During the solidification of a lava lake heat is released convectively from the top surface as well as conductively into the country rock from the base, leading to non-uniform solidification. The upper solidified layer grows at a faster rate than the lower solidified layer. Similarly, solidification of magma intrusion within the crust is also non-uniform due to the presence of thermal gradient in the crust. Available analytical solution for solidification of a melt layer assumes only symmetric cooling about the centre of the layer. In the present work a moving boundary solution for thermal evolution and non-uniform solidification of a melt layer incorporating time-varying contact temperature conditions at both of its boundaries is developed. The solution is obtained by using the Fourier spectral approach in the space domain and a modified finite difference scheme in the time domain, and is validated with available analytical solutions for simple cases and a semi-analytical solution for the case involving temperature gradient in the country rock. This solution can be used to analyse solidification of lava lakes and magma intrusions experiencing time-dependent temperature variation at their contacts with the country rock.

In many parts of the world sedimentary horizons with potential for hydrocarbon are located below flood basalt provinces.However,the presence of high velocity basaltic overburden makes delineation of sediments difficult due to the low velocity layer problem.Electrical and electromagnetic methods have been used in such scenarios because of the good electrical conductivity contrast between basalts and underlying sediments.However,mapping of the target sediments becomes difficult when the layer is thin as the data errors due to inherent noise lead to equivalent solutions.To tackle such difficult situations,a joint inversion scheme incorporating seismic reflection and refraction, magnetotelluric and deep electrical resistivity datasets is presented. Efficacy of the scheme is tested for a model comprising a thin sedimentary layer sandwiched between a thick basalt cover and a granitic basement.The results indicate that the parameters of the target sedimentary layer are either poorly resolved or equivalent solutions are obtained by the inversion of individual datasets. Joint inversions of seismic reflection (RFLS)and refraction (RFRS),or DC and MT dataset pairs provide improved results and the range of equivalent solutions is narrowed down.Combination of any three of the above datasets leads to further narrowing of this range and improvements in mean model estimates.Joint inversion incorporating all the datasets is found to yield good estimates of the structure.Resolution analysis is carried out to appraise estimates of various model parameters obtained by jointly inverting different combinations of datasets.