A method for determining pore pressure in a formation through a metal casing of a borehole , comprising: generating strain in a volume surrounding the borehole by focusing a low frequency, sinusoidal acoustic signal in the volume, the low frequency, sinusoidal acoustic signal having a first frequency and a first amplitude; transmitting pulsed, high frequency acoustic signals through the volume when the strain is generated in the volume with the low frequency, sinusoidal acoustic signal; measuring signals generated in the formation in the volume relating to particle velocity or particle acceleration in the formation via a sensor disposed inside the borehole and in contact with the metal casing ; determining the strain in the volume from the signals generated in the formation in the volume relating to the particle velocity or the particle acceleration in the formation ; measuring time-of-flight of the pulsed, high frequency acoustic signals through the volume as a function of the strain in the volume; determining change of the time-of-flight of the pulsed, high frequency acoustic signals as a function of the strain in the volume; determining nonlinear elastic parameters α, β, and δ based on the change of the time-of-flight of the pulsed, high frequency acoustic signals as a function of the strain in the volume, wherein determination of the nonlinear elastic parameters includes determination of the nonlinear elastic parameter α based on an inverse of the particle acceleration and a ratio of change in perturbed velocity to linear velocity; and determining pore pressure in the volume based on the nonlinear elastic parameters α, β, and δ. generating strain in a volume surrounding the borehole by focusing a low frequency, sinusoidal acoustic signal in the volume, the low frequency, sinusoidal acoustic signal having a first frequency and a first amplitude; transmitting pulsed, high frequency acoustic signals through the volume when the strain is generated in the volume with the low frequency, sinusoidal acoustic signal; measuring signals generated in the formation in the volume relating to particle velocity or particle acceleration in the formation via a sensor disposed inside the borehole and in contact with the metal casing ; determining the strain in the volume from the signals generated in the formation in the volume relating to the particle velocity or the particle acceleration in the formation ; measuring time-of-flight of the pulsed, high frequency acoustic signals through the volume as a function of the strain in the volume; determining change of the time-of-flight of the pulsed, high frequency acoustic signals as a function of the strain in the volume; determining nonlinear elastic parameters α, β, and δ based on the change of the time-of-flight of the pulsed, high frequency acoustic signals as a function of the strain in the volume, wherein determination of the nonlinear elastic parameters includes determination of the nonlinear elastic parameter α based on an inverse of the particle acceleration and a ratio of change in perturbed velocity to linear velocity; and determining pore pressure in the volume based on the nonlinear elastic parameters α, β, and δ. <EOS>