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Channel Remapping Channel remapping allows you to change: the Order of channels on each analog spread cable that connects to the Geode reorder the Geode boxes. You would use this option if your cables were wired opposite to the default Order normally used in Geometrics wiring, if you wished to turn your line around to have the low channels at the opposite end, or if your cables had a wiring error. Channel remapping is also often necessary when using more that a single network cable. Default cable wiring of Geometrics seismographs Default Order is defined as the natural electrical Order in which channels are oriented when the system first powers up before remapping. Refer to Section 3 under Connector Wiring that discusses standard wiring configurations. You may have requested a custom wiring configuration from Geometrics. If you are confused about your wiring, contact the factory and refer to the serial number and job number. Geode cables are typically wired in a ‘high-side configuration’, meaning that the Geode connects closest to the highest numbered channel on the analog cable. The 149 figure above shows this configuration for a single box system, with 24 channels. Multiple Geodes The following diagram shows a default single digital line (one network card) system with 3 Geodes. Note that Geode one is always closest to the controller in a default configuration. Multiple Network Lines The next diagram below shows a default configuration with two digital lines (two network cards) with the controller positioned in the middle. Line 1 is on the left and line 2 is on the right. One might use two lines to increase data throughput to reduce time between shots. Like the configuration above, the Geodes are numbered starting closest to the controller. The seismic controller Software labels all of the channels contiguously even though they are on two separate digital lines. However, if the lines are collinear, the first line will have the channels Ordered backwards. This can be easily rectified with the remapping feature. There are two ways of remapping channels: automatic mode and manual mode. Automatic mode settings are listed on the top of the remapping dialog box, and manual mode on the bottom. Automatic Channel Remapping Automatic channel remapping allows you to reverse either the Order of the Geodes on the line, or reverse the Order of the channels on the spread cable. The above diagram shows the result after both channels and Geodes have been reversed, renumbering the line so that low channels start on the left hand side and increase towards the right. In the dialog box, the automatic remapping boxes referencing line 2 remain unchecked, since the default orientation on line two was correct. Manual Channel Remapping Channels can be remapped on an individual basis using the Manual Map Mode. Select the appropriate check box, and enter the Order in which you would like the channels that differs from the default Order. You can specify individual channels separated by a comma (1, 3, 4, 6 etc) or a range of channels (1-13, 24-14 etc). For example, if you wanted the channels Ordered backwards on a 24-channel system, you would enter 24-1. If you wished to reverse the Order of channels 1- 12 in a 24 channel system, you would type 12-1, 13-24. Other examples are shown opposite, and are available by pressing the See Examples button on the remapping menu.

The cesium used in our magnetometers is the non-radioactive elemental metal, isotope Cs 133. We employ approximately 120 to 240 micrograms of cesium metal in the sensor divided between the lamp and absorption cell. These are small glass ampules, each containing a volume of 1/32 to 1/16 of a cubic millimeter of cesium. If either or both the lamp and cell should break the cesium will instantaneously react with the air and moisture in the air to become Cs2O and/or CsOH. Both compounds are caustic but the quantity is so small that it is of no health concern. Finally, the lamp and the cell ampules are contained in a G10 housing that is then contained inside a sealed PVC housing. If the sensor should cease working due to a broken lamp and/or cell, it is not field repairable. Return the sensor to Geometrics for repair, replacement and/or disposal.

I have attached the instructions that are sent with a new Order acknowledgment. (Installation and Transfer) The license is assigned to a specific Registration ID once fully purchased. This ID can be assigned to a person (we like to know for our own records) if possible but not required and can be transferred to other PC’s as needed. The ID works like a Softkey dongle. The Software can be active on only one machine at a time. I attached a simplified “Steps with windows_SI Transfer procedure that shows how the Software can be moved. The PC must connected to the internet to affect the first part of the transfer (which removes the ID from the PC, making available for the next). Then to place the Reg ID on the next computer is just following the original registration process. Do not lose the ID. Make sure that the ID has been removed before a disc is reimaged or an employee leaves with the PC. If for some reason the Reg ID has to be reset, (computer dies before the ID can be removed) I will require a statement and an end user then for my records. I am available to discuss if needed at the number below 0700-1500 PST. Best, RandL P RiveraCustomer Service Repair Supervisor+1 (408) 428-4254 (direct)+1 (408) 954-0522 (office)support@geometrics.com Attachment : SeisImager_LicenseTransfer_Instructions_v1.2.pdf Attachment : Steps with windows_SI Transfer.pdf Attachment : SeisImager_Installation_Instructions_v7.6.pdf

The best source for seismic reflection is not always the most practical. Parameters such as cost, size, access, surface materials, and depth of penetration must all be taken into account. As always, a sledgehammer always supplies the most bang for the buck when practical. If the ground surface is too Soft for a sledgehammer, you might consider a downhole seisgun. Small explosives are ideal in terms of portability and power, but for obvious reasons are often not feasible. Less portable sources like weight drops and vibrators should be considered when access allows and required depth of penetration exceeds that of a sledgehammer or seisgun. Although depth of penetration varies widely depending on the geology and cultural noise, you can expect to see somewhere in the range of 0.25 - 0.5 seconds with the latter two sources.

All of the 300 series stainless (austenitic) steel is considered to be weakly magnetic in its annealed state. These include the common 303, 304, and 316 alloys. 18-8 stainless is another name for 304 stainless (18% chromium and 8% nickel). Surprisingly it is the nickel content in the stainless that makes the steel less magnetic. Nickel usually makes things more magnetic in other metals. The 400 series are very magnetic (martensitic). They do not contain nickel. 17-4 stainless is a different class of stainless, and contains a little nickel (4%) but has other stuff in it that makes it magnetic. To make it even more confusing: All stainless steels, including the 300 series, become very magnetic when hardened. A Soft ductile 316 stainless cotter pin is not very magnetic, but a 316 stainless spring is highly magnetic. If it is stainless and "springy" it will most likely be very magnetic.

As of 08/2023 these are good batteries to use (links are to USA Amazon site): OVONIC 3s Lipo Battery 35C Gens ace 3S LiPo Battery 11.1V 2200mAh 35C Soft Case Pack with XT60 Plug These "shorty" battery packs have the advantage of being much shorter for a given milliamp hour rating, making them easier to fit in the MagArrow battery compartment.

A seismograph with an active trigger input like the Geode Seismograph or ES-3000 Seismograph can be triggered many different ways. The most commonly used methods are with a trigger switch or a trigger geophone. Typically a trigger switch (known as a hammer switch) is attached to the handle of a sledgehammer near the striking end, so when the sledgehammer is hit against a striker plate to create an active source of energy, the piezoelectric crystal in the hammer switch is activated and the seismograph is triggered to record data along the preset parameters. A trigger geophone does this too, but it is placed near the source itself, and is more commonly used with larger energy sources like a propelled energy generator. If the seismograph isn't triggering with either a hammer switch or a trigger geophone, then the signal may be weak, so turning up the sensitivity could be a workable solution. If the sensitivity is set too high in SCS then false triggers might be encountered. In most situations having the sensitivity set to the middle works best. Depending on where the trigger geophone is it, there may be a difference between when it is triggered and when a hammer switch would have triggered. Especially in Soft ground the trigger geophone signal may be delayed. In general the hammer trigger is a more reliable timing device. The differences in trigger time when using a trigger geophone could be due to things like not striking the center of the plate or differences in the strength of the impact. More trigger circuit information: The seismograph can be triggered by shorting the two input pins A and B on the trigger connector of the seismograph. In fact, that is what the hammer switch does (contact closure device) when it impacts a striker plate. The inertia of the impact causes a momentary closure in the device, which in turn, triggers the Geode. There are no internal components that need to be added. Externally, you could construct trigger device or switch, if that is what you desire. If you were to measure the pins on the Trigger connector on your seismograph (pin A +, pin B -) you would see about 5VDC. The trigger circuit will sense a contact closure or a pulse. The Geode trigger input is capacitively coupled, with a 2mS time constant, to the midpoint of a resistive voltage divider. The voltage difference between the two ends of the divider constitute a voltage "window", which size is set by the trigger sensitivity parameter and can range from essentially zero at the highest sensitivity, to about +/- 2.5V at the lowest sensitivity. The Geode triggers (if enabled) if and when the coupled signal exceeds the window, in either direction. The signal, after the capacitor, is clamped by diodes to the range between the trigger signal ground and +5VDC. The trigger detector output is disabled when the system is disarmed, during a parameter change, and during a shot, up to the trigger hold-off time after the end of the shot. The trigger hold-off time is a parameter set by the user. Preceding the coupling capacitor (i.e., essentially the node accessible at pin A of the external connector), there is a 3.3K-Ohm pull-up resistor to +5VDC (relative to pin B). Also a fast transient suppressor clamps the input at about +/-14VDC. It is advised that the DC + AC level of any voltage applied to pin A relative to pin B be kept within the range of +/-7V, giving some margin of safety. If a DC voltage somewhat less than +5VDC is applied when the connector is first mated, the instrument may trigger at that moment. But, subsequently, because of the capacitive coupling, it will trigger on the next positive or negative going pulse that exceeds the window level. If the duration of the applied voltage pulse is less than the record length + delay time + hold-off time, then the Geode will effectively be ready to trigger on the same edge of another similar pulse.

The time associated with each data point in a SEG-2 data file generated by a Geode is related to the time of the “trigger” event which was instrumental in the production of the file and its content. The Trigger Master and Trigger Distribution The trigger event occurs at the Geode designated within the Controller Software as the Trigger Master. Although all Geodes are capable of being Trigger Masters, there must be one and only one Trigger Master in any properly functioning Geode system. The Controller automatically takes care of this requirement when the designation is made by a user, and when the system is established at the time of Controller start-up based on a previous designation (or a default setting in the case of a “new survey”). All other Geodes in the system will have their Trigger Master circuit disabled. A trigger event can be initiated by an external electrical pulse provided to the trigger input connector of the Trigger Master Geode, or by a command sent via Ethernet from the Controller to the Trigger Master (usually for test purposes), but only when all conditions are satisfied to allow data recording. There is also a special trigger initiation situation, called “self-triggering” which will not be discussed further here. Upon acceptance of a trigger event, the Trigger Master will distribute the trigger signal to all Geodes in the system, itself included, via an RS-485 network that resides within the digital interconnect cabling. (Proper termination of this RS-485 network is automatically taken care of by the Controller.) The trigger signal is propagated through the cabling and Geodes at the nominal speed of 70% of the speed of light, or approximately 2.1x10^8 m/sec. The maximum distance of successful propagation depends on a number of factors such as the number of Geodes involved, the noise environment, the quality of the cables, and the acceptable amount of timing uncertainty for the particular application. Distances approaching or exceeding 1km should be given careful attention in this regard. In a 3-D Geode system involving LTUs, each LTU, unlike a Geode, will reconstruct the trigger signal before sending it on, effectively confining the maximum distance issue to each sub-network separated by LTUs. The penalty is an additional delay of about 100nS for each LTU in the route. The External Trigger Circuit The external trigger input is capacitively coupled, with a 2mS time constant, to the midpoint of a resistive voltage divider. The voltage difference between the two ends of the divider constitute a voltage "window", which size is set by the trigger sensitivity parameter and can range from essentially zero at the highest sensitivity, to about +/- 2.5V at the lowest sensitivity. The Geode will trigger (if enabled) if and when the coupled signal exceeds the window, in either direction (i.e., positive or negative going). The signal, after the capacitor, is clamped by diodes to the range between the trigger signal ground and +5VDC. The trigger detector output is disabled when the system is disarmed, during a parameter change, and during a shot, up to the trigger hold-off time after the end of the shot. The trigger hold-off time is a parameter set by the user. Preceding the coupling capacitor (i.e., essentially the node accessible at pin A of the external connector), there is a 3.3K-Ohm pull-up resistor to +5VDC (relative to pin B). Also a fast transient suppressor clamps the input at about +/-14VDC. It is advised that the DC + AC level of any voltage applied to pin A relative to pin B be kept within the range of +/-7V, giving some margin of safety. If a DC voltage somewhat less than +5VDC is applied when the connector is first mated, the instrument may trigger at that moment. But, subsequently, because of the capacitive coupling, it will trigger on the next positive or negative going pulse that exceeds the window level. If the duration of the applied voltage pulse is less than the record length + delay time + hold-off time, then the Geode will effectively be ready to trigger on the same edge of another similar pulse. Sub-sample Synchronization The Geode supports a sub-sample timing synchronization feature used for synchronizing the data acquisition after a trigger event to the distributed trigger signal, so that subsequent time points will be known to within 1/32 (~1/20 at the fastest two sampling rates) sample interval. It does this by increasing the sample interval at the trigger time by 0 to 31/32 of a sample interval in increments of 1/32, so that the first sample after the trigger would represent a time of one sample interval after the trigger event, with a tolerance within 1/32 of a sample interval. The following samples continue from there at the expected intervals. For example, with a selected sampling interval of ¼ mS and a recording delay of 0mS, the first sample in the recorded file for each channel would represent data at 250 to 258uS after the trigger event. This of course potentially introduces a small discontinuity at the time of the trigger, observable depending on the nature of the channel waveform(s). (The zero-phase anti-alias filter will smear the discontinuity into the nearby samples both before and after, consistent with the bandwidth of the filter.) Sub-sample synchronization can be disabled if it is deemed to be detrimental for the particular application, at the expense of losing the 1/32 interval timing accuracy. Timing Errors The principal errors in Geode timing are of two types: those associated with the trigger mechanism and which are static over the duration of the record, and those associated with the time base and which change over the duration of the record. Excluding the trigger propagation delay mentioned above, the trigger timing uncertainty is about 1uS. The known fixed errors have been lumped together and are reported in the SEG-2 file trace headers as channel SKEW. (The actual channel skew is zero, since all channels are effectively sampled simultaneously, but the SKEW value in the header is used as the only place permitting small timing corrections. Note that the SKEW value for every channel is identical.) If the size of this correction is important to the application, the SKEW value should be added to the calculated time points when the data is being processed. The Geode time base has a +/-15ppm stability over temperature (-20C to +70C) and component variations. Thus time drift relative to absolute time and relative to other Geodes is possible. (However, all channels within any Geode enclosure use the same time base, so there is no relative drift between channels in the same enclosure.) Therefore timing uncertainty increases from that existing at the time of the trigger until the time of the next trigger (or end of record). Special Timing Issues Involved with “Continuous” Recording “Continuous” recording is a method that allows unending 100% time coverage with recorded Geode data. It produces a series of time-overlapped records created by the use of a negative time delay set equal to the record length such that each record consists of completed history at the time of the trigger event. This technique circumvents the problem of data transmission overrunning data acquisition. The principle constraint is that the cycle time from trigger to trigger must always be less than the chosen record length. Otherwise, gaps rather than overlap would result. Commonly it is used with GPSderived triggering in Order to provide time-stamping of each trigger event. Upon consideration of the above, it will become clear that the time-stamp associated with a particular trigger event will pertain to the data in the following record, not to the data in the record in which the time-stamp is written. This comes about because the trigger event ends the record. Because there is data overlap between records, the precise trigger point in the following record at which the time-stamp applies can be found by comparison of the data values at the end of the former record with those near the beginning of the subsequent record. The overlapping data will be exactly identical in both records (since they are read from the same memory location, twice). The earliest data in the subsequent record that goes beyond the data of the previous record is the data that is one sample interval (assuming sub-sample synchronization is enabled) past the time-stamp. Note well that this comparison must be made independently for at least one channel of each 8-channel Geode board set, because the discrete time at which data values are written to the memory buffer, relative to the trigger event, is a function of each individual board set in the Geode system. Correct GPS Time-Stamping There are differences between various GPS models that can affect accurate time stamping. The 1PPS signal from a GPS has a “timing edge” and return edge, of which only the former is the true whole-second edge. Some models use a rising edge as the timing edge, some the falling edge, and some have it selectable. Consult the GPS manual to determine the definition of its timing edge. As indicated earlier, the Geode can be triggered on either a rising or falling edge. It is important to insure that the Geode is being triggered on the proper edge in Order to avoid timing that may be a fraction of a second off. This is expanded upon below. Some GPS units provide a very narrow timing pulse, others one that has a nearly 50/50 duty cycle. For the narrow pulse units, almost certainly it is the leading edge (rising or falling) that is the “timing edge”. This case can be easily handled by using the Geode Trigger Hold-off feature. If a 10-second cycle time is desired, set the Trigger Hold-off time to about 9.5 seconds. In this case, there is a very small chance that the very first trigger could occur on the wrong (trailing) edge, but from then on the leading edge will be used as the triggering edge. If the GPS provides a 50/50 duty cycle edge, and it is not alterable, then the Geode by itself could as easily start on the wrong edge as on the correct timing edge, and continue thusly until restarted. For this case, Geometrics can provide a Trigger Timing Interface Box (TTIB) that will correct the situation. The TTIB can be programmed to respond only to the correct edge (rising or falling), change the polarity if needed, and gate through only one of every N 1PPS pulses, where N is programmable. (The TTIB also incorporates an alarm system that can provide a remote alert if a record is missed.) Another potential issue comes from the variations between GPS models of the time that the serial time string (containing the time value of the associated 1PPS) is issued relative to the 1PPS itself. The Geode Controller attempts to pick the correct serial string based on a calculation involving the known record length, the PC times, and the trigger notification message from the Geodes. But if the GPS issues the serial string at an unusual time (and the time has been seen to vary somewhat with a given GPS unit) then it could pick up the incorrect time, off by 1 second. If rare, it can be subsequently detected and corrected during data processing, but if consistent it may not be easily detected. Again, the TTIB can accommodate the situation by only gating through to the Controller PC the string belonging to the gated-through 1PPS pulse. The Controller Serial Input Time Window can then safely be widened to 2 seconds (assuming the cycle time is more than 2 seconds) if need be, to expand the Controller’s search for the string around the calculated trigger time.

Our cesium-vapor magnetometers do not require periodic calibration in Order to maintain the accuracy as described in our published specification when the instrument is operated within specified environmental ranges. Geometrics cesium-vapor magnetometers are manufactured and tested based on the discoveries and the basic designs of Carian Associates (U.S. Patent 3,071,721). This method of total magnetic field measurement relies upon the measurement of the optical absorption of a particular cesium spectral frequency by the cesium vapor enclosed in a small glass cell. This method is similar to those used in the measurement of atomic emission and absorption frequencies using spectroscopic reference cells. The technique thus relies on well-known fundamental quantum mechanical constants for accurate and precise measurement of the magnetic field. As a result, no adjustments to the sensor are needed in Order to correct or maintain its accuracy and Geometrics sensor and sensor driver electronics are designed to either work correctly or to not work at all and to report both the strength of the magnetic field as well as the strength of the electrical signal produced by the working sensor. In this way, the signal strength measurement provides a direct indication of the operational state of the magnetometer while it is running and serves to alert the operator if the magnetometer encounters environmental conditions that are outside of its operating range. Occasional maintenance of the instrument at Geometrics facility should be performed when the instrument's internal diagnostics indicate substandard performance as described in the operator's manual. Please contact Geometrics Support for technical advice and additional information pertaining to your specific model.

Very often I am asked what the difference is between the Lite, Std and Pro versions of the 2D Refraction Software licenses. SeisImager/2D Software Packages • Standard version: for use on seismograph with mouse or PC with mouse; allows up to 16K samples per trace, 128 traces per shot, 360 traces per interpretation, and 65 shots per interpretation.• Professional version: for use on seismograph with mouse or PC with mouse; allows virtually unlimited input up to 2M samples per trace, 48K traces per shot, 48K traces per interpretation, and 48K shots per interpretation.• Lite version: included with purchase of Geometrics Windows-based seismographs. For use on seismograph with mouse or PC with mouse; allows up to 16K samples per trace, 64 traces per shot, 51 traces per interpretation, and 12 shots per interpretation.• Demonstration version: for use on PC with mouse, may be launched 15 times; same allowances as Lite version; no printing capability.Note: The number of shots per spread and spreads per interpretation are dependent on the actual trace number used. The Standard and Professional versions are also available for rent. SeisImager Software Suite* Refraction & Surface Wave Data Analysis Software 40 hr - $200 75 hr - $300 250 hr- $500. See Rentals - Geometrics : Geometrics and email rentals@geometrics.com to set up an Order.

Attachment : New SeisImager Lite registration.pdf Attachment : SeisImager_Installation_Instructions_v7.6.pdf Please see the attached instructions. Registration ID's are typically found on the customer invoice, but can also be found using your Order number or seismograph SN and company name here.

The cables between the sensors and the MFAM module are flexible circuit boards, and the length is limited to 20 inches. It is possible to remove the MFAM module from the Development kit box and then reconnect it using a ribbon cable. That would allow you to extend the MFAM module and sensors away from the Dev Kit box. Our engineers have tested it to 4 meters. Below are some details about the ribbon cable. The connector on the MFAM unit is Samtec FSH-110-04-F-DH. Its mating connector is Samtec SFMH-110-02-L-D-WT. The easiest option for an extender cable between the MFAM and the Dev Kit is a pair of cable assemblies from Samtec www.samtec.com which has male/female mass terminate connectors put onto a ribbon cable.  These connectors plug directly into the MFAM I/O connector and also into the Development Kit.  We are comfortable with lengths to 10 feet total.  The samtec P/N for this cable is:  FFMD-10-T-60.00-01-F-N The ‘60.00’ number specifies the cable length in inches (which equals 5 feet).  We have found that there is generally a 2-4 week lead, time since they are made to Order and not an off-the-shelf part. (There is another solution as well if you want to make adapter boards at each end (Dev Kit and MFAM).  The exact Samtec mates for the MFAM / Dev Kit connectors are made in PCB mount connectors only, so if you make simple small adapter board to adapt the samtec connector to another connector of your choice.  We've done this with ExpressPCB which is fast and inexpensive.  A board set from ExpressPCB is about $70 including shipping.  Our Engineering Team has a design and parts list they can send you if you're interested in going this route.)

The US Department of Commerce category for the cesium-vapor magnetometers listed in this quotation is ECCN 6A006. It is necessary to obtain a US export license before a magnetometer in this category can be shipping to most countries. If an export license is required, Geometrics Export Administrator will assist you in applying for this license. The export license process takes around 6 weeks, and we are not able to speed up that processes as it is the time the US Government takes to review the export license requests. A license is required for both renting and purchasing the MagArrow, so we are not able to send you the equipment for your use until we receive it. An Export License is NOT required for shipment of cesium-vapor magnetometers to the following countries: Argentina, Australia, Austria, Belgium, Bulgaria, Canada, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, India, Ireland, Italy, Japan, Latvia, Lithuania, Liechtenstein, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Slovenia, Slovakia, South Korea, South Africa, Spain, Sweden, Switzerland, Turkey, and the United Kingdom. (Updated April 2019) Export or re-export of the quoted items to Cuba, North Korea, Iran, Rwanda, Sudan, and Syria is prohibited by the US Dept. of Commerce as these are embargoed countries. The MagArrow-SX is a special version of the MagArrow that has a reduced sensitivity in Order to comply with US regulations and does not require an export license. Please contact us us for more information

The MFAM Development Kit is usually set to a fixed address of 192.168.2.2 (port 1000). The Ethernet port on the Windows PC must also be switched from DHCP to a fixed IP Address mode in Order to connect to the Dev Kit. The procedure for doing this is described in the Dev Kit User Guide. If there are more than one Dev Kits connecting through an Ethernet switch they cannot have the same address. Therefore it is possible to set the Dev Kit IP address to something other than the default. 192.168.2.3 and 192.168.2.4 firmware are included in the USB drive shipped with Dev Kit and can be downloaded here: For other IPs, please contact Geometrics or reply to this post. You may need to install the Uniflash program from Texas Instruments.

Snell’s Law describes quantitatively how wave fronts refract or "bend" at boundaries between contrasting velocities. You've seen it manifest in light waves by the apparent bend of the straw in your glass of water; light travels slower in water than it does in air. Refraction is well illustrated using Huygen's Principle. Consider a wave front (for our purposes, a seismic one) emanating from a point energy source, as shown in the animation above. For simplification, assume we are far enough from the energy source that the wave front is essentially planar, and is approaching an abrupt change in seismic velocity: Applying Huygen's Principle, we see that after time t, the plane wave has advanced a distance d equal to the radii of a series of spherical wave fronts emanating from the plane wave: The radii of the spheres, i.e., the distance the plane wave travels in time t, is equal to V1t. The tangent to the spherical wave fronts is the new position of the plane wave. The planar wavefront continues at velocity V1. Again applying Huygen, we see that "every point on the wave front" (see discussion of Huygen above) includes the points where the wave front intersects the velocity boundary: As the planar wave front advances, the velocity boundary becomes a new source of spherical wave fronts expanding at V2. Hence, part of the plane wave (the tangent to the spherical wave fronts emanating from the velocity boundary) is now traveling at V2. Note that within V2, its direction of advance has changed. This is because in V2, which is higher than V1, Huygen's spheres grow faster during time t. The refracted wave front continues in the new direction until another velocity boundary is encountered. Here is a simplified version at higher speed: Zooming out, we see the effect of this on a spherical wave: It should be obvious from the above that in Order for a wave front to refract, it must strike the velocity boundary at an angle other than 90 degrees. It should also be obvious that in the case of V2 < V1, refraction will be in the opposite direction, and if V1 = V1, no refraction will occur. Snell's Law quantifies refraction in terms of angle of incidence and velocity contrast. Combining the above diagrams and adding rays, we can now describe Snell's Law: In the figure above, i is the incident angle, and r is the refracted angle, measured between the ray and a line perpendicular to the refracting interface. In the example above, the velocity contrast is positive; V2 > V1. There are numerous derivations of Snell's Law on the web if you wish to understand the math. From the equation, you can see that for any given positive velocity contrast, as i increases, r increases faster: This is important; it is the property of refraction that allows us to use refracted energy to measure subsurface velocities. Conversely, a negative velocity contrast results in refraction in the opposite direction: