Renormalization of the magnitude scale

Seismic source parameters of 27 earthquakes in the magnitude range 7.0–8.5 that occurred during 1906–1969 and that were determined mostly from inversion of long-period seismic surface waves in the period range 100–200 s are re-examined. Among these are five re-evaluations (Chile, May 1960; Sanriku, March 1933; Assam, August 1950; Alaska, July 1958; Alaska, March 1964) and six new analyses (Aleutian Ils., March 1957; Peru, Nov. 1947; New Guinea, Feb. 1938; Queen Charlotte Ils., August 1949; San Francisco, April 1906; Kern County, July 1952).It is shown both theoretically and experimentally that the strong azimuthal dependence of the far displacement field makes the 20-s magnitude vulnerable to uncertainties up to $\text{2}\text{3}$ unit of magnitude. These uncertainties are inherent in the magnitude definition, depend on the azimuth of the observer and are unremovable.A remedy is offered in the form of a new magnitude scale, based on the cube root of the potency (product of fault area S and average slip $\text{U}$). In the magnitude range 6.75–8.5 this scale is centigrade. It is shown that $\text{(}\text{U}\text{S)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ is the “azimuth-free” part of the Richter magnitude and its adoption as a basis for a new magnitude scale may rid observations of azimuthal ambiguities.     

Seismic codas on the Earth and the Moon: a comparison

The phenomenon of the seismic coda, which is composed of seismic energy delayed by scattering, is seen on both the Earth and the Moon. On the Moon the scattered coda is very large relative to body wave arrivals with a delay of the time of maximum energy, whereas on Earth scattered codas are relatively small and show no delay of the energy maximum. In both cases the form of the coda is controlled by three distance scales, the mean free path L, which is the average distance seismic energy travels before it is scattered, the attenuation distance $\text{x1}$, which is the average distance seismic energy travels before it is attenuated, and the source-receiver distance R. Two coda models are discussed based on these parameters; a strong scattering (diffusion) model, and a weak scattering (single scattering) model. A discussion of the diffusion scattering model indicates that if $\text{x1/L ? 1}$, diffusion scattering is an appropriate model, but if $\text{x1/L ? 1}$, single scattering is the appropriate model, within the appropriate range of R. A survey of the literature indicates that for the frequency range 0.5–10 Hz, diffusion scattering is important in lunar codas, but for the frequency range 1–25 Hz single scattering is important in terrestrial codas. Another important effect of attenuation is the elimination of scattering paths much longer than $\text{x1}$. On the Moon, this means that seismic energy in the coda can only propagate directly in the near-surface strong scattering zone between surface sources and the seismometer for source-seismometer separations of the order of $\text{(x1L)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$; otherwise, scattering is limited to regions near the source and the receiver. On Earth, this effect probably prevents multiple scattering.     

Source mechanism of the 1906 San Francisco earthquake

Surface-wave amplitudes in the period range 50–100 s at eight European and North American stations, horizontal slip profiles along the rupture zone and the timing of certain events along the fault during rupture time are all engaged in unison to reconstruct the motion at the source. A modified source model is used to accommodate a moving rupture with variable dislocation in the direction of propagation.It is inferred that the rupture started at about 13 h 11 m 55 s GMT near San Juan Bautista and propagated unilaterally northwestward along N35°W over 400 km with an average rupture velocity of 3.5 km/s. At 13 h 12 m 12 s, the dynamic shear front, moving with the rupture speed, hit the Lick Observatory. Then, at 13 h 12 m 18 s, the rupture arrived to the vicinity of the epicenter in the Santa Cruz Mountains given by B. Bolt. There the slip changed sharply from an average of 0.5 m to a high value of 3 m causing extensive landslides and avalanches. At 13 h 12 m 32.5 s two railroad clocks at San Rafael were stopped. Finally, at 13 h 12 m 36 s the offset front hit the Naval Observatory at Mare Island and stopped the astronomical clocks there. Conspicuous surface waves, visible on Wiechert seismograms in Europe in the period range 55–65 s, reflect the true rupture time.The seismic data inversion yields an effective radiation source some 240 km long with an average vertical extent of some 34 km over a total fault length of 400 km ($\text{U}\text{d}\text{S ? 29,000}\text{m km}{}^2\text{or}\text{μ}\text{U}\text{d}\text{S ? 9 · 10}{}^{27}\text{dyn cm}$). It began at the Santa Cruz Mountains and ended some 20 km off coast Point Arena. Thus, due to the nonuniform slip profile, only $\text{3}\text{5}$ of the total fracture length contributed to the far radiation field.Although the product of the average source displacement (over the entire fault) and the vertical extent appears to be fairly well determined from the surface-wave spectrums, the separate values of these entities cannot be uniquely determined. If the average surface displacements (～ 3.2 m) are diagnostic of the entire fault, a vertical extent of H = 34 km is required.Finally, a new analysis of surface waves from the Alaska earthquake of July 10, 1958, the Queen Charlotte Islands earthquake of August 22, 1949 and the Kern County shock of July 21, 1952, enables us to draw parallels between the three biggest major events which occurred along the NE Pacific coast during 1906–1958. A common feature of all of these earthquakes is that vertical failure extents of 30–40 km are implied.     

The Vrancea,Romania, earthquake of March 4, 1977 — a quite successful prediction

The available data on the destructive intermediate earthquakes ($\text{M ? 6}\text{3}\text{4}$) in the Vrancea, Romania, region have been examined with the aim of revealing some time-magnitude regularities. The basic idea is that the total sequence (? 1100–1973 yr.), which appears as random, could be decomposed in some regular source-components which, by extrapolation, are superimposed to predict the future total sequence.The common nature of faulting (reverse dip-slip) and inferred regularities in the time-magnitude pattern of destructive Romanian earthquakes — (a) three active (seismic) time-bands alternating with quiet periods, the existence of (b) “quasicycles” and of (c) “supercycles” — led to the following predictions: (1) the occurrence of a shock with $\text{M ≈ 6}\text{3}\text{4}\text{? 7}$ in 1980 ± 13 years; and (2) later earthquakes are predicted in 2005, in 2030–2040 ($\text{M ≈ 6}\text{3}\text{4}\text{? 7}$), and one with nearly maximum magnitude ($\text{M = 7}\text{1}\text{2}\text{?7}\text{3}\text{4}$) in 2070–2090.In every century, about 40 years represent a time interval of high seismic danger for Romania and, according to the proposed long-term time-magnitude model, three destructive earthquakes arc to occur in (and/or near) the evidenced seismic periods P₁, P₂ and P₃.It is shown that, taking into account the actual difficulties involved in the earthquake prediction, the Vrancea destructive earthquake of March 4, 1977 (M = 7.1) was quite successfully predicted.     

Q-structure beneath the Tibetan Plateau from the inversion of Love- and Rayleigh-wave attenuation data

The fundamental mode Love and Rayleigh waves generated by ten earthquakes and recorded across the Tibet Plateau, at QUE, LAH, NDI, NIL, KBL, SHL, CHG, SNG and HKG are analysed. Love- and Rayleigh-wave attenuation coefficients are obtained at time periods of 5–120 s using the spectral amplitudes of these waves for 23 different paths. Love wave attenuation coefficient varies from 0.0021 km^?1, at a period of 10 s, to 0.0002 km^?1 at a period of 90 s, attaining two maxima at time periods of 10 and 115 s, and two minima at time periods of 25 and 90 s. The Rayleigh-wave attenuation coefficient also shows a similar trend. The very low value for the dissipation factor, Q_β, obtained in this study suggests high dissipation across the Tibetan paths. Backus-Gilbert inversion theory is applied to these surface wave attenuation data to obtain average Q_β^?1 models for the crust and uppermost mantle beneath the Tibetan Plateau. Independent inversion of Love- and Rayleigh-wave attenuation data shows very high attenuation at a depth of ～50–120 km ($\text{Q}{}_{\mathrm{\beta }}\text{? 10}$). The simultaneous inversion of the Love and Rayleigh wave data yields a model which includes alternating regions of high and low Q_β^?1 values. This model also shows a zone of high attenuating material at a depth of ～40–120 km. The very high inferred attenuation at a depth of ～40–120 km supports the hypothesis that the Tibetan Plateau was formed by horizontal compression, and that thickening occurred after the collision of the Indian and Eurasian plates.     

Applications of liquid state physics to the Earth's core

By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) dK/$\text{d}\text{P ? 5 ? 5. 6P}$/K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of dK/dP proposed by Birch (1939) and Bullen (1949). (2) dlnT_M/dlnρ = (γC_V ? 1)/($\text{C}{}_{\mathrm{<mtext>V</mtext>}}\text{?}\text{3}\text{2}\text{),}\text{where}\text{T}{}_{\mathrm{<mtext>M</mtext>}}$ is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and C_V the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for C_V = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if $\text{γ <}\text{2}\text{3}$. However, it is shown that $\text{γ <}\text{2}\text{3}\text{? ∫}{}^{\mathrm{\infty }}{}_0\text{(?g/?T)}{}_{\mathrm{\rho }}\text{r(}\text{d}\text{/}\text{d}\text{r)(r}{}^2\text{φ)}\text{d}\text{r > 0}$, which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that $\text{γ >}\text{2}\text{3}$ and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ～ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory.     

The thermal boundary-layer interpretation of D″ and its role as a plume source

The “anomalous” layer in the lowermost mantle, identified as D″ in the notation of K.E. Bullen, appears in the PREM Earth model as a 150 km-thick zone in which the gradient of incompressibility with pressure, $\text{d}\text{K}\text{d}\text{P}$, is almost 1.6, instead of 3.2 as in the overlying mantle. Since PREM shows no accompanying change in density or density gradient, we identify D″ as a thermal boundary layer and not as a chemically distinct zone. The anomaly in $\text{d}\text{K}\text{d}\text{P}$ is related to the temperature gradient by the temperature dependence of K_s, for which we present a thermodynamic identity in terms of accessible quantities. This gives the numerical result (?K_s/?T)_P=?1.6×10⁷ Pa K^?1 for D″ material. The corresponding temperature increment over the D″ range is 840 K. Such a layer cannot be a static feature, but must be maintained by a downward motion of the lower mantle toward the core-mantle boundary with a strong horizontal flow near the base of D″. Assuming a core heat flux of 1.6 × 10¹² W, the downward speed is 0.07 mm y^?1 and the temperature profile in D″, scaled to match PREM data, is approximately exponential with a scale height of 73 km. The inferred thermal conductivity is 1.2 W m^?1 K^?1. Using these values we develop a new analytical model of D″ which is dynamically and thermally consistent. In this model, the lower-mantle material is heated and softened as it moves down into D″ where the strong temperature dependence of viscosity concentrates the horizontal flow in a layer ～ 12 km thick and similarly ensures its removal via narrow plumes.     

Physical constraints for the analysis of the geomagnetic secular variation

Slow changes in the magnetic field are believed to originate in the core of the Earth. Interpretation of these changes requires knowledge both of the vertical component of the field and of its rate of change at the core-mantle boundary (CMB). While various spherical harmonic models show some agreement for the field at the CMB, those for secular variation (SV) do not. SV models depend heavily on annual means at relatively few and poorly distributed magnetic observatories. In this paper, the SV at the CMB is modelled by fitting 15-year differences in the annual means of the X, Y and Z components (from 1959 to 1974). The model is made unique by imposing the constraint that $\text{?}{}_{\mathrm{CMB}}\text{B}\text{?}{}_{\mathrm{r}}{}^2\text{d}\text{S}$ be a minimum, using the method of Shure et al. (1982). If SV is attributed to motions of core fluid, then this model will yield, in some sense, the slowest core motions. The null space is determined by the distribution of observations, and therefore, to be consistent, only those observatories have been retained which recorded almost continuously throughout the interval 1959–1974.The method allows misfit between the model and the observations. The best value for the misfit can be derived from estimates of errors in the data, or alternatively, because larger misfit leads to smoother models (i.e., smaller $\text{?}\text{B}\text{?}{}_{\mathrm{r}}{}^2\text{d}\text{S}$), the best value can be estimated subjectively from the final appearance of the model. Both procedures have their counterparts in the conventional spherical harmonic expansion approach, when smoothing is achieved by lowering the truncation level. The new proposal made in this paper is to use objective criteria for determining the misfit, based on the assumption that diffusion is negligible, in which event all integrals $\text{∫}\text{B}\text{?}{}_{\mathrm{r}}{}^2\text{d}\text{S}$ will vanish when S_i is a region on the CMB bounded by a contour of zero vertical component of field. For the 1965 definitive model which is adopted here, and for most other contemporary models, there are six such areas, giving five independent integrals (the integrals over the six regions must sum to zero if ? · B = 0). Tabulating these integrals for various choices of the misfit gives minimum values near 2 nT y^?1. It is impossible to achieve this good a fit to the data using a reasonable model derived by truncating the spherical harmonic expansion. The value 2 nT y^?1 corresponds to errors of ～ 20 nT in individual annual means, which is rather larger than expected from the scatter in the data.     

Frequency relationship for seismic Qβ of central southern Italy from accelerograms for the Irpinia earthquake (1980)

The frequency dependence of Q_β for seismic waves in a distance range with a maximum of 150 km from the epicentre of the Irpinia earthquake of November 23, 1980 has been sought using displacement spectral ratios computed from strong-motion accelerograms recorded in the region. The method has been applied to calculate the behaviour of Q_β as a function of frequency in the band 0.1–25 Hz, and to investigate whether azimuthal variations appear in seismic Q_β for the lithosphere in central southern Italy. The same result is obtained using data from stations in western south Italy as using data from eastern south Italy, namely,

$\text{Q}{}_{\mathrm{\beta }}\text{(f) = 40f (}\text{Hz}\text{)}$

The linear relationship suggest that apparent Q_β depends more on the scale of heterogeneity of the lithosphere, affecting reflection and scattering mechanisms, than on intrinsic energy losses related to the anelasticity of the materials through which the seismic waves propagate.The existence of a peak in Q_β^?1 has been investigated in the low-frequency band (0.1–2.5 Hz) using a higher resolution power. A stable result in this low-Q_β zone is not possible on the basis of the available data: only in six Q_β(f) profiles does an evident minimum exist, between 0.2 and 1 Hz, while in nine cases the curves are monotonically increasing from the lowest observable frequencies; a further nine cases appear of uncertain interpretation.     

Observational study of terrestrial eigenvibrations

A comprehensive analysis has been made of analog and digital recordings of eigenvibration ground motion obtained following four great earthquakes; August 1976 (Philippines), August 1977 (Indonesia), September 1979 (West Irian), and December 1979 (Colombia). The time series (ranging in length from ～28 to ～140 h) are assumed to be linear combinations of damped harmonics in the presence of noise. Tables are calculated from values of the four parameters: Θ, used in describing eigenvibrations, period of oscillation, amplitude, damping factor Q, and phase together with their statistical uncertainties (53 spheroidal modes, ${}_0\text{S}{}_4\text{to}{}_0\text{S}{}_{48}$, and 13 torsional modes, ${}_0\text{T}{}_8\text{to}{}_0\text{T}{}_{45}$). The estimation procedures are by the methods of complex demodulation and non-linear regression that specifically incorporate into the basic model the decaying aspect of the oscillations. These methods, extended to simultaneous estimations of groups of modes, help to eliminate measurement error and measurement bias from estimations of Θ. The result is that overtone modes very near in frequency to fundamental modes can, under certain conditions, be resolved through a non-linear regression technique, although parameter uncertainties are underestimated in general.Of the time series analyzed, 17 were from a northern California regional network of ultra-long period seismographs at Berkeley (three components), Jamestown (vertical component), and Whiskeytown (vertical component) following the four listed earthquakes. The other 7 time series were recorded digitally by the worldwide IDA network following the 1977 Indonesian earthquake. Weighted regional and worldwide averages were made for period and Q of each eigenvibration mode.From the theoretical viewpoint, comparisons of measured period, Q, amplitude, and phase for all modes analyzed led to five conclusions. First, there are no detectable systematic shifts in period, Q, or phase of eigenvibrations within a region whose dimensions are less than a wavelength. Second, though not conclusive, there may be slight systematic shifts in period (<0.65 s) and relative amplitudes within the California regional network due to different source positions and mechanisms. Differences in Q values are not statistically significant. Third, even though differences in period obtained worldwide were as great as 1.33 s (≈0.33%), differences between Q values (as great as 20%) for the same mode were not significant. The conclusion is that the damping characteristics of singlet eigenfunctions are not observed to be significantly different. Fourth, the assumption that a multiplet ${}_{\mathrm{n}}\text{S}{}_{\mathrm{l}}$ behaves as a single oscillation is valid from at least ${}_0\text{S}{}_7$ through ${}_0\text{S}{}_{30}$. Fifth, no systematic pattern emerged for the shift of eigenperiod as a function of order / or posit on the Earth.     

High-temperature anelasticity and elasticity of mantle peridotite

An apparatus has been devised which allows precise creep and relaxation measurements to be made on minerals and rocks at temperatures up to 1600°C and at very low deviatoric stresses (1 < σ < 300 bar). This paper is concerned with measurements on mantle peridotite (lherzolite) from Balmuccia (Zone of Ivrea, Italy).The reaction of the sample to a step-like increase in stress is called its “creep function”. It is shown that the creep function contains all the necessary information to derive the spectra of the quality factor Q(ω) and of Young's modulus E(ω), within the seismic range of frequencies, provided the material behaves as a linear system. This has been proven up to a strain of 5 × 10^?5.The Q^?1-spectra at 1200 and 1300°C, obtained by Fourier inversion from the creep function, show no pronounced peak in the frequency band 0.01 < tf < 1 Hz and exhibit a general tendency to decrease slightly with frequency. The creep function: ?(t) = ?_u · [1 + 3.7 · q · {(1 + 50t)^0.27 ? }], where q is related to Q, satisfactorily describes the data at high temperatures and leads to $\text{Q}{}^{\mathrm{?1}}\text{(ω, T) = 3 × 10}{}^3\text{· ω}{}^{\mathrm{<mtext>?0.27\; ·\; </mtext><mtext>exp</mtext>}}\text{(}\text{?30}\text{RT}\text{)}$E(ω) is related to Q(ω) by the material dispersion equation. Above 1100°C the unrelaxed Young's modulus decreases rapidly with temperature according to an activation energy of about 20 kcal/mole. A lowering of short period S-wave velocity by 40% and P-wave velocity by 10% occurs below the solidus. Therefore, no partial melting is required in the asthenosphere.Steady-state creep at low axial stresses (20 < σ < 100 bar), obtained from the same rock, follows the relation $\text{?}\text{?}\text{= 3 × 10}{}^7\text{· δ}{}^{1.4}\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ indicative of grain boundary diffusion or superplasticity. At higher stresses a power law $\text{?}\text{?}\text{= 45 · δ}{}^4\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ typical of dislocation creep, is found.The frequency dependence of Q and the ratio of the activation energies of Q and are indicative of so called “high-temperature background absorption”, as the dominant mechanism, and of a diffusion-controlled dislocation mobility common to both absorption and creep. From a, b, and c, relations between the effective viscosity η_f and Q of the form: $\text{log}\text{η}{}_{\mathrm{e??}}\text{=}\text{1}\text{α}\text{·}\text{log}\text{Q ? (n ? 1) ·}\text{log}\text{ω +}\text{log}\text{D}$ are derived, where α ～ 0.25, n is the power of σ, and D is a constant.     

Earthquake similarity laws

Source parameters of 27 major shallow earthquakes in the magnitude range 7.0–8.6, which occurred during 1906–1969, are used to establish dimensionless invariants involving the fault dimensions, average slip, and the rise time. It is found that these entities are expressible as simple functions of the subsonic shear Mach number (M) and the cube root of the seismic potency, $\text{(}\text{U}\text{S)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$. Moreover, a new principle is suggested according to which all dimensionless numbers which can be constructed from the basic fault elements are simple powers of the contraction factor $\text{(1-M}{}^2\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ with coefficients of the order unity. The laws of dynamical similarity thus found are those appropriate for subsonic rupture in which the Mach number is very close to unity and the radiation efficiency is between $\text{1}\text{6}$ and $\text{1}\text{3}$. The empirical similarity laws are shown to be compatible with a source model in which the fault plane is simulated by a flexible membrane with additional restoring stiffness forces provided by an elastic medium attached to it on one side. Results suggest the possibility that earthquake rupture, together with the radiation of seismic waves, terminates at the moment that Mach 1 is reached.     

Regionalization of global electromagnetic induction data: a theoretical model

Systematic differences are noted between those global response functions (Q = I₁/E₁; $\text{W}\text{= Z/H}$) derived from single observatories and those derived from global averages. Using a simple first-order model to simulate global scale lateral heterogeneities, we argue that reasonable differences in the depth to the conductosphere (d (average) = 400 km in one hemisphere, 600 km in the other) result in significant differences in the response functions at single observatories. These differences appear to be easily resolvable within the expected error-bars of actual observations. At this point it is believed that regional differences in global response parameters can indeed be used to infer large-scale differences in the depth to the conductosphere, providing that systematic biases introduced in data processing and interpretation are minimized.     

The correlation between gravitational and geomagnetic fields caused by interaction of the core fluid motion with a bumpy core-mantle interface

The correlation discovered by Hide and Malin between the variable parts of the Earth's gravitational field and magnetic field (suitably displaced in longitude) was tentatively and qualitatively explained by them in terms of the influence on both fields of irregularities (or “surface bumps”) at the core-mantle interface. In this paper, a quantitative analysis of this phenomenon is developed, through study of an idealised problem in which conducting fluid occupying the region z < η(x) flows over the surface z = η(x) in the presence of a magnetic field (B₀,0,0), the whole system rotating with angular velocity (0,0,Ω). It is assumed that $\text{|η′(x)| « 1}$ so that perturbation methods are applicable. Determination of the magnetic potential in the “mantle” region z < η(x) requires solution of the full hydromagnetic problem in the fluid. It is shown that three wave modes are excited, two of which (for values of the parameters of the problem of geophysical interest) have a boundary layer character. Phase interactions between these modes lead to a shift and a distortion of the magnetic pattern relative to the gravitational pattern. The correlation between the gravitational potential and the magnetic potential (shifted by a distance x₀) is determined on the plane $\text{z = d (d}\text{a}\text{?}\text{|η|)}$ as a function of x₀/d and the curves obtained are qualitatively similar to that based on the observed data; the maximum correlation obtained varies between 0.67 and 1, depending on values of the parameters of the problem, and is about 0.72 for reasonable estimates of these parameters in the geophysical context.     

Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Lowes (1966, 1974) has introduced the function R_n defined by $\text{R}{}^{\mathrm{n}}\text{=(n + 1)}\text{∑}\text{m=0}\text{∞}\text{[(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{+ (h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{]}\text{where}\text{g}{}_{\mathrm{n}}{}^{\mathrm{m}}\text{and}\text{h}{}_{\mathrm{n}}{}^{\mathrm{m}}$ are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = ??V on a sphere of radius r > α is given by $\text{〈}\text{B}\text{·〉 =}\text{∑}\text{n=1}\text{∞}\text{R}{}^{\mathrm{n}}\text{(}\text{a/}\text{r}\text{)}{}^{\mathrm{2n=4}}\text{where}\text{a}$ is the Earth's radius. We refer to R_n as the spherical harmonic spatial power spectrum of the geomagnetic field.In this paper it is shown that Rⁿ = R^M_n = R^C_n where the components R_n^M due to the main (or core) field and R_n^C due to the crustal field are given approximately by $\text{R}{}^{\mathrm{M}}{}_{\mathrm{n}}\text{= [}\text{(n =1)/}\text{(n + 2)}\text{](1.142 × 10}{}^9\text{)(0.288}{}^{\mathrm{n}}\text{Λ}{}^2\text{R}{}^{\mathrm{C}}{}_{\mathrm{n}}\text{= [}\text{(n =1){[1 — exp(-n/290)]/}\text{(n/290)} 0.52 Λ}{}^2\text{where}\text{Iγ = 1 nT}$. The two components are approximately equal for n = 15.Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963).The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model.Equations relating average great circle power spectra of the geomagnetic field components to R_n are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the R_n for celestial bodies from average great circle power spectra of the magnetic field components.