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The aim of this paper is to provide a local attenuation method with applications to tissue heterogeneity estimation based on the peaks of ultrasound echo envelop data. To handle the frequency shift in the broadband ultrasound system, we use nonlinear least squares (NLS) data fitting directly to the local amplitude changes due to the tissue attenuation. By looking at the convergence of the NLS method, e.g., the Levenberg-Marquardt (LM) algorithm, we proposed a technique to test the tissue heterogeneity locally. System calibrations have been presented to compensate the aperture growth and beam diffraction effects. Algorithms have been verified both in phantom and in vivo images. Results showed that the proposed method can have 3.8% relative error in estimating attenuation coefficients of phantom images in a broadband system. It also showed the possible tissue heterogeneity from in vivo image.