Average Strike Research Articles

Linkages between hydrothermal alteration, natural fractures, and permeability: Integration of borehole data for reservoir characterization at the Fallon FORGE EGS site, Nevada, USA

Between 2015 and 2018, the Fallon FORGE EGS (Engineered or Enhanced Geothermal System) site in Churchill County, Nevada, USA, underwent detailed geoscientific characterization to evaluate its suitability to operate as a field demonstration site to test and develop EGS technologies. This included the compilation, synthesis and acquisition of geophysical, geological, geochemical, hydrological, down-hole log, and mineralogy datasets. Site activities culminated in the drilling of a 2481 m-deep EGS observation well (21−31) to further verify the geology and rock properties of the proposed EGS reservoir formations, which are older than the Miocene and include felsic intrusions, felsic volcanics, and meta-sedimentary lithologies. In this paper, we integrate and evaluate borehole data from well 21−31, including drill cuttings and sidewall cores (petrographic, XRD, hyperspectral), wireline geophysical logs (e.g., gamma, neutron porosity, resistivity, sonic scanner), borehole imagers (FMI, BHTV), and pressure and temperature logs. Hydrothermal alteration and veining is found throughout the entire pre-Miocene interval of well 21−31, and includes epidote mineral assemblages that suggest past temperatures >250 °C. This is higher than the hottest measured equilibrated temperature at similar depths in other wells on the FORGE site today, and suggests that the system was higher temperature in the past. Overall lithologic variability is high, with volcanic, intrusive, metamorphic, and sedimentary rocks present in the bottom 700 m of the well. Natural fractures are abundant throughout the pre-Miocene section, but are more frequent in the felsic intrusive and felsic volcanic lithologies. The dominant orientation of these natural fractures observed in FMI logs is NNE-SSW with an average strike of 010° ± 40°, subparallel to the interpreted SHmax orientation of 009° ± 14° that is indicated by drilling-induced structures in the wellbore in the BHTV log. Therefore, natural fractures appear optimally oriented for reactivation via hydraulic stimulation. Mud loss locations and a non-equilibrated temperature log suggest that there are some zones with relatively-higher permeability and/or open fractures. However injection test results indicate an injectivity index of 0.025 L/min/kPa, which is an order of magnitude lower than a typical threshold for commercial wells. Analytical modeling of injection test results indicate that the majority of the well is low permeability (< 10−16 m²), with some discrete, localized zones of higher permeability (∼ 10 -12 m², less than 0.5 percent of the pre-Miocene (deep) section intersected by the well).

Finite Slip Models of the 2019 Ridgecrest Earthquake Sequence Constrained by Space Geodetic Data and Aftershock Locations

ABSTRACTThe July 2019 Ridgecrest, California, earthquake sequence involved two large events—the M 6.4 foreshock and the M 7.1 mainshock that ruptured a system of intersecting strike-slip faults. We present analysis of space geodetic observations including Synthetic Aperture Radar and Global Navigation Satellite System data, geological field mapping, and seismicity to constrain the subsurface rupture geometry and slip distribution. The data render a complex pattern of faulting with a number of subparallel as well as cross-cutting fault strands that exhibit variations in both strike and dip angles, including a “flower structure” formed by shallow splay faults. Slip inversions are performed using both homogeneous and layered elastic half-space models informed by the local seismic tomography data. The inferred slip distribution suggests a moderate amount of the shallow coseismic slip deficit. The peak moment release occurred in the depth interval of 3–4 km, consistent with results from previous studies of major strike-slip earthquakes, and the depth distribution of seismicity in California. We use the derived slip models to investigate stress transfer and possible triggering relationships between the M 7.1 mainshock and the M 6.4 foreshock, as well as other moderate events that occurred in the vicinity of the M 7.1 hypocenter. Triggering is discouraged for the average strike of the M 7.1 rupture (320°) but encouraged for the initial orientation of the mainshock rupture suggested by the first-motion data (340°). This lends support to a scenario according to which the earthquake rupture nucleated on a small fault that was more optimally oriented with respect to the regional stress and subsequently propagated along the less-favorably oriented pre-existing faults, possibly facilitated by dynamic weakening. The nucleation site of the mainshock experienced positive dynamic Coulomb stress changes that are much larger than the static stress changes, yet the former failed to initiate rupture.

Fine‐Scale Structure of the 2016–2017 Central Italy Seismic Sequence From Data Recorded at the Italian National Network

AbstractWe explore the three‐dimensional structure of the 2016–2017 Central Italy sequence using ~34,000 ML ≥ 1.5 earthquakes that occurred between August 2016 and January 2018. We applied cross‐correlation and double‐difference location methods to waveform and parametric data routinely produced at the Italian National Institute of Geophysics and Volcanology. The sequence activated an 80 km long system of normal faults and near‐horizontal detachment faults through the MW 6.0 Amatrice, the MW 5.9 Visso, and the MW 6.5 Norcia mainshocks and aftershocks. The system has an average strike of N155°E and dips 38°–55° southwestward and is segmented into 15–30 km long faults individually activated by the cascade of MW ≥ 5.0 shocks. The two main normal fault segments, Mt. Vettore‐Mt. Bove to the North and Mt. della Laga to the South, are separated by an NNE‐SSW‐trending lateral ramp of the Sibillini thrust, a regional structure inherited from the previous compressional tectonic phase putting into contact diverse lithologies with different seismicity patterns. Space‐time reconstruction of the fault system supports a composite rupture scenario previously proposed for the MW 6.5 Norcia earthquake, where the rupture possibly propagated also along an oblique portion of the Sibillini thrust. This dissected set of normal fault segments is bounded at 8–10 km depth by a continuous 2 km thick seismicity layer of extensional nature slightly dipping eastward and interpreted as a shear zone. All three mainshocks in the sequence nucleated along the high‐angle planes at significant distance from the shear zone, thus complicating the interpretation of the mechanisms driving strain partitioning between these structures.

Co-Seismic Deformation and Fault Slip Model of the 2017 Mw 7.3 Darbandikhan, Iran–Iraq Earthquake Inferred from D-InSAR Measurements

The 12 November 2017 Darbandikhan earthquake (Mw 7.3) occurred along the converence zone. Despite the extensive research on this earthquake, none of this work explained whether this earthquake rupture was limited to the thick sedimentary cover or it extends to the underlying crystalline basement rock (or both). Besides, whether this region will generate devastating earthquakes again and whether there is a one-to-one correlation between these anticlines and blind-reverse faults need further investigation. In this study, we derived the co-seismic interferograms from the Sentinel-1A/B data and successfully described the surface deformation of the main seismic zone. The fringe patterns of both the ascending and descending interferograms show that the co-seismic deformation is dominated by horizontal movements. Then, using the along- and across-track deformation fields of different orbits, we retrieved the three-dimensional deformation field, which suggests that the Darbandikhan earthquake may be a blind thrust fault close to the north–south direction. Finally, we inverted the geometrical parameters of the seismogenic fault and the slip distribution of the fault plane. The results show that the source fault has an average strike of 355.5° and a northeast dip angle of −17.5°. In addition, the Darbandikhan earthquake has an average rake of 135.5°, with the maximum slip of 4.5 m at 14.5 km depth. On the basis of the derived depth and the aftershock information provided by the Iranian Seismological Center, we inferred that this event primarily ruptured within the crystalline basement and the seismogenic fault is the Zagros Mountain Front Fault (MFF). The seismogenic region has both relatively low historical seismicity and convergent strain rate, which suggests that the vicinity of the epicenter may have absorbed the majority of the energy released by the convergence between the Arabian and the Eurasian plates and may generate Mw &gt; 7 earthquakes again. Moreover, the Zagros front fold between the Lurestan Arc and the Kirkuk Embayment may be generated by the long-distance slippage of the uppermost sedimentary cover in response to the sudden shortening of the MFF basement. We thus conclude that the master blind thrust may control the generation of the Zagros front folding.

Earthquake-Rotated Headstones as a Means of Re-evaluating Epicentral Location of the 1944 Massena-Cornwall Earthquake: New York, United States and Ontario, Canada

The Massena-Cornwall earthquake (September 5th, 1944) is the largest earthquake in New York state history. Two epicenters have been previously proposed (Milne, 1949; Dewey and Gordon, 1984); however, they are separated by 15 km, an error that could associate each proposed epicenter with two different local faults. Due to the lack of standardized seismic-array data, there is value in approaching this event using an unconventional data set. The methodology of MacDonald and Wentworth (1952) was executed through ArcMap 10.5.1 to yield an area most likely to contain the epicenter. One-hundred fifty-four earthquake-rotated headstones from 15 cemeteries within ~35 km of Massena, New York/Cornwall, Ontario were measured for angle of rotation via a digital goniometer (0.1 ̊ resolution). The mean angle of rotation is 1.9° (cf., 0.1° for unaffected, post-1944 headstones: p&lt;0.0001), independent of rotation direction. Factoring in the average strike of headstones in each cemetery, an octant was projected based on whether the cemetery had predominantly experienced clockwise or counter-clockwise rotation. The area of densest overlap between the projected octants is an ~20km2 area centered in the Saint Lawrence River (proposed epicenter at N45.014, W74.815) six miles northeast of Massena, NY. This area is bisected by the Gloucester Fault; an extension of the Ottawa-Bonnechere Graben. This project is an improvement on previous studies of the 1944-rotated headstones (e.g., Berkey, 1945) by analyzing quantitative rotational data within an ArcMap framework. These refined data implicate a rupture along an extension of the Gloucester Fault—a potential threat to the nearby Moses-Saunders Power Dam.

Neotectonic, morphotectonic and paleoseismologic analysis of the Las Chacras Fault System, Sierras Pampeanas Occidentales, San Juan, Argentina

Las Chacras Fault System is a Quaternary structure located in the western piedmont of Sierra de la Huerta in the Sierras Pampeanas Occidentales, in west-central Argentina. This fault system is subsidiary of the Valle Fértil Megafault System, the NW-striking master structure that affects the western flank of the Valle Fértil - La Huerta ranges. The Las Chacras Fault System comprise several sections including the Pan de Azúcar fault, which presents the most conspicuous evidence of tectonic Quaternary activity. The Pan de Azúcar fault affects three Quaternary alluvial surfaces (Q1, Q2 and Q3) along 26 km in the western piedmont of Sierra de La Huerta, where three natural exposures allowed us to observe Triassic rocks thrust over Quaternary deposits. The observation of different kinematic markers and the relative position of the units affected by the fault, allow us to define this fault as a reverse fault. This structure trends 325° and dips 25° NE. With a DGPS we carried out detailed topographic profiles perpendicular to the average strike of the fault, along interfluves and rivers that cross the structure, for the purpose of establishing the relationship between the topography and the slope of the terrain. This analysis indicates that Quaternary activity of the fault has played an essential role in controlling the piedmont geomorphology, generating west-facing scarps and drainage anomalies such as rivers with convex Hack profiles. Paleoseismic analyses indicate that the fault has moved after 18.360 ± 2990 yr BP. Furthermore, we calculated a net displacement for the Pan de Azúcar fault of ∼50 ± 0.2 m since the Late Pleistocene to Holocene, yielding a shortening rate and a slip rate of ∼0.16 ± 0.1 mm/yr. Thus, the Pan de Azúcar fault is a potential seismogenic source, which could produce a moderate earthquake between Mw = 6.4 and 7.0, with a recurrence interval between 2600 and 6900 years.

Pricing 'partial-average' Asian options with the binomial method

An Asian option is path-dependent derivatives whose payoff depends on the average of the underlying asset price over a certain pre-specified period of time. There is no simple closed-form solution for arithmetic Asian option hence the development of efficient and accurate numerical methods has become critical. In this paper, a modified binomial method is presented for pricing a more common arithmetic Asian option, by averaging the asset between two time periods in the life span of the option. This option is called the 'partial-average' Asian option. Subsequently, the representative averages are used instead of the actual ones for pricing the option. The set of representative averages is constructed first by determining the maximum and the minimum averages, where other averages are calculated by dividing equally the distance between the maximum and the minimum averages. For Asian option with average strike, if the distance between two time periods is widened by shifting the second time period to the right then the price becomes lower. But if the distance is widened by shifting the first time period to the left then the price becomes higher. The algorithm is not only simple but also easy to implement.

Pricing Partial-Average Asian Options with the Binomial Method

An Asian option is path-dependent derivatives whose payoff depends on the average of the underlying asset price over a certain pre-specified period of time. There is no simple closed-form solution for arithmetic Asian option hence the development of efficient and accurate numerical methods has become critical. In this paper, a modified binomial method is presented for pricing a more common arithmetic Asian option, by averaging the asset between two time periods in the life span of the option. This option is called the 'partial-average' Asian option. Subsequently, the representative averages are used instead of the actual ones for pricing the option. The set of representative averages is constructed first by determining the maximum and the minimum averages, where other averages are calculated by dividing equally the distance between the maximum and the minimum averages. For Asian option with average strike, if the distance between two time periods is widened by shifting the second time period to the right then the price becomes lower. But if the distance is widened by shifting the first time period to the left then the price becomes higher. The algorithm is not only simple but also easy to implement.

Source model of 2016 Mw6.6 Aketao earthquake, Xinjiang derived from Sentinel-1 InSAR observation

On 25 November 2016 (14:24:30 UTC), an Mw6.6 earthquake occurred in Aketao county of Xinjiang. We derived the coseismic deformation field of the earthquake from ESA's Sentinel-1B images and inverted the fault geometry and slip distribution by using a homogenous half-space elastic model and the Steepest Decent Method (SDM) program. The slip model shows that the rupture plane is about 68 km in length and 40 km in width and has an average strike of 105.2°SE and an average dip of 76.0°S. The average amount of slip is ∼0.16 m and the maximum amount of slip is 0.59 m. The estimated seismic moment is 1.31 × 1019 N·m and the corresponding moment magnitude is Mw6.68. The dislocation is mainly distributed in the depth of 5–22 km, where the rupture center is located at 39.17°E, 74.38°N, and a depth of ∼8.8 km, so this earthquake is a shallow earthquake. In terms of the tectonic settings, the earthquake was triggered by the release of residual stresses on the seismogenic Muji fault. The ruptures were stimulated simultaneously by the main shock, which made the slip distribution pattern of a strike-slip fault with a double fracture. Due to the tectonic setting and the seismic gap between the ruptures, the Muji fault would have a risk of rupture to some extent and trigger an earthquake in future.

THE CORINI ACTIVE FAULT IN SOUTHWESTERN VIOTIA REGION, CENTRAL GREECE: SEGMENTATION, STRESS ANALYSIS AND EXTENSIONAL STRAIN PATTERNS

The Corini normal fault is an active structure of Quaternary age in Southwestern Viotia. This is a region of low finite strain, located between the Quaternary rifts of the Gulf of Corinth and the Gulf of Evia. The fault is segmented into several segments with an average strike of N58°E and dip direction to the SE. The architecture of the fault zone is characterized by a 15 cm thick gouge rock, observed along the fault plane on the footwall side. At several localities along strike we observed a well-defined basal strip of un-eroded fault plane that represents the width (uplift) of the last co-seismic slip. The width of the strip ranges 20-30 cm. Slip inversion data show a mean orientation ofsigmaS (leastprincipal stress) as Ν328Έ which implies similar kinematics with the active faults of the south coast of the Gulf of Corinth.

Numerical analysis of seismic wave propagation in fluid-saturated porous multifractured media

Elastic wave propagation and attenuation in porous rock layers with oriented sets of fractures, especially in carbonate reservoirs, are anisotropic owing to fracture sealing, fracture size, fracture density, filling fluid, and fracture strike orientation. To address this problem, we adopt the Chapman effective medium model and carry out numerical experiments to assess the variation in P-wave velocity and attenuation, and the shear-wave splitting anisotropy with the frequency and azimuth of the incident wave. The results suggest that velocity, attenuation, and anisotropy vary as function of azimuth and frequency. The azimuths of the minimum attenuation and maximum P-wave velocity are nearly coincident with the average strike of the two sets of open fractures. P-wave velocity is greater in sealed fractures than open fractures, whereas the attenuation of energy and anisotropy is stronger in open fractures than sealed fractures. For fractures of different sizes, the maximum velocity together with the minimum attenuation correspond to the average orientation of the fracture sets. Small fractures affect the wave propagation less. Azimuth-dependent anisotropy is low and varies more than the other attributes. Fracture density strongly affects the P-wave velocity, attenuation, and shear-wave anisotropy. The attenuation is more sensitive to the variation of fracture size than that of velocity and anisotropy. In the seismic frequency band, the effect of oil and gas saturation on attenuation is very different from that for brine saturation and varies weakly over azimuth. It is demonstrated that for two sets of fractures with the same density, the fast shear-wave polarization angle is almost linearly related with the orientation of one of the fracture sets.

Structural control on the directional amplification of seismic noise (Campo Imperatore, central Italy)

Seismic signals propagating across a fault may yield information on the internal structure of the fault zone. Here we have assessed the amplification of seismic noise (i.e., ambient vibrations generated by natural or anthropogenic disturbances) across the Vado di Corno Fault (Campo Imperatore, central Italy). The fault zone is considered as an exhumed analogue of the normal faults activated during the L'Aquila 2009 earthquake sequence. Detailed structural geological survey of the footwall block revealed that the fault zone is highly anisotropic and is affected by a complex network of faults and fractures with dominant WNW–ESE strike. We measured seismic noise with portable seismometers along a ∼500 m long transect perpendicular to the average fault strike. Seismic signals were processed calculating the horizontal-to-vertical spectral ratios and performing wavefield polarization analyses. We found a predominant NE–SW to NNE–SSW (i.e., ca. perpendicular to the average strike of the fault-fracture network) amplification of the horizontal component of the seismic waves. Numerical simulations of earthquake-induced ground motions ruled out the role of topography in controlling the polarization and the amplitude of the waves. Therefore, the higher seismic noise amplitude observed in the fault-perpendicular direction was related to the measured fracture network and the resulting stiffness anisotropy of the rock mass. These observations open new perspectives in using measures of ambient seismic noise, which are fast and inexpensive, to estimate the dominant orientation of fracture networks within fault zones.

Geophysical and Hydrogeological Groundwater Prospectivity Mapping in the Kraaipan Granite-Greenstone Terrain, Southeast Botswana

Application of regional geophysical methods for hydrogeological purposes has increased over the last two decades especially in arid and semi-arid areas. A project to map the Kraaipan granite-greenstone terrain in southeast Botswana has recently been undertaken using regional aeromagnetic and gravity data with the aim to map the rocks at depth to understand the geology while the secondary objective was to subsequently assess the mineralization and groundwater potential in the area. An integrated analysis of the aeromagnetic and gravity data and their derived/processed products is hereby investigated for groundwater for drinking and agricultural purposes. The studies include: subsurface characterisation and delineation of structural framework suitable for groundwater exploration and determination of petrophysical relationships used to link the geophysical properties (e.g., density) to hydrological properties (e.g., porosity). The results of interpretation indicate that the rocks are under ~50 m of Kalahari cover and the study area is composed of three aquifers: the extensive hard rock aquifer (granitic and volcanic), the important (fractured) karst aquifer and the minor sedimentary aquifer. The area is dissected by an ENE-to-EW-trending dyke swarm visible on the regional aeromagnetic data and much clearer on high resolution aeromagnetic data. Minor fault and/or dyke elements of NW-SE and NE-SW trend are observed. Spectral analysis reveals three main average ensample interfaces at depths of 0.7 km, 1.99 km and 4.8 km. The linear Euler solutions maps reveal that the majority depths to top of magnetic bodies range from 40 m to 400 m throughout the survey area. The shallowest depths are the most significant one in this case as they probably relate to depth of bedrock and thickness of regolith or thickest sediments. For 2695 existing boreholes analysed, maximum borehole depth is 482 m (mean 108 m), and almost half (1263) were dry with another 972 having low yield (1 - 5 m3/hr) and 432 yielding 6 - 49 m3/hr and only 28 above 50 m3/hr (maximum ~160 m3/hr) and an average water strike of 64 m. There is very little correlation between interpreted hydrogeological features and the existing borehole locations. The study shows the importance of preliminary geophysical investigations before ground borehole siting and drilling in order to improve borehole success rates and/or reduce costs inherent in groundwater projects.

Preliminary magnetotelluric results across Dalma Volcanics, Eastern India: Inferences on metallogeny

The regional magnetotelluric (MT) survey across Dalma Volcanics (DVs) in North Singhbhum Mobile Belt (NSMB) was carried out to obtain the conductivity model and to understand the metallogeny. The structure in general is 2-D and the average strike is N60°W. 2-D inversions using TE+TM and TE+TM+Tzy were carried out. Both inversions derived models with similar features but with modified shape. The TE+TM+Tzy inversion brings up two conducting zones enveloping three anomalous conducting bodies. Inductively coupled plasma atomic emission spectroscopy (ICP-AES) analysis of the samples collected from 8 to 10m pit from different stratigraphic units of Dalma volcano-sedimentary belt indicates the presence of gold, silver, uranium and copper. The study area is a felsic dominated rifted margin and shows high conductivity contrast along with high gravity, magnetic and significant radiometric anomaly. Thus, the conducting zones indicate the presence of volcanogenic massive sulfide (VMS) or volcano hosted gold deposit (Au-VMS) in NSMB.

Geoelectric structure estimated from magnetotelluric data from the Uttarakhand Himalaya, India

Geoelectric strike and resistivity structure of the crust have been estimated from 37 magnetotelluric (MT) data sites along a profile from Roorkee to Gangotri in Uttarakhand Himalaya. Impedance decomposition schemes based on Bahr’s, Groom Bailey and Phase tensor were implemented in a MATLAB code for the average strike estimation. Geoelectric strike direction varies with period as well as in different litho-tectonic units along the profile. In the period band from 1 to 100 s average geoelectric strike in the southern end of the profile (Indo-Gangetic Plains) is N79°W, which is slightly rotated to the north in the Lesser Himalayan region and becomes N68°W whereas it is N81°W in the Higher Himalayan region. However, average strike is stabilized to N77°W for the entire profile in the long period band (100–1000 s). Geoelectrical structure of the crust has been obtained along the profile by 2D inversion of MT data. Major features of 2D resistivity model are: (i) southern part of the model is a low resistivity (<50 Om) zone at shallow depth (5–7 km) representing the loose sediments of the Indo-Gangetic Plains (IGP), whose thickness increases in the south; (ii) highly resistive (>1000 Om) layer below the IGP sediments is the basement rock, representing the resistivity of the top of the subducting Indian Plate; (iii) the Main Boundary Thrust (MBT) and the Main Central Thrust (MCT) zones can be seen in the electrical image. However, the Himalayan Frontal Thrust (HFT) could not be resolved and (iv) a low resistivity (<10 Om) feature in the MCT zone extending to the depth of 30 km is delineated. This low resistivity could be due to fluid-filled fractured rock matrix or partial melt zone. Hypocenters of many earthquakes are concentrated along the boundary of this low resistivity zone and relatively high resistivity blocks around it. The resulted model supports flat-ramp-flat geometry of the Main Himalayan Thrust along which the Indian Plate is subducting.

Crustal stress and fault strength in the Canterbury Plains, New Zealand

The Mw=7.1 Darfield (Canterbury) and Mw=6.2 Christchurch earthquakes and related aftershocks in Canterbury, New Zealand have revealed a major hazard in the Canterbury region in the form of the Greendale Fault and a number of associated faults. The strength of these apparently low slip-rate faults may affect the recurrence intervals of subsequent earthquakes. We use P- and S-wave picks from a dataset of aftershocks of the Darfield earthquake to estimate earthquake locations and focal mechanisms. We use S waveforms to determine shear-wave splitting (SWS) parameters and we estimate the azimuth of the axis of maximum horizontal compression (SHmax) from inversions of focal mechanisms. Two 2D methods of clustering the focal mechanisms for stress inversion are used, one to estimate the regional stress field and another to investigate variations in SHmax with distance from the Greendale Fault. A 3D method is also used to investigate variations in SHmax with depth. The tectonic stress field is remarkably uniform and has an average maximum horizontal compressive stress orientation of SHmax=116±18°, forming an angle with the average strike of the Greendale Fault of c. 25°. However, several SHmax estimates along the Greendale Fault from the regional 2D clustering method are sub-parallel to the fault strike (93.6±13.1°, 100.8±11.5° and 100.8±12.6°), indicating that the fault may be frictionally weak, in an Andersonian sense. This variation occurs via an anti-clockwise rotation of SHmax southwards across the Greendale Fault. SWS fast directions (ϕ) generally match nearby SHmax, suggesting stress-aligned micro-cracks, but ϕ estimates at stations Cch3 and MQZ, which are near known and inferred faults, are sub-parallel to these faults and differ greatly from nearby stress orientations, indicating structure-dependent anisotropy. A lack of seismicity in the area prior to the Darfield earthquake precludes detailed analysis of time variations. However, there are two end member scenarios: if the pre-seismic stress orientation near the Greendale Fault was in the same direction as we have measured after the earthquake, then it was mis-oriented for rupture. Alternatively, if the stress rotated from the average regional orientation during the earthquake, then we can use the rotation to determine that an average of c. 40% of the pre-seismic differential stress on the Greendale Fault was released during the Darfield earthquake.

Pricing Asian call option with average strike using a non-uniform grid

The problem of pricing Asian call option with average strike on a non-uniform grid is examined. The backward partial differential equation (PDE) along with the final and boundary conditions for an Asian call option with average strike is presented. A Crank Nicolson Implicit Method based scheme on a non-uniform grid for both spatial and temporal direction is derived, making use of a transformation to generate the non-uniform grid. The scheme is implemented to obtain the price of the Asian option for various values of drift and volatility. The results show a close match with the values obtained using Monte Carlo simulation and numerical PDE methods on uniform grid. The values obtained using the non-uniform grid (as compared to uniform grid) were closer to the values from Monte-Carlo simulation for smaller volatilities, thereby indicating that non-uniform grid could lead to more accurate results in case of smaller volatilities.

Morphometric analysis of the submarine arc volcano Monowai (Tofua–Kermadec Arc) to decipher tectono-magmatic interactions

Morphometric analysis of multibeam bathymetry and backscatter data is applied to Monowai, a submarine volcano of the active Tofua–Kermadec Arc to map and document the structure and evolution of the volcanic centre. Low rates of erosion and sedimentation, and pervasive tectonic and magmatic processes, allow quantification through detailed structural analysis and measurement of deformation. The Slope, Aspect, Curvature, Rugosity, and Hydrology (flow) tools of ArcGIS provide a robust structural interpretation and the development of a model of Monowai evolution.A nested caldera structure with a volume of ~31km3 and a stratovolcano of ~18km3 dominate the magmatic constructs. The outer caldera is elongate along 125°, and the inner caldera along 135°. Numerous parasitic cones and fissure ridges are also observed, oriented at 039° and 041°, respectively. Northeast trending faults (with a regional average strike of 031°) are widespread within this part of the backarc, forming a nascent rift graben to the west of the Monowai caldera complex. The distribution of throw varies spatially, reaching a maximum total along-rift of 320m and across rift of 120m, with greater throw values measured in the west.Elongation directions of the two nested calderas are near-perpendicular to the trends of faults and fissure ridges. The inner caldera is more orthogonal to the magmatic constructs (fissure ridges and aligned vent cones) and the outer caldera is approximately orthogonal to the regional fault fabric, suggesting a strong interaction between magmatic and tectonic processes, and the directions of the horizontal principal stress. We present a detailed morphometric analysis of these relationships and the data are used to interpret the spatial and temporal evolution of the tectono-magmatic system at Monowai, and classify the type of rifting as transtensional. Similar analysis is possible elsewhere in the Kermadec backarc and within other regions of submarine volcanism.

The 2008 West Bohemia earthquake swarm in the light of the WEBNET network

A swarm of earthquakes of magnitudes up to M L = 3.8 stroke the region of West Bohemia/Vogtland (border area between Czechia and Germany) in October 2008. It occurred in the Nový Kostel focal zone, where also all recent earthquake swarms (1985/1986, 1997, and 2000) took place, and was striking by a fast sequence of macroseismically observed earthquakes. We present the basic characteristics of this swarm based on the observations of a local network WEBNET (West Bohemia seismic network), which has been operated in the epicentral area, on the Czech territory. The swarm was recorded by 13 to 23 permanent and mobile WEBNET stations surrounding the swarm epicenters. In addition, a part of the swarm was also recorded by strong-motion accelerometers, which represent the first true accelerograms of the swarm earthquakes in the region. The peak ground acceleration reached 0.65 m/s2. A comparison with previous earthquake swarms indicates that the total seismic moments released during the 1985/1986 and 2008 swarms are similar, of about 4E16 Nm, and that they represent the two largest swarms that occurred in the West Bohemia/ Vogtland region since the M L = 5.0 swarm of 1908. Characteristic features of the 2008 swarm are its short duration (4 weeks) and rapidity and, consequently, the fastest seismic moment release compared to previous swarms. Up to 25,000 events in the magnitude range of 0.5 < M L < 3.8 were detected using an automatic picker. A total of nine swarm phases can be distinguished in the swarm, five of them exceeding the magnitude level of 2.5. The magnitude–frequency distribution of the complete 2008 swarm activity shows a b value close to 1. The swarm hypocenters fall precisely on the same fault portion of the Nový Kostel focal zone that was activated by the 2000 swarm (M L ≤ 3.2) in a depth interval from 6 to 11 km and also by the 1985/1986 swarm (M L ≤ 4.6). The steeply dipping fault planes of the 2000 and 2008 swarms seem to be identical considering the location error of about 100 m. Furthermore, focal mechanisms of the 2008 swarm are identical with those of the 2000 swarm, both matching an average strike of 170° and dip of 80° of the activated fault segment. An overall upward migration of activity is observed with first events at the bottom and last events at the top of the of the activated fault patch. Similarities in the activated fault area and in the seismic moments released during the three largest recent swarms enable to estimate the seismic potential of the focal zone. If the whole segment of the fault plane was activated simultaneously, it would represent an earthquake of M L ~5. This is in good agreement with the estimates of the maximum magnitudes of earthquakes that occurred in the West Bohemia/Vogtland region in the past.

Path integral approach to Asian options in the Black–Scholes model

We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.