In today’s world we are faced with many problems in which geophysics can play an important role. Some of these are visualized in the following Figure %s and include: (a) finding resources (minerals, water, hydrocarbons, geothermal energy); (b) environmental problems (contaminants, salt water, UXO, permafrost), (c) geotechnical (tunnels, infrastructure, slope stability); (d) natural hazards (earthquakes, volcanoes, tsunami); (e) subsurface storage (radioactive waste, CO2 sequestration, water).
To address these problems we need to be able to obtain information about the earth without directly sampling the domain. This is precisely the roll that geophysics can fulfill. A typical geophysical experiment is portrayed in Figure 2 below.
Energy from a source is input to ground and propagates through the earth in a way that is governed by physical equations. The parameters in the governing equations are the physical properties of the earth (e.g. density, susceptibility, electrical conductivity, magnetic permeability, elastic parameters) and the distribution of these parameters determine how the energy flows. Sensors, usually at the surface, record potentials, fields and/or fluxes. These are the “observations” or “data”. In a general geophysical experiment we are given knowledge about the source, the equations governing the physics, and the observations. The goal is to extract information about the earth by recovering the distribution of the physical properties associated with the particular experiment.
In the following we introduce some of the experiments we shall be working with.
1.2.1. Cross-well Tomography¶
The physical property of interest is the seismic velocity or its reciprocal, slowness
Transmitters (Tx) in a borehole produce an acoustic signal which is measured by receivers (Rx) in another borehole. The governing equations are those used in seismology and involve density and the elastic constants. Here we simplify the physical problem and assume energy travels in straight rays. A value of a datum will be the time it takes for a seismic pulse to travel from a Tx to a Rx. Data can be plotted as a 2D image.
1.2.2. Direct Current (DC) Resistivity¶
The physical property is electrical conductivity σ or its reciprocal, resistivity
Current is input to the earth using a generator and two electrodes and the electric potential difference is measured between two other electrodes. The data are converted to an apparent resistivity and plotted as a pseudo-section.
1.2.3. Airborne Time-Domain EM¶
The physical property is the electrical conductivity. The transmitter is a large loop of wire in which a current is flowing. In its simplest form, a steady-state current is turned off and a receiver, usually mounted beneath the aircraft, measures the resultant magnetic field or its time derivative. Data can be plotted as individual decays for a transmitter or in plan-view for a particular time channel.
The physical property is magnetic susceptibility κ. This is related to magnetic permeability through the equation
The source is the earth’s magnetic field. This magnetizes earth materials and their resultant magnetic field can be measured with a magnetometer. The sensor can be on the surface of the earth or carried by various aircraft. The data are generally plotted in map form.
The above examples illustrate the relationship between earth physical property models, a geophysical experiment, and the resulting data. In each of these, the data on the right hand side of the figures, are generated by carrying out a forward simulation of the geophysical experiment. This is a well posed problem with a unique answer. In practise however, we are provided with the data and the ability to forward model and our goal is obtain the model on the left. This is the goal of the inverse problem.
Katika ulimwengu wa leo tunakabiliwa na matatizo mengi ambayo geophysics inaweza kucheza jukumu muhimu. "Miongoni mwa mambo hayo ni: (a) kutafuta rasilimali (madini, maji, hidrokarboni, nishati ya joto); (b) matatizo ya mazingira (wasambazaji, maji ya chumvi, UXO, permafrost); (c) geotechnical (mabwawa, miundombinu, utulivu wa mteremko); (d) hatari za asili (tetemeko la ardhi, volkano, tsunami); (e) kuhifadhi chini ya ardhi (matope ya radioactive, CO2 kuhifadhi, maji)." Ili kushughulikia matatizo haya tunahitaji kuwa na uwezo wa kupata habari kuhusu dunia bila moja kwa moja sampuli ya uwanja. Hii ni hasa jukumu ambalo geophysics inaweza kutimiza. Mfano wa majaribio ya geophysical ni kuonyeshwa katika Picha ya 2 hapa chini. Nishati kutoka chanzo ni pembejeo ya ardhi na kuenea kwa njia ambayo inaongozwa na fizikia equations. Vigezo katika equations kutawala ni mali ya fizikia ya dunia (kwa mfano Uwezo wa kuongoza umeme, mwelekeo wa umeme, uingizaji wa sumaku, na uingizaji wa umeme huamua jinsi nishati inavyozunguka. Sensors, kwa kawaida juu ya uso, rekodi uwezo, mashamba na au mtiririko. Hizi ni <unk>maoni<unk> au <unk>data<unk>. Katika jaribio la jumla la kijiografia tunapewa ujuzi kuhusu chanzo, equations zinazoongoza fizikia, na uchunguzi. Lengo ni kupata habari kuhusu dunia kwa kurudisha usambazaji wa mali za kimwili zinazohusiana na jaribio hususa. Katika zifuatazo sisi kuanzisha baadhi ya majaribio tutakuwa kufanya kazi na. 1.2.1 Uwezo wa kuongoza Cross-well tomography ni kipengele cha fizikia cha maslahi ya kasi ya tetemeko la ardhi au mwelekeo wake wa polepole, na inatoa ishara ya sauti ambayo hupimwa na receivers katika shimo lingine. Mlinganisho wa utawala ni wale kutumika katika seismology na kuhusisha wiani na constants elastic. Hapa sisi kurahisisha tatizo fizikia na kudhani nishati husafiri katika miale moja kwa moja. Thamani ya datum itakuwa wakati inachukua kwa msukumo seismic kusafiri kutoka Tx kwa Rx. Data inaweza kupangwa kama picha ya 2D. 1.2.2 Uwezo wa kuongoza Mzunguko wa moja kwa moja (DC) ni mwelekeo wa umeme (S) au mwelekeo wa umeme (S) unaoingiliwa na umeme wa umeme (S) na umeme wa umeme (S) unaoingiliwa na umeme (S) na umeme (S). Takwimu ni kubadilishwa kwa resistivity dhahiri na plotted kama pseudo-sehemu. 1.2.3. Airborne Time-Domain EM¶ Mali ya kimwili ni conductivity umeme. Kipeperushi ni kitanzi kikubwa cha waya ambacho umeme unapita ndani yake. Katika hali yake rahisi, umeme wa hali ya kudumu unazimwa na kipokeaji, kwa kawaida kilicho chini ya ndege, hupima uwanja wa sumaku unaotokana na umeme au mtiririko wake wa wakati. Data inaweza kuwa plotted kama decays mtu binafsi kwa transmitter au katika mpango-view kwa ajili ya kituo fulani cha muda. Mali ya kimwili ni magnetic susceptibility κ. Hii inahusiana na magnetic permeability kupitia equation Chanzo ni uwanja wa sumaku wa dunia. Hilo hufanya vifaa vya dunia viwe na sumaku na uwanja wao wa sumaku unaotokana na hilo unaweza kupimwa kwa kutumia kipimo cha sumaku. Sensorer inaweza kuwa juu ya uso wa dunia au kubebwa na ndege mbalimbali. Takwimu kwa ujumla ni plotted katika fomu ya ramani. Mifano iliyotajwa hapo juu inaonyesha uhusiano kati ya mifano ya mali ya kimwili ya dunia, jaribio la kijiografia, na data inayotokana. Katika kila moja ya hizi, data upande wa kulia wa takwimu, ni yanayotokana na kufanya simulation mbele ya majaribio geophysical. Hii ni tatizo vizuri kuweka na jibu la kipekee. Hata hivyo, katika mazoezi, sisi ni zinazotolewa na data na uwezo wa mbele mfano na lengo letu ni kupata mfano upande wa kushoto. Hii ni lengo la tatizo kinyume.