions with different growth rates. An analytic expression for the amplitude of longitudinal displacement near the ionosphere is derived. A stability criterion for flute and incompressible modes are obtained.