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On the different flavours of 1D seismic reference models

Introduction

To a very good first order approximation, the earth is made up of concentric spherical shells, and its average internal structure can be described in terms of variations of properties as a function only of depth. Measurements of travel times and amplitudes of seismic waves generated by large earthquakes and observed at distant stations contain information about the elastic and anelastic properties of the medium through which they travel. These measurements can be used to build models of seismic velocity, density, and attenuation structure with depth through mathematical inversion. Earth properties are observed to change laterally and vertically, but change most strongly with depth (lateral velocity variations are at most 10% laterally compared with 500% vertically) thus Earth structure can be well approximated by a 1-dimensional (spherically symmetric) model of elastic velocities, density, and attenuation as a function of depth (Fig. 1). Different 1D reference seismological earth models have been constructed using different data types, different parametrisation, and computation procedures. Knowing what choices have been made in the construction of a 1D seismological reference earth model is important when one wants to use such a model, depending on the application.

^[1]

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Figure 1 – 1-Dimensional Earth structure and velocities for the Preliminary Reference Earth Model or PREM ^[2] a. Radial Earth structure showing the major divisions. Solid lines mark discontinuities due to phase changes or compositional changes. b. Corresponding depth-dependent velocity structure for compressional and shear-waves (Vp and Vs, respectively). c. Depth-dependent density structure.

The differing sensitivities of the seismic observables used and the scatter in the measurements caused by lateral velocity structure (Fig. 2) mean that the resulting velocity structure is only an approximation of the true Earth and not representative of any real physical structure, mineral assemblage, or location. Caution must be taken when 1D reference models are used to interpret results from other disciplines, such as measurements or calculations of elastic properties of different mineral assemblages.

While reference models are approximations of the real Earth, they are needed for, among others, the following purposes:

• Determining earthquake locations, which involves converting times to distances and thus requires an understanding of wave propagation velocities.
• Identifying different kinds of seismic waves (phases) on seismic records is guided by calculations of predicted travel-times
• Predicting ray paths requires knowing the velocity structure
• Modelling the propagation of waves from earthquakes requires an understanding of the velocity structure
• Construction of 3D seismic models requires a starting model for the inversion process. Indeed, most of the non-linearity resides in the 1D model.
• Reference models are used to forward model standard travel-times and waveforms against which to compare observations to help identify variability
• Providing a reference for the interpretation of mineral physics experimental and computational data
• Providing a reference structure to inform dynamic modelling

Many current seismological studies rely upon reference models. While global 3D models of the Earth's mantle have been developed for over 30 years (e.g.

^[4]

[5]

), 1D models are still commonly used.

References

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