Martian Cataclysm: Impact energy analysis in support of the origin of multiple anomolies on Mars (cont.)
by Gary R. Spexarth
2.0 Impact Energy of Hellas
First, lets look at the impact energy of the Hellas Basin so that it may be determined if enough energy was transferred to the planet to cause massive destruction.
The calculation of the Hellas energy of impact is given in Appendix I and is shown to be 5.33x1026 Joules. By comparison, the impact energy of the K/T impact over 65 million years ago that extinguished 75% of life on Earth and excavated a crater at least 200 km in diameter (Chicxulum in Mexico) was 4.21x1023 Joules .
It can be seen that the energy imparted to the Mars system by the Hellas Impactor is over 1200 times more energy than was input into the Earth system by the K/T impactor, and Mars is only 1/8 the volume of Earth! It will be shown that this amount of energy is capable of extensive global transformations and destruction of Mars.
3.0 Formation of Valles Marineris and Tharsis Montes
The formations of the Tharsis Montes and the Valles Marineris are still a topic of debate. It has been suggested that they have been formed out of geological processes such as volcanism, erosion, etc .
However, Patten suggests that Valles Marineris is a rupture in the Mars surface due to massive multiple impacts in the Southern hemisphere . Similarly, Williams, et. all proposed that the Tharsis Region is a formation of impact-induced features, which are created as the energy of the Hellas Impact is attenuated through the interior of the planet, and focused 180 degrees from the Hellas impact (Tharsis Montes) .
But, was there enough energy associated with the massive impact that created the Hellas Basin to bulge the planet on the other side and rupture the surface of the planet? Appendix II derives the equations for, and computes, the energy required to rupture Mars.
Figure-3: Formation of the Tharsis Montes and Valles Marineris
Credit: G. Hancock
For analysis purposes, Mars will be treated as a thin-walled spherical pressure vessel. When performing structural analysis of pressure vessels, the equations for thin-walled pressure vessels should be used when the ratio of the radius to the wall thickness is greater than 10 . Willemann and Turcotte  show that the Mars lithosphere thickness is estimated to be anywhere from 110 km to 260 km. Therefore, the ratio of the radius of Mars (3375 km) to the lithosphere thickness may range from 30 to 13 and the equations for thin-walled pressure vessels apply.
Appendix II shows that the energy required to rupture the Martian lithosphere is calculated to be 1.90x1026 to 4.50x1026 Joules (depending on the lithosphere thickness assumed), which is 36% to 84% of the total energy input to the Martian system by the Hellas impactor. In other words, only 36% to 84% of the total energy created by the Hellas impact would be required to rupture the planet. So, yes, there was sufficient energy to rupture the planet and form the Valles Marineris!
Excessive yielding prior to ultimate failure would deform the lithosphere at the location of rupture; thus "bulging the planet" and forming the Tharsis Montes, which is located at the 180 degrees away from the Hellas Basin . This has been discussed by Hancock  as illustrated in Figure-3 .