Michel Bouchon

The state of stress on some faults of the San Andreas System as inferred from near‐field strong motion data

We present a simple method to calculate the stress produced on an earthquake fault during rupture. This method allows the complete evaluation of the stress spatio-temporal history over the fault. We apply this approach to study the changes in shear stress produced during four of the largest earthquakes which occurred along the San Andreas fault system over the last 20 years: the Imperial Valley earthquake of 1979, the Morgan Hill earthquake of 1984, the Loma Prieta earthquake of 1989, and the Northridge earthquake of 1994. We use for this study the tomographic models of the fault rupture obtained from the inversion of the near-field seismic data recorded during these earthquakes. The results obtained show that the static and the dynamic stress drops vary greatly over the fault. The peak values obtained for the four earthquakes studied range from about 20 to 100 MPa. These high values imply that the initial shear stress level on the fault at the onset of the earthquake was high on at least a significant portion of the fault. The regions of the fault which break with a high stress drop are also the regions where slip is large. This suggests that most of the slip produced in a large earthquake takes place over the “strong” areas of the fault. Low slip regions tend to break with low stress drops. After the earthquake, the shear stress is increased over a significant portion of the fault, which corresponds to low slip regions. Aftershock activity tends to be concentrated in these areas of stress increase. The apparent strength of the fault before the earthquake (that is the local shear stress increase which is required for rupture) is also extremely heterogeneous. The rupture velocity seems to be inversely correlated with this apparent fault strength, the rupture accelerating over the “weak” areas of the fault and slowing down over the high strength areas.

Extended Nucleation of the 1999 Mw 7.6 Izmit Earthquake

Low-frequency seismic events may have been part of slip accumulation before a large earthquake. Laboratory and theoretical studies suggest that earthquakes are preceded by a phase of developing slip instability in which the fault slips slowly before accelerating to dynamic rupture. We report here that one of the best-recorded large earthquakes to date, the 1999 moment magnitude (Mw) 7.6 Izmit (Turkey) earthquake, was preceded by a seismic signal of long duration that originated from the hypocenter. The signal consisted of a succession of repetitive seismic bursts, accelerating with time, and increased low-frequency seismic noise. These observations show that the earthquake was preceded for 44 minutes by a phase of slow slip occurring at the base of the brittle crust. This slip accelerated slowly initially, and then rapidly accelerated in the 2 minutes preceding the earthquake.

Space and Time Evolution of Rupture and Faulting during the 1999 İzmit (Turkey) Earthquake

We use the records of the ground motion obtained at near-fault accelerometers to study the space and time evolution of rupture and faulting during the Izmit earthquake. We find that the rupture propagated at the sub-Rayleigh speed of about 3 km/sec on the western and eastern segments of the fault, but that the central segment (Izmit-Sapanca Lake-Sakarya), nearly 50 km long, broke at the supershear speed of about 4.8 km/sec. This value, within the range of uncertainties, is the one theoretically predicted ( \(\sqrt{2}V_{\mathrm{S}}\) ) in fracture dynamics for stable shear crack growth at intersonic speed. We infer an average fault slip of about 2.9 m over a total rupture length of about 150 km, with the largest values (of up to 6 m) occurring in the Golcuk area to the west and in the Sakarya region to the east. The strong-motion data also indicate that the slip diminished gradually to the west beyond the Hersek peninsula over about 30 km, whereas it stopped abruptly at depth at the termination of the eastern (Karadere) segment. The slip duration is between 2 and 4 sec, except in the hypocentral area, which slipped in about 1 sec. The seismic moment inferred is about 2.5 × 10 20 N m.

A Review of the Discrete Wavenumber Method

We present a review of the discrete wavenumber (DWN) method. The method, introduced by BOUCHON and ART (1977), allows the simple and accurate calculation of the complete Green’s functions for many problems in elastodynamics.

Effect of three-dimensional topography on seismic motion

We present a semianalytical, seminumerical method to calculate the diffraction of elastic waves by an irregular topography of arbitrary shape. The method is a straightforward extension to three dimensions of the approach originally developed to study the diffraction of SH waves [Bouchon, 1985] and P-SV waves [Gaffet and Bouchon, 1989] by two-dimensional topographies. It relies on a boundary integral equation scheme formulated in the frequency domain where the Green functions are evaluated by the discrete wavenumber method. The principle of the method is simple. The diffracted wave field is represented as the integral over the topographic surface of an unknown source density function times the medium Green functions. The Green functions are expressed as integrals over the horizontal wavenumbers. The introduction of a spatial periodicity of thc topography combined with the discretization of the surface at equal intervals results in a discretization of the wavenumber integrals and in a periodicity in the horizontal wavenumber space. As a result, the Green functions are expressed as finite sums of analytical terms. The writing of the boundary conditions of free stress at the surface yields a linear system of equations where the unknowns are the source density functions representing the diffracted wave field. Finally, this system is solved iteratively using the conjugate gradient approach. We use this method to investigate the effect of a hill on the ground motion produced during an earthquake. The hill considered is 120 m high and has an elliptical base and ratios of height-to-half-width of 0.2 and 0.4 along its major and minor axes. The results obtained show that amplification occurs at and near the top of the hill over a broad range of frequencies. For incident shear waves polarized along the short dimension of the hill the amplification at the top reaches 100% around 10 Hz and stays above 50% for frequencies between 1.5 Hz and 20 Hz. For incident shear waves polarized along the direction of elongation of the topography, the maximum amplification occurs between 2 Hz and 5 Hz with values ranging from 50% to 75%. The results also show that the geometry of the topography exerts a very strong directivity on the wave field diffracted away from the hill and that at some distance from the hill this diffracted wave field consists mostly of Rayleigh waves.

A boundary integral equation-discrete wavenumber representation method to study wave propagation in multilayered media having irregular interfaces

We present a method which combines boundary‐integral equation techniques with the discrete wavenumber Green’s function representation to study wave propagation in multilayered media having irregular interfaces. The approach is based on the representation of the interfaces by distributions of body forces, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green’s functions are evaluated by the discrete wavenumber method. Propagator matrices are introduced to relate force distributions on neighboring interfaces. The solution then requires the inversion of a matrix at each interface. The dimensions of the linear system are independent of the number of layers considered, and the computation time varies linearly with the number of interfaces. We apply the method to calculate surface and vertical seismic profiles in the presence of synclinal or anticlinal structures.

Seismic imaging of the 1999 Izmit (Turkey) Rupture inferred from the near-fault recordings

We use near-fault accelerograms to infer the space-time history of rupture on the fault during the Izmit earthquake. The records show that the ground displacement and velocity near the fault were surprisingly simple. Rupture propagated toward the west at a velocity of about 3 km/s, and toward the east at a remarkably high average velocity of 4.7 km/s over a distance of about 45 km before decelerating to about 3.1 km/s on the eastern segment. Slip on the fault is particularly large down to a depth of 20 km on the central portion of the fault where it reaches about 7 m. Slip is large also below 10 km on the eastern fault segment, and this may have contributed to the loading of shear stress on the Duzce fault. On the western fault segment, large slip seems confined to shallow depths.

The Seismicity in the Eastern Marmara Sea after the 17 August 1999 İzmit Earthquake

We used seismic stations that we deployed after the Izmit earthquake along the shores and islands of the Izmit Bay-Cinarcik basin to study the seismic activity that took place after the earthquake in the eastern Marmara Sea. The aftershock distribution indicates the existence of three clusters of activity there in the days that followed the earthquake. One of the clusters shows the extension of the E-W-trending Izmit rupture into the eastern Marmara Sea. The seismic activity there clearly outlines the fault plane of the main rupture and shows its termination 35 km beyond the Hersek peninsula. Two other clusters of activity are present in the region. One is in the Armutlu peninsula and the other one is located a few kilometers southwest of the Tuzla peninsula beneath the northern slope of the Cinarcik basin. The focal mechanism solutions indicate strike-slip faulting along the main branch of the Izmit rupture and normal faulting within the two swarms. The presence of the different mechanisms suggests the existence of slip partitioning in the region. A remarkable feature of the aftershock data is the absence of seismicity above 4 km in the Marmara Sea. Manuscript received 30 August 2000.

Attenuation of crustal waves across the Alpine Range

We present observational evidence of an anomalous propagation of Lg waves across the south-western part of the Alpine range, and we use numerical simulations to model these observations. We consider a set of 48 earthquakes which occurred in Switzerland, northern Italy, and southeastern France and were recorded by the French (Laboratoire de Detection et de Geophysique) and northwest Italian (Istituto Geofisico di Genova) seismic networks. While the amplitude of the Pn phase is stable throughout the region studied, Lg wave amplitude undergoes strong variations. We map this anomaly in Lg wave propagation by dividing the region into a grid and attributing to each cell a value equal to the mean value of the Lg/Pn amplitude ratios computed for all the paths which cross this cell. The image obtained shows that the extinction of Lg waves occurs in a limited region of the western Alps which corresponds to the zone of highest positive Bouguer anomaly. This zone located to the east of the high peaks of the Massifs Cristallins Externes does not correspond either to the region of the highest topographies or to the one of the deepest Moho. At a frequency of 2 Hz, the crustal waves that cross this anomalous region have amplitudes divided by more than 10 with respect to waves that propagate along other paths. In order to investigate the cause of the anomaly we perform numerical simulations of SH wave propagation through a model of the western Alps which includes the main characteristics of the geological structure. Our results indicate that the geometrical effect of the lateral variations of the medium does not account entirely for the actual vanishing of crustal waves. The simulation predicts a decay of the amplitude by only a factor between 2 and 3. The introduction of corrugation in the interface shapes further adds to the decay. However, other sources of attenuation such as anelasticity or severe heterogeneity must be invoked to explain fully the observations.

Stress field associated with the rupture of the 1992 Landers, California, earthquake and its implications concerning the fault strength at the onset of the earthquake

We investigate the space and time history of the shear stress produced on the fault during the 1992 Landers earthquake. The stress is directly calculated from the tomographic image of slip on the fault derived from near-source strong motion data. The results obtained shed some light on why the earthquake rupture cascaded along a series of previously distinct fault segments to produce the largest earthquake in California in over 40 years. Rupture on the 30 km long northernmost segment of the fault was triggered by a large dynamic increase of the stress field, of the order of 20 to 30 MPa, produced by the rupturing of the adjacent fault segments. Such a large increase was necessary to overcome the static friction on this strand of the fault, unfavorably oriented in todays tectonic stress field. This misorientation eventually led to the arrest of rupture. The same mechanism explains why rupture broke only a small portion of the Johnson Valley fault on which the earthquake originally started, before jumping to an adjacent fault more favorably oriented. We conclude from these results that the dynamic stress field could not sustain and drive the rupture along the strongly misoriented NW-SE strands of the preexisting fault system. Instead, the dynamic stress field produced new fractures favorably oriented in a N-S direction and connecting parts of the old fault system.