Before revision:  In the paper, we elaborate one-dimensional and two-dimensional MFDMA theoretically and apply the methods to synthetic multifractal measures  .
After revision:  In the paper, we elaborate one-dimensional and two-dimensional MFDMA theoretically and apply the methods to synthetic multifractal measures with analytical solutions for backward (\theta=0), centered (\theta=0.5), and forward (\theta=1) detrending windows .