Ha. Spetzler et A. Yoneda, PERFORMANCE OF THE COMPLETE TRAVEL-TIME EQUATION OF STATE AT SIMULTANEOUS HIGH-PRESSURE AND TEMPERATURE, Pure and Applied Geophysics, 141(2-4), 1993, pp. 379-392
The complete travel-time equation of state (CT-EOS) is presented by ut
ilizing thermodynamics relations, such as; K(T) = K(S)(1 + alphagammaT
)-1, gamma = alphaK(S)/rhoC(P), partial derivative C(P)/partial deriva
tive P)T = -T/rho[alpha2 + partial derivative alpha/partial derivative
T)P], etc. The CT-EOS enables us to analyze ultrasonic experimental d
ata under simultaneous high pressure and high temperature without intr
oducing any assumption, as long as the density, or thermal expansivity
, and heat capacity are also available as functions of temperature at
zero pressure. The performance of the CT-EOS was examined by using syn
thesized travel-time data with random noise of 10(-5) and 10(-4) ampli
tude up to 4 GPa and 1500 K. Those test conditions are to be met with
the newly developed GHz interferometry in a gas medium piston cylinder
apparatus. The results suggest that the combination of the CT-EOS and
accurate experimental data (10(-4) in travel time) can determine ther
modynamic and elastic parameters, as well as their derivatives with un
precedented accuracy, yielding second-order pressure derivatives (part
ial derivative 2M/partial derivative P2) of the elastic moduli as well
as the temperature derivatives of their first-order pressure derivati
ves (partial derivative 2M/partial derivative P partial derivative T).
The completeness of the CT-EOS provides an unambiguous criterion to e
valuate the compatibility of empirical EOS with experimental data. Fur
thermore because of this completeness, it offers the possibility of a
new and absolute pressure calibration when X-ray (i.e., volume) measur
ements are made simultaneously with the travel-time measurements.