Geomagnetically Induced Currents and Space Weather: Pi3 Pulsations and Extreme Values of Time Derivatives of the Geomagnetic Field’s Horizontal Components

The problem of estimating the time derivatives of the horizontal components of the geomagnetic field and forecasting the probability of the occurrence of perturbations that exceed a given threshold level (the over-threshold perturbations) arises in the applications concerned with the geomagnetically induced currents (GICs). In this work, we consider the temporal and spatial structure of the Pi3 pulsations with quasi-periods of 10² to 10³ s during which the auroral and subauroral stations of the IMAGE network record over-threshold values in the derivatives of the meridional (along the longitudinal circle) B_X component and latitudinal (along the latitudinal circle) B_Y component. The extreme |dB_X/dt| values mainly develop against the background of the Pi3 pulsations with a complex frequency content, whereas the extreme |dB_Y/dt| values appear when the buildup (decay) phases of the bay-like disturbance associated with the evolution of a substorm coincide with the respective phases of the field of pulsations. The conditions under which the derivatives |dB_X/dt| and |dB_Y/dt| reach their over-threshold values are studied for subauroral latitudes by the technique of superposed epoch analysis. The extreme values of the derivatives most frequently occur during the main phase of moderate magnetic storms or beyond the storm—during high substorm activity under the conditions of a negative vertical component of the interplanetary magnetic field. The probability of the occurrence of over-threshold values increases at high amplitudes of the Pi3 pulsations and depends on their spectral content. The problem of analyzing and forecasting the over-threshold |dB_Y/dt| perturbations is complicated by the fact that the scale of the perturbations is small along the lines of latitude and large along the meridians. This can result in GIC excitation in the North–South oriented electric power lines by the geomagnetic perturbations localized within a narrow band in longitude which can be missed during the measurements.     

Influence of the plasma zonal E × B drift on the electron concentration in the low-latitude ionospheric F region at the minimum of solar activity near the spring equinox

The three-dimensional nonstationary theoretical model of the concentrations and temperatures of electrons and ions in the ionospheric F region and plasmasphere at low and middle latitudes is used to study variations in the concentration NmF2 and height hmF2 of the ionospheric F2 layer under the action of the plasma zonal drift in the direction geomagnetic west-geomagnetic east perpendicularly to the electric E and geomagnetic B fields. The calculated and measured values of NmF2 and hmF2 for 16 ionospheric sounding stations during the quiet geomagnetic period on March 28–29, 1964 at low solar activity are compared. This comparison made it possible to correct the input parameters of the model: [O] from the NRLMSISE-00 model and the meridional component of the neutral wind velocity from the HWW90 model. It is shown that the nighttime NmF2 values decrease up to twice at low solar activity in the low-latitude ionosphere, and the hmF2 values change by up to 16 km, if the plasma zonal E×B drift is not taken into account. Under the daytime conditions, the influence of the plasma zonal E×B drift on NmF2 can be neglected.     

Effect of the zonal E × B plasma drift on the electron number density in the low-latitude ionospheric F region at high solar activity near the December solstice

The variations in the electron number density of the ionospheric F2 layer maximum (NmF2) under the action of the zonal plasma drift in the geomagnetic west-geomagnetic east direction perpendicularly to the electric (E) and geomagnetic (B) fields during a geomagnetically quiet period on December 7, 1989, at high solar activity have been studied based on a three-dimensional nonstationary theoretical model of electron number densities and temperatures in the ionospheric F region. Calculated and measured NmF2 values for 12 low-latitude ionospheric sounding stations have been compared. When the zonal E × B plasma drift is ignored, the NmF2 values become smaller by up to a factor of 3 under nighttime conditions in the low-latitude ionosphere. The average effect of the zonal E × B plasma drift on NmF2 in the low-latitude ionosphere is larger during winter nights than under summer nighttime conditions.     

Effect of zonal E × B plasma drift on electron density in the low-latitude ionospheric <Emphasis Type="Italic">F</Emphasis> region at a solar activity maximum near vernal equinox

The variations in the density of the ionospheric F2 layer maximum (NmF2) under the action of the zonal plasma drift perpendicularly to the magnetic (B) and electric (E) fields in the direction geomagnetic west-geomagnetic east have been studied using the three-dimensional nonstationary theoretical model of electron and ion densities (N _e and N _i ) and temperatures (T _e and T _i ) in the low-latitude and midlatitude ionospheric F region and plasmasphere. The method of numerical calculations of N _e , N _i , T _e , and T _i , including the advantages of the Lagrangian and Eulerian methods, is used in the model. A dipole approximation of the geomagnetic field (B), taking into account the non-coincidence of the geographic and geomagnetic poles and differences between the positions of the Earth’s and geomagnetic dipole centers, is accepted in the calculations. The calculated NmF2 and altitudes of the F2 layer maximum (hmF2) have been compared with these quantities measured at 16 low-latitude ionospheric sounding stations during the geomagnetically quiet period October 11–12, 1958. This comparison made it possible to correct the input model parameters: the NRLMSISE-00 model [O], the meridional component of the neutral wind velocity according to the HWW90 model, and the meridional component of the equatorial plasma drift due to the electric field specified by the empirical model. It has been indicated that the effect of the zonal E × B plasma drift on NmF2 can be neglected under daytime conditions and changes in NmF2 and hmF2 under the action of this drift are insignificant under nighttime conditions north of 25° and south of ?26° geomagnetic latitude. The effect of the zonal E × B plasma drift on NmF2 and hmF2 is most substantial in the nightside ionosphere approximately from ?20° to 20° geomagnetic latitude, and the neglect of this drift results in an up to 2.4-fold underestimation of NmF2. The found dependence of the effect of the zonal E × B plasma drift on NmF2 and hmF2 on geomagnetic latitude is related to the longitudinal asymmetry of B, asymmetry of the neutral wind about the geomagnetic equator, and changes in the meridional E × B plasma drift at a change in geomagnetic longitude.     

The relation between solar activity and orientation of the solar wind electric field relative to the Earth’s magnetic moment

The relation of the Kp index of geomagnetic activity to the solar wind electric field (E _SW) and the projection of this field onto the geomagnetic dipole has been estimated. An analysis indicated that the southward component of the IMF vector (B _z < 0) is the main geoeffective parameter, as was repeatedly indicated by many researchers. The presence of this component in any combinations of the interplanetary medium parameters is responsible for a high correlation between such combinations and geomagnetic activity referred to by the authors of different studies. Precisely this field component also plays the main role in the relation between the Kp index and the relative orientation of E _SW and the Earth’ magnetic moment.     

Inverse modeling of dissolved O2 and δ18O-DO to estimate aquatic metabolism,reaeration and respiration isotopic fractionation: effects of variable light regimes and input uncertainties

A transient model, hereafter referred to as ROM-TM, was developed to quantify river ecosystem metabolic rates and reaeration rates from field observation of changes in dissolved O₂ (DO) and the ratio of ¹⁸O to ¹⁶O in DO (δ¹⁸O-DO). ROM-TM applies an inverse modeling approach and is programmed using MATLAB. Parameters describing photosynthesis, ecosystem respiration, gas exchange, and isotopic fractionation, such as maximum photosynthetic rate (P _m ), photosynthetic efficiency parameter (a), respiration rate at 20 °C (R ₂₀ ), gas exchange coefficient (K), respiration isotopic fractionation factor (a _R ), and photorespiration coefficient (β _R ), can be abstracted by minimizing the sum of square errors between the fitted data and the observed field data. Then DO and δ¹⁸O-DO time series can be reconstructed using estimated parameters and input variables. Besides being capable of teasing apart metabolic processes and gas exchange to provide daily average estimates of metabolic parameters at the ecosystem scale, ROM-TM can be used to address issues related to light including light saturation phenomena at the ecosystem level, the effect of cloud cover on the metabolic balance, and photorespiration. Error and uncertainty analysis demonstrates that ROM-TM is stable and robust for the random errors of DO time series. The photosynthetic parameters P _m and a are more sensitive than other parameters to lower-resolution time series data.     

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

Rock masses contain ubiquitous multiscale heterogeneities, which (or whose boundaries) serve as the surfaces of discontinuity for some characteristics of the stress state, e.g., for the orientation of principal stress axes. Revealing the regularities that control these discontinuities is a key to understanding the processes taking place at the boundaries of the heterogeneities and for designing the correct procedures for reconstructing and theoretical modeling of tectonic stresses. In the present study, the local laws describing the refraction of the axes of extreme principal stresses T ₁ (maximal tension in the deviatoric sense) and T ₃ (maximal compression) of the Cauchy stress tensor at the transition over the elementary area n of discontinuity whose orientation is specified by the unit normal n are derived. It is assumed that on the area n of discontinuity, frictional contact takes place. No hypotheses are made on the constitutive equations, and a priori constraints are not posed on the orientation on the stress axes. Two domains, which adjoin area n on the opposite sides and are conventionally marked + and ?, are distinguished. In the case of the two-dimensional (2D) stress state, any principal stress axis on passing from domain ? to domain + remains in the same quadrant of the plane as the continuation of this axis in domain +. The sign and size of the refraction angle depend on the sign and amplitude of the jump of the normal stress, which is tangential to the surface of discontinuity. In the three-dimensional (3D) case, the refraction of axes T ₁ and T ₃ should be analyzed simultaneously. For each side, + and ?, the projections of the T ₁ and T ₃ axes on the generally oriented plane n form the shear sectors S ⁺ and S ^?, which are determined unambiguously and to whose angular domains the possible directions p ⁺ and p ^? of the shear stress vectors belong. In order for the extreme stress axes T ₁ ⁺ ,T ₃ ⁺ and T ₁ ^? , T ₃ ^? to be statically compatible on the generally oriented plane n, it is required that sectors S ⁺ and S ^? had a nonempty intersection. The direction vectors p ⁺ and p ^? are determined uniquely if, besides axes T ₁ ^? , T ₃ ^? and T ₁ ⁺ , T ₃ ⁺ , also the ratios of differential stresses R ⁺ and R ^? (0 ≤ R ^± ≤ 1) are known. This is equivalent to specifying the reduced stress tensors T _R ⁺ and T _R ^? The necessary condition for tensors T _R ⁺ and T _R ^? being statically compatible on plane n is the equality p ⁺ = p ^?. In this paper, simple methods are suggested for solving the inverse problem of constructing the set of the orientations of the extreme stress axes from the known direction p of the shear stress vector on plane n and from the data on the shear sector. Based on these methods and using the necessary conditions of local equilibrium on plane n formulated above, all the possible orientations of axes T ₁ ⁺ , T ₃ ⁺ are determined if the projections of axes T ₁ ^? , T ₃ ^? axes on side — are given. The angle between the projections of axes T ₁ ⁺ , T ₁ ^? and/or T ₃ ⁺ , T ₃ ^? on the plane can attain 90°. Besides the general case, also the particular cases of the contact between the degenerate stress states and the special position of plane n relative to the principal stress axes are thoroughly examined. Generalization of the obtained results makes it possible to plot the local diagram of the orientations of axes T ₁ ⁺ , T ₃ ⁺ for a given sector S ^?. This diagram is a so-called stress orientation sphere, which is subdivided into three pairs of areas (compression, tension, and compression-extension). The tension and compression zones cannot contain the poles of T ₃ ⁺ and T ₁ ⁺ axes, respectively. The compression-extension zones can contain the poles of either T ₁ ⁺ or T ₃ ⁺ axis but not both poles simultaneously. In the particular case when the shear stress vector has a unique direction p ^? on side ?, the areas of compression-extension disappear and the diagram is reduced to a beach-ball plot, which visualizes the focal mechanism solution of an earthquake. If area n is a generally oriented plane and if the orientation of the pairs of the statically compatible axes T ₁ ^? , T ₃ ^? and T ₁ ⁺ , T ₃ ⁺ is specified, then, the stress values on side + are uniquely determined from the known stress values on side ?. From the value of differential stress ratio R ^?, one can calculate the value of R ⁺, and using the values of the principal stresses on side ?, determine the total stress tensor T ⁺ on side +. The obtained results are supported by the laboratory experiments and drilling data. In particular, these results disclose the drawbacks of some established notions and methods in which the possible refraction of the stress axes is unreasonably ignored or taken into account improperly. For example, it is generally misleading to associate the slip on the preexisting fault with the orientation of any particular trihedron of the principal stress axes. The reconstruction should address the potentially statically compatible principal stress axes, which are differently oriented on opposite sides of the fault plane. The fact that, based on the orientation of the intraplate principal stresses at the base of the lithosphere, one cannot make a conclusion on the active or passive influence of the mantle flows on the lithospheric plate motion is another example. The present relationships linking the stress values on the opposite sides of the fault plane on which the orientations of the principal stress axes are known demonstrate the incorrectness of the existing methods, in which the reduced stress tensors within the material domains are reconstructed without allowance for the dynamic interaction of these domains with their neighbors. In addition, using the obtained results, one can generalize the notion of the zone of dynamical control of a fault onto the case of the existence of discontinuities in this region and analyze the stress transfer across the system of the faults.     

Dependence of time derivative of horizontal geomagnetic field on sunspot number and aa index

This work investigated an interrelationship between the monthly means of time derivatives of horizontal geomagnetic field, dH/dt, sunspot number, R _z , and aa index for the period of substorms (from ?90 to ?1800 nT) during the years 1990–2009. A total of 232 substorms were identified during the period of study. The time derivative of horizontal geomagnetic field, dH/dt, used as a proxy for geomagnetically induced current (GIC) exhibited high positive correlation with sunspot number (0.86) and aa index (0.8998). The obtained geomagnetic activity is in 92.665% explicable by the combined effect of sunspot number and aa index. The distribution of substorms as a function of years gives a strong support for the existence of geomagnetic activity increases, which implies that as the sunspot number increases the base level of geomagnetic activity increases too.     

Mechanism of formation of <Emphasis Type="Italic">Q</Emphasis>-disturbances in the <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> region of the equatorial ionosphere

Using model simulations, the morphological picture (revealed earlier) of the disturbances in the F ₂ region of the equatorial ionosphere under quiet geomagnetic conditions (Q-disturbances) is interpreted. It is shown that the observed variations in the velocity of the vertical E × B plasma drift, related to the zonal E _y component of the electric field, are responsible for the formation of Q-disturbances. The plasma recombination at altitudes of the lower part of the F ₂ region and the dependence of the rate of this process on heliogeophysical conditions compose the mechanism of Q-disturbance formation at night. The daytime positive Q-disturbances are caused exclusively by a decrease in the upward E × B drift, and this type of disturbances could be related to the known phenomenon of counter electrojet. Possible causes of formation of the daytime negative Q-disturbances are discussed.     

Geomagnetic Storm Effects at <Emphasis Type="Italic">F</Emphasis>1 Layer Altitudes in Various Periods of Solar Activity (Irkutsk Station)

The influence of geomagnetic disturbances on electron density Ne at F1 layer altitudes in different conditions of solar activity during the autumnal and vernal seasons of 2003–2015, according to the data from the Irkutsk digital ionospheric station (52° N, 104° Е) is examined. Variations of Ne at heights of 150–190 km during the periods of twenty medium-scale and strong geomagnetic storms have been analyzed. At these specified heights, a vernal–autumn asymmetry of geomagnetic storm effects is discovered in all periods of solar activity of 2003–2015: a considerable Ne decrease at a height of 190 km and a weaker effect at lower levels during the autumnal storms. During vernal storms, no significant Ne decrease as compared with quiet conditions was registered over the entire analyzed interval of 150?190 km.     

Response of some ionospheric parameters to geomagnetic disturbances at heights below the <Emphasis Type="Italic">F</Emphasis>2-layer maximum in September and April 2005

An analysis of ionospheric data obtained during geomagnetic disturbances in April and September 2005 is performed in order to obtain information on the behavior of some ionospheric parameters at heights of the F1 layer. The results of measurements by an Irkutsk digisonde at hourly and 5- and 15-min time intervals were used. It is shown that in September all parameters very actively responded to geomagnetic disturbances in short measurement time intervals. It is also shown that the electron concentration behaves more stable at lower heights of the F1 layer both during strong and moderate disturbances.     

Influence of Solar Wind Plasma Parameters on the Intensity of Isolated Magnetospheric Substorms

Parameters of the interplanetary magnetic field and solar wind plasma during periods of 163 isolated substorms have been studied. It is shown that the solar wind velocity V and plasma density N remain approximately constant for at least 3 h before substorm onset Т _o and 1 h after Т _o . On average, the velocity of the solar wind exhibits a stable trend toward anticorrelation with its density over the whole data array. However, the situation is different if the values of V and N are considered with respect to the intensity of substorms observed during that period. With the growth of substorm intensity, quantified as the maximum absolute value of AL index, an increase in both the solar wind plasma velocity and density, at which these substorms appear, is obsreved. It has been found that the magnitude of the solar wind dynamic pressure P is closely related to the magnetosphere energy load defined as averaged values of the Kan–Lee electric field E_KL and Newell parameter dΦ/dt averaged for 1 h interval before Т _o . The growth of the dynamic pressure is accompanied by an increase in the load energy necessary for substorm generation. This interrelation between P and values of EKL and dΦ/dt is absent in other, arbitrarily chosen periods. It is believed that the processes accompanying increasing dynamic pressure of the solar wind result in the formation of magnetosphere conditions that increasingly impede substorm generation. Thus, the larger is P, the more solar wind energy must enter the Earth’s magnetosphere during the period of the growth phase for substorm generation. This energy is later released during the period of the substorm expansion phase and creates even more intense magnetic bays.     

Methods for reconstructing harmonic functions from the magnetic field ΔT and V.N. Strakhov’s function ΔS: A review

We give an overview of the methods designed for reconstructing close-to-harmonic functions from the magnetic field ΔT. The formula of Yu.P. Tafeev is refined. It is shown that this refined formula directly leads to the relation derived by V.M. Gordin and his colleagues that allows isolating the harmonic component in the function ΔT. V.N. Strakhov’s linearized representation of the function ΔT is immediately derived from the main approximate Tafeev formula for Q ΔT. The experience of using Strakhov’s ΔS function in the interpretation of the magnetic anomaly ΔT generated by the Krivoi Rog structure is described. It is noted that the problem of reconstructing the corresponding harmonic functions from the data of magnetic and gravity surveys has much in common. The specific features of measuring the magnetic field H and magnetic induction B in the material media are considered, and the physical interpretation of these fields is presented.     

Relation of long-period variations in the critical frequencies of the <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> layer to geomagnetic activity

The relation of the long-period variations in the midnight and noon values of the critical frequency of the ionospheric F ₂ layer at three midlatitude stations (Irkutsk, Moscow, and Boulder) to the daily mean index of geomagnetic activity in years of different solar activity has been studied. It has been found that the correlation coefficients between the above parameters depend on time of day, season, and solar activity level. The correlation coefficients are higher at night than in the daytime, especially at low solar activity. The highest absolute values of the correlation coefficient most often appear during equinoxes: April–May and September–October. It has been shown that the variability of the critical frequencies of the midlatitude ionospheric F ₂ layer depends not only on geomagnetic activity but also (to a considerable degree) on the effect of the lower atmosphere.     

On the reduction of time variations for geomagnetic repeat station measurements

For most previous geomagnetic surveys, the time variations of the observatory closest to the site of observation have been used for reduction. The accuracy of repeat station measurements depends upon the distance between the station and the observatory. Nowadays, the requirements for the accuracy of repeat station measurements are much higher, especially with respect to local secular variation anomalies. On the other hand, transportable variograph stations are available, by means of which time variations can be recorded closer to the station site. The reduction steps for this method are:

1. Reduction of measured values to the base-line of the nearby variograph station;
2. Computation of the nearest quiet night value using the baseline of the variograph;
3. Computation of the difference between this value and the corresponding one at the observatory.

The problems are:

- the stability of the base-line values of the variographs;

- the question as to what degree a quiet night value represents the normal value at that time (e.g. influence of aD _st field and/or other fields).

A repeat station survey of the Federal Republic of Germany was carried out in 1982. During the same time, eleven stations recorded the time variations in that area. We discuss the aforementioned aspects by way of an example taken from this survey.     

Numerical experiments of air–ice drag coefficient and its impact on ice–ocean coupled system in the Sea of Okhotsk

Sensitivity study of the air–ice drag coefficient C _Dai is presented with an ice–ocean coupled model for the Sea of Okhotsk. The C _Dai?×?10³ value is varied from 2 to 5 based on the direct measurements in the region. The maximum volume transport of the East Sakhalin Current and the mean sea ice velocity were intensified as C _Dai increased. The sensitivity experiment with the ice–water drag coefficient C _Diw showed that the East Sakhalin Current volume transport is hardly affected by C _Diw but significantly intensified by C _Dai. While the ice drift in the off-ice-edge direction was intensified by the increase in C _Dai and the decrease in C _Diw, the ice edge location was nearly unchanged. This was due to melting caused by the relatively warm water inflow from the North Pacific. That is, sea ice extent in the region is strongly influenced by melting caused by a large ice–ocean heat transfer. In the active melting regions, the ice–ocean heat transfer of more than 100 W/m² occurred even in mid-winter. This is the same order as the cooling by air in winter, and a heat insulation capacity of sea ice is weakened in such regions.     

Variations of Geomagnetic Cosmic Ray Thresholds and Their Latitudinal Behavior in the Period of Solar Disturbance in September 2005

The period of interplanetary, geomagnetic and solar disturbances of September 7–15, 2005, is characterized by two sharp increases of solar wind velocity to 1000 km/s and great Dst variation of the geomagnetic field (~140 nT). The time variations of theoretical and experimental geomagnetic thresholds observed during this strong geomagnetic storm, their connection with solar wind parameters and the Dst index, and the features of latitudinal behavior of geomagnetic thresholds at particular times of the storm were studied. The theoretical geomagnetic thresholds were calculated with cosmic ray particle tracing in the magnetic field of the disturbed magnetosphere described by Ts01 model. The experimental geomagnetic thresholds were specified by spectrographic global survey according to the data of cosmic ray registration by the global station network.     

The Marmara Sea region: Seismic behaviour in time and the likelihood of another large earthquake near Istanbul (Turkey)

The North Anatolian Fault (NAF) extends for about 1500 km from Karliova to the east, to the Egean Sea in the west. The Marmara region, located near the western end of the NAF, is a tectonically active zone characterized by the transition between a strike slip stress regime and an extensional one in the Aegean Sea. Microseismic studies performed around the Marmara Sea in 1995 [Tectonophysics 316, 2000, 1], and just before the 1999 Izmit Earthquake Bull. Seism. Soc. Am. 92, 2002a, 361;J. Seismol. 6, 2002b, 287) permitted the analysis of the evolution of seismicity connected to this destructive earthquake and its sequels. Several observations indicate that the aftershock distribution fits well the EW orientation of the NAF, but the ruptures are not simple and linear as a first glance would suggest. Instead they are segmented in at least five pieces as shown by the slip variation and aftershock clusters, showing complexity at different scales (Bull. Seism. Soc. Am. 92, 2002a, 361). There is still a gap, across the northern border of the Marmara Sea that has not ruptured, and this is the only sector that did not break on the NAF since the 1939 great Erzincan earthquake. Will it rupture as a whole with a large magnitude earthquake, or by segments with smaller magnitude events? The Hurst analysis of the overall behaviour of the seismicity in the Marmara region since historical times shows that if a large earthquake occurs in the near future, it might break the complete gap. The Hurst character of the time variation of seismicity is persistent with H= 0.82. The aftershocks of the 1999 Izmit earthquake can be analyzed by using the Hurst method, showing an exceptionally high persistent memory.     

Ground-motion prediction equations for interface earthquakes of M7 to M9 based on empirical data from Japan

Ground motion prediction equations (GMPEs) have a major impact on seismic hazard estimates, because they control the predicted amplitudes of ground shaking. The prediction of ground-motion amplitudes due to mega-thrust earthquakes in subduction zones has been hampered by a paucity of empirical ground-motion data for the very large magnitudes (moment magnitude (M) $>$ 7) of most interest to hazard analysis. Recent data from Tohoku M9.0 2011 earthquake are important in this regard, as this is the largest well-recorded subduction event, and the only such event with sufficient data to enable a clear separation of the overall source, path and site effects. In this study, we use strong-ground-motion records from the M9 Tohoku event to derive an event-specific GMPE. We then extend this M9 GMPE to represent the shaking from other M $>$ 7 interface events in Japan by adjusting the source term. We focus on events in Japan to reduce ambiguity that results when combining data in different regions having different source, path and site effect attributes. Source levels (adjustment factors) for other Japanese events are determined as the average residuals of ground-motions with respect to the Tohoku GMPE, keeping all other coefficients fixed. The mean residuals (source terms) scale most steeply with magnitude at the lower frequencies; this is in accord with expectations based on overall source-scaling concepts. Interpolating source terms over the magnitude range of 7.0–9.0, we produce a GMPE for large interface events of M7–M9, for NEHRP B/C boundary site conditions (time-averaged shear-wave velocity of 760 m/s over the top 30 m) in both fore-arc and back-arc regions of Japan. We show how these equations may be adjusted to account for the deeper soil profiles (for the same value of $\hbox {V}_\mathrm{S30})$ in western North America. The proposed GMPE predicts lower motions at very long periods, higher motions at short periods, and similar motions at intermediate periods, relative to the simulation-based GMPE model of Atkinson and Macias (2009) for the Cascadia subduction zone.