A method for estimation of propagation and scattering parameters in an object (200, 606,700), comprising transmitting at least two pulse complexes, each composed of an overlapping high frequency HF and a low frequency LF pulse (203, 205) along at least one common HF transmit beam axis, where said HF pulse propagates close to the crest or trough of the LF pulse, and where one of the amplitude and polarity of the LF pulse varies between the at least two transmitted pulse complexes, where the amplitude of the LF pulse can be zero for a pulse complex and the amplitude of the LF pulse for at least one pulse complex of said at least two transmitted pulse complexes is non-zero, and directing at least one HF receive cross-beam (209, 609, 612, 704, 705, 814) to cross said at least one HF transmit beam axis at an angle > 20 deg to form cross-beam observation cells (Rij) by the cross-over regions defined by the product between each of said at least one HF receive cross-beam and each of said at least one HF transmit beam (202, 605, 807), and recording at least two HF cross-beam receive signals scattered from object structures in each cross-beam observation cell (Rij) from said at least two transmitted pulse complexes with different LF pulses, and processing said HF cross-beam receive signals for each said at least one HF receive cross-beams to provide at least one of i) an estimated nonlinear propagation delay NPD and ii) an estimated nonlinear pulse form distortion PFD of the transmitted HF pulse at image points along said at least one HF transmit beam axis where said HF transmit beam axis and said at least one HF receive cross-beam axis have shortest distance within each of said cross-beam observation cells (Rij), and using said estimated PFD and/or NPD for further processing to form measurements of object propagation and scattering parameters at said image points. where said HF pulse propagates close to the crest or trough of the LF pulse, and where one of the amplitude and polarity of the LF pulse varies between the at least two transmitted pulse complexes, where the amplitude of the LF pulse can be zero for a pulse complex and the amplitude of the LF pulse for at least one pulse complex of said at least two transmitted pulse complexes is non-zero, and directing at least one HF receive cross-beam (209, 609, 612, 704, 705, 814) to cross said at least one HF transmit beam axis at an angle > 20 deg to form cross-beam observation cells (Rij) by the cross-over regions defined by the product between each of said at least one HF receive cross-beam and each of said at least one HF transmit beam (202, 605, 807), and recording at least two HF cross-beam receive signals scattered from object structures in each cross-beam observation cell (Rij) from said at least two transmitted pulse complexes with different LF pulses, and processing said HF cross-beam receive signals for each said at least one HF receive cross-beams to provide at least one of i) an estimated nonlinear propagation delay NPD and ii) an estimated nonlinear pulse form distortion PFD directing at least one HF receive cross-beam (209, 609, 612, 704, 705, 814) to cross said at least one HF transmit beam axis at an angle > 20 deg to form cross-beam observation cells (Rij) by the cross-over regions defined by the product between each of said at least one HF receive cross-beam and each of said at least one HF transmit beam (202, 605, 807), and recording at least two HF cross-beam receive signals scattered from object structures in each cross-beam observation cell (Rij) from said at least two transmitted pulse complexes with different LF pulses, and processing said HF cross-beam receive signals for each said at least one HF receive cross-beams to provide at least one of i) an estimated nonlinear propagation delay NPD and ii) an estimated nonlinear pulse form distortion PFD i) an estimated nonlinear propagation delay NPD and ii) an estimated nonlinear pulse form distortion PFD of the transmitted HF pulse at image points along said at least one HF transmit beam axis where said HF transmit beam axis and said at least one HF receive cross-beam axis have shortest distance within each of said cross-beam observation cells (Rij), and using said estimated PFD and/or NPD for further processing to form measurements of object propagation and scattering parameters at said image points.