alone (Table 1, column 1D TDSE) are systematically too small by about a factor two. This
discrepancy is robust with respect to realistic
variations of the MFP (4 to 5 Å), the electron-hole (e-h)–interaction screening length, and the
exact position of the attosecond clock (±0.5 Å).
Neither atomic delays nor propagation effects
alone account for the experimentally observed
delays. However, if propagation-induced delays
and atomic delays are joined, the total delay (
column “Theory S” in Table 1) matches the experimental observations. On the basis of this, we
conclude that the angular momentum of the
initial localized atomic state affects the time delay of photoelectrons in solids. Intra-atomic interactions substantially contribute to the total delay.
This observation is in contrast to state-of-the-art photoemission models that emphasize the
translational invariance in the solid for the initial
and excited states. As demonstrated, the initially
excited localized wave packet is dominated by
the spherical symmetry of the atom from which
the electron is emitted. Only after some time,
as the wave propagates to neighboring atoms, does
the photoelectron feel the structure of the crystal.
This complex evolution of a many-body system is
not captured in common photoemission models,
and attosecond time-resolved photoemission spectroscopy thus provides access to investigating
this initial phase of the photoemission process
in more detail. Incorporating this initial stage,
which is localized at the particular atom from
which the electron is emitted, is the cornerstone
of our model and any future models of solid-state
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This work was supported by the German Research Foundation
(DFG) within the Collaborative Research Center (SFB) 613 (F.S.,
P.B., W.P., and U.H.), the Priority Programs SPP 1931 (C.S.,
M.H., and W.P.), and SPP 1840 (St.F., S.N., and W.P.); the Basque
Government (grant IT-756-13 UPV/EHU) (V.M.S., E.E.K.,
R.D.M., P.M.E., and A.K.K.); and the Spanish Ministerio de
Economía y Competitividad (grants FIS2016-76617-P and
FIS2016-76471-P) (V.M.S., E.E.K., R.D.M., P.M.E., and A.K.K.)
and Fondo Europeo de Desarrollo Regional (FEDER) (CTQ2016-
80375-P) (M. T.-S.). N.M.K. acknowledges hospitality and financial
support from the theory group in cooperation with the small
quantum systems (SQS) research group of European XFEL. All
data needed to evaluate the conclusions in this study are
presented in the paper and/or in the supplementary materials.
Additional data related to this study may be requested from
W.P. ( firstname.lastname@example.org). F.S. and S.N. performed
the experiments. F.S., S.N., P.B., M.H., C.S., and N.M. contributed
to the development and operation of the experimental setup
and Se.F. provided the WSe2 crystals and supervised in situ
preparation. F.S., S.N., and W.P. analyzed the experimental
results. A.K.K. developed the 1D TDSE propagation model and
coordinated the various theoretical activities concerned with
intra-atomic delays (A.K.K., St.F., and N.M.K.), electron MFP in
WSe2 and the dynamically IR streaking-field distribution at the
WSe2-vacuum interface (V.M.S. and R.D.M.), effective mass of
photoelectrons in WSe2 (E.E.K.), and the projected initial states
(M. T.-S.). P.M.E., U.H., and W.P. supervised the project.
Materials and Methods
Figs. S1 to S9
Tables S1 to S3
28 April 2017; accepted 11 August 2017
The hidden simplicity of subduction
M.-A. Meier,* J. P. Ampuero, T. H. Heaton
The largest observed earthquakes occur on subduction interfaces and frequently cause
widespread damage and loss of life. Understanding the rupture behavior of megathrust
events is crucial for earthquake rupture physics, as well as for earthquake early-warning
systems. However, the large variability in behavior between individual events seemingly
defies a description with a simple unifying model. Here we use three source time function
(STF) data sets for subduction zone earthquakes, with moment magnitude Mw ≥ 7, and
show that such large ruptures share a typical universal behavior. The median STF is
scalable between events with different sizes, grows linearly, and is nearly triangular. The
deviations from the median behavior are multiplicative and Gaussian—that is, they are
proportionally larger for larger events. Our observations suggest that earthquake
magnitudes cannot be predicted from the characteristics of rupture onsets.
Advances in earthquake research are often sparked by observations of “peculiarities” of individual earthquakes [e.g., (1–3)], implying that there is a “normal” or aver- age earthquake behavior from which such
events deviate. This expected normal behavior,
however, is not well defined from an observational perspective; more often, our expectations
are driven by conceptual rupture models—for
example, that of self-similar cracks (4) or pulses
(5)—that may or may not be supported by observational evidence. For large earthquakes in
particular, whose rupture processes are obviously
complex, it is questionable whether such simple
models are meaningful.
Having a realistic and data-driven model for
rupture evolution is important beyond earthquake
source physics because the question of rupture
predictability hinges on it. Although there is
virtually unanimous consensus that the occurrence
of earthquakes currently cannot be predicted (6),
numerous studies have suggested that the evo-
lution of earthquake ruptures themselves may
follow a predictable pattern. These studies sug-
gest that the characteristics of the rupture onset
can be used to predict the final size of a rupture.
In particular, it has been suggested that rup-
tures that start impulsively may be more likely
to grow into large events (7) and, conversely,
that larger ruptures start more slowly, with a
longer (and seismically observable) nucleation
phase (8). However, observational reports on cor-
relations between rupture-onset characteristics
and final magnitudes (9, 10) have been con-
troversial (11, 12), and there is strong observa-
tional evidence that small and large shallow
continental crust earthquakes start in indistin-
guishable ways (12).
Earthquake early warning (EEW) algorithms
(13–15) could provide substantially longer warning
times if future rupture evolution could indeed be
predicted. Longer warning times would allow
alert recipients to perform more or better real-time
damage mitigation procedures, such as shutting
down gas lines and slowing trains (16). In the
absence of a rigorous statistical description for
Seismological Laboratory, California Institute of Technology,
Pasadena, CA, USA
*Corresponding author. Email: email@example.com