Part I: Lower limit of the total energy of earthquakes and partitioning of energy among seismic waves. Part II: Reflected waves and crustal structures
<p>Part I:</p> <p>The basic formulae for estimating the energy in the seismic waves are derived. The formulae take into account the radiation pattern of the source, the compensation for the non-elastic absorption of the waves, the velocity-density structure of the earth, the effec...
| Summary: | <p>Part I:</p>
<p>The basic formulae for estimating the energy in the seismic waves are derived. The formulae take into account the radiation pattern of the source, the compensation for the non-elastic absorption of the waves, the velocity-density structure of the earth, the effects of the crustal structure under the receiver and the response of the recording instruments. Operations are performed in the frequency domain.</p>
<p>Estimation of the seismic energy of an earthquake is closely related to the determination of the source mechanism and the radiation pattern of the source. We have determined the surface wave radiation pattern of a shallow shock and the P wave radiation pattern of an intermediate shock to show the correspondence between the fault-plane solutions and the fault mechanisms derived from radiation pattern.</p>
<p>We have obtained the energies of the two earthquakes mentioned above as well as 7 other earthquakes with known fault-plane solutions and/or radiation patterns. The "total" seismic energies for these earthquakes (magnitudes between 6 1/2 and 7 1/2) using the present procedures are at least an order of magnitude higher than those arrived at from the current magnitude-energy formula. The S wave energies are approximately an order higher than that of the P waves.
The surface wave energies for the shallow shocks are three orders of magnitude less than the body wave energies. Thus, the S wave seems to be the main seismic wave energy carrier.</p>
<p>Energies in the lower order spheroidal oscillations (ℓ = 2, 15) for the 1964 Alaskan earthquake have been calculated from Isabella strain data and Berkeley ultra-long period pendulum seismometer data. The sum of the energies is 10<sup>23</sup> ergs.</p>
<p>Part II:</p>
<p>Haskell's formulation for reflection of the body waves at the
base of a solid crust is extended to include overlying liquid layers.
Normalized displacement and the phase shift at the base of the crust
as a function of angle of incidence and frequency are calculated for
two continental models and an oceanic model. Complex reflection
coefficients are inverse-Fourier transformed numerically to the
time domain to show the change of pulse shape upon reflection. These
time traces show that the water layer of the oceanic model causes
the main difference between continental and oceanic reflections.
Sample seismograms from a deep shock were compared to the theoretical
records; they are found to be consistent. PP waves from a deep
earthquake recorded at Tonto Forest Seismic Array were processed to
display the details of an oceanic PP wave.</p>
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