Many low-mass white dwarfs are being discovered in the field of our galaxy and some of them exhibit $g$-mode pulsations, comprising the extremely low-mass variable (ELMV) stars class. Despite it is generally believed that these stars are characterized by thick H envelopes, from stellar evolution considerations, the existence of low-mass WDs with thin H envelopes is also possible. We have performed detailed asteroseismological fits to all the known ELMVs to search for a representative model by employing a set of fully evolutionary models that are representative of low-mass He-core white dwarf stars with a range of stellar masses $[0.1554-0.4352] M_{odot}$, effective temperatures $[6000-10000] $K, and also with a range of H envelope thicknesses $-5.8 lesssim log(M_{rm H}/M_{star}) lesssim -1.7$, hence expanding the space of parameters. We found that some of the stars under analysis are characterized by thick H envelopes, but others are better represented by models with thin H envelope.
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