Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Transform faultA transform boundary occurs when two tectonic plates move past one another. Shear stress operates at transform boundaries, which involves sliding motion. No lithosphere is destroyed or created, and mountain chains are not built at transform boundaries. They accommodate the lateral offset between segments of divergent boundaries, forming a zigzag pattern. This is a result of oblique seafloor spreading where the direction of motion is not perpendicular to the trend of the overall divergent boundary.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
Surface-wave magnitudeThe surface wave magnitude () scale is one of the magnitude scales used in seismology to describe the size of an earthquake. It is based on measurements of Rayleigh surface waves that travel along the uppermost layers of the Earth. This magnitude scale is related to the local magnitude scale proposed by Charles Francis Richter in 1935, with modifications from both Richter and Beno Gutenberg throughout the 1940s and 1950s. It is currently used in People's Republic of China as a national standard (GB 17740-1999) for categorising earthquakes.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Reflection seismologyReflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized air gun or a seismic vibrator. Reflection seismology is similar to sonar and echolocation. Reflections and refractions of seismic waves at geologic interfaces within the Earth were first observed on recordings of earthquake-generated seismic waves.
Seismic hazardA seismic hazard is the probability that an earthquake will occur in a given geographic area, within a given window of time, and with ground motion intensity exceeding a given threshold. With a hazard thus estimated, risk can be assessed and included in such areas as building codes for standard buildings, designing larger buildings and infrastructure projects, land use planning and determining insurance rates.
San Andreas FaultThe San Andreas Fault is a continental right-lateral strike-slip transform fault that extends roughly through the Californias. It forms the tectonic boundary between the Pacific Plate and the North American Plate. Traditionally, for scientific purposes, the fault has been classified into three main segments (northern, central, and southern), each with different characteristics and a different degree of earthquake risk. The average slip rate along the entire fault ranges from per year.
Apparent magnitudeApparent magnitude (m) is a measure of the brightness of a star or other astronomical object. An object's apparent magnitude depends on its intrinsic luminosity, its distance, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer. The word magnitude in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer Claudius Ptolemy, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest).
Seismic waveA seismic wave is a mechanical wave of acoustic energy that travels through the Earth or another planetary body. It can result from an earthquake (or generally, a quake), volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. Seismic waves are studied by seismologists, who record the waves using seismometers, hydrophones (in water), or accelerometers.
