This paper describes the detection and classification of targets against clutter by distinguishing between linear and nonlinear scatterers and, further, by distinguishing those nonlinear targets that scatter energy at the even-powered harmonics from those that scatter in the odd-powered harmonics. This is done using twin inverted pulse sonar (TWIPS), which can also, in some manifestations, require no range correction (and therefore does not require the a priori knowledge of the environment needed for most remote detection technologies). The method applies, in principle, to a range of sensor technologies, including the use of radar to distinguish between circuitry, metal and soil; Light Detection and Ranging (LIDAR) to detect combustion products; and Magnetic Resonance Imaging (MRI). A sonar application is demonstrated, detecting objects in bubbly water (including in the wake of a ship of 3953 gross register tonnage). A manmade sonar that can operate in bubbly water is relevant: Cold War sonar is not optimized for the shallow coastal waters that typify many current operations. The US Navy use dolphins in such waters. TWIPS arose as a demonstration that echolocation was possible in bubbly water in response to a video showing dolphins generating bubble nets when hunting: if echolocation were impossible in these nets, then during this hunt, the dolphins would have blinded their sonar.