We present an algorithm to estimate blocky images of the subsurface acoustic impedance (AI) from seismic reflection data. We use the total variation semi-norm (TV) to regularize the inversion and promote blocky solutions which are, by virtue of the capability of TV to handle edges properly, adequate to model layered earth models with sharp contrasts. In addition, the use of the TV leads to a convex objective function that can be minimized using a gradientbased algorithm that only requires matrix-vector multiplications and no direct matrix inversion. The latter makes the algorithm numerically stable, easy to apply, and economic in terms of computational cost. Besides, given appropriate a priori information, the algorithm allows to easily incorporate into the inversion scheme the low frequency trend that is missing from the data. Numerical tests on noisy 2D synthetic and field data show that the proposed method is capable of providing consistent and blocky AI images that preserve edges and the subsurface layered structure.Facultad de Ciencias Astronómicas y Geofísicas