Estimation of mechanical properties of transversely isotropic media

A method for determining mechanical properties of an anisotropic media, the method comprising:

• disposing a logging tool in a wellbore;
• transmitting a plurality of waves from one or more transmitters disposed on the logging tool;
• receiving a corresponding response with one or more receivers disposed on the logging tool;
• obtaining log data of the anisotropic media, wherein the log data comprises the corresponding responses collected with the logging tool;
• determining values for a plurality of first stiffness components of a stiffness matrix based on horizontal and vertical velocities derived from the log data;
• determining an upper bound for a second stiffness component of the stiffness matrix based on the values for the plurality of first stiffness components;
• estimating a value for the second stiffness component based on the determined upper bound;
• determining a mechanical property of the anisotropic media based on the estimated value of the second stiffness component;
• and
• providing the determined mechanical property.