  The convergence of Levenberg-Marquard method is discussed for the inverse
problem to reconstruct the storage modulus and loss modulus for the so called
scalar model by single interior measurement. The scalar model is the most
simplest model for data analysis used as the modeling partial differential
equation in the diagnosing modality called the magnetic resonance elastography
which is used to diagnose for instance lever cancer. The convergence of the
method is proved by showing that the measurement map which maps the above
unknown moduli to the measured data satisfies the so called the tangential cone
condition. The argument of the proof is quite general and in principle can be
applied to any similar inverse problem to reconstruct the unknown coefficients
of the model equation given as a partial differential equation of divergence
form by one single interior measurement. The performance of the method is
numerically tested for the two layered picewise homogneneous scalar model in a
rectangular domain.
