  The use of simultaneous sources in geophysical inverse problems has
revolutionized the ability to deal with large scale data sets that are obtained
from multiple source experiments. However, the technique breaks when the data
has non-uniform standard deviation or when some data are missing. In this paper
we develop, study, and compare a number of techniques that enable to utilize
advantages of the simultaneous source framework for these cases. We show that
the inverse problem can still be solved efficiently by using these new
techniques. We demonstrate our new approaches on the Direct Current Resistivity
inverse problem.
