A task-specific, multiparameter (more than one mechanical property changes across a reflector), direct nonlinear inversion subseries of the inverse-scattering series is derived and tested for an acoustic medium in which velocity and density vary vertically. Task-specific means that terms in the distinct subseries corresponding to tasks for imaging only and inversion only are identified and separated. Direct means there are formulas that solve explicitly for and output the physical properties, without, e.g., search algorithms, model matching and optimization schemes, and proxies that typically characterize indirect methods. Numerical test results with analytic data indicate that one term beyond linear provides added value beyond standard linear techniques, and the improved estimates are valid over a larger range of angles. The direct acoustic inversion is nonlinear. It serves as an important step for new concepts and methods to guide the much more complicated and minimally realistic elastic inverse for exploration seismology target identification purposes.