We present a simple and effective method for deterministic estimation of time-space characteristics of seismic sources. These characteristics (time signature, spatial distribution, and radiation pattern) can be important for such geophysical applications as deconvolution, inversion, and Amplitude Versus Offset (AVO) analysis. The proposed method can be applied to two-dimensional marine data obtained using the dual streamer acquisition technique. Our estimation procedure is based on decomposition of the measured wave field into plane waves with subsequent separation of up- and downgoing components. After the separation, a simple estimation algorithm formulated for the one-dimensional case is applied to each plane wave. Then the amplitudes of the plane waves measured at various propagation angles can be used to estimate the angular distribution of source radiation. Finally, the source time function and spatial distribution are estimated by synthesis of the plane waves. A number of numerical examples show that the proposed estimation procedure can produce good estimates of the source characteristics.