JP2009074953A - Electromagnetic surveying device, electromagnetic surveying method, and program - Google Patents

Electromagnetic surveying device, electromagnetic surveying method, and program Download PDF

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JP2009074953A
JP2009074953A JP2007244716A JP2007244716A JP2009074953A JP 2009074953 A JP2009074953 A JP 2009074953A JP 2007244716 A JP2007244716 A JP 2007244716A JP 2007244716 A JP2007244716 A JP 2007244716A JP 2009074953 A JP2009074953 A JP 2009074953A
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magnetic field
field strength
calculated
distribution model
resistivity distribution
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Yutaka Sasaki
裕 佐々木
Jung Ho Kim
金▲貞▼浩
Jeong-Sul Son
孫正術
Changryol Kim
金昌烈
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Kyushu University NUC
Korea Institute of Geoscience and Mineral Resources KIGAM
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Korea Institute of Geoscience and Mineral Resources KIGAM
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Abstract

<P>PROBLEM TO BE SOLVED: To provide an electromagnetic surveying device, an electromagnetic surveying method, and a program capable of easily and precisely processing an offset error when electromagnetically surveying the underground using a small-loop coil. <P>SOLUTION: The electromagnetic surveying device assumes an underground resistivity distribution model and calculates magnetic field strength based on the model, compares the calculated magnetic field strength with actually measured magnetic field strength, continues updating and calculating the resistivity distribution model until the difference converges to not more than a prescribed amount for estimating underground resistivity distribution. The electromagnetic surveying device has an inverse analysis means for calculating linearized magnetic field strength near an initial value based on the updated resistivity distribution model, relating the amount of offset to the calculated magnetic field strength, calculating the difference between the actually measured magnetic field strength and the magnetic field strength of the resistivity distribution model before updating, and updating and calculating the resistivity distribution model until the difference between the magnetic field strength of the resistivity distribution model and the amount of offset converges to not more than a prescribed amount in reference to the difference. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

本発明は、本発明は、電磁誘導作用を利用して地中探査を行い、２次磁場の測定値から地下の比抵抗分布を高精度に推定する電磁探査装置であって、とくに１次磁場の影響を除いたとき残留するオフセット誤差等を演算処理によって容易に処理できる電磁探査装置、及びその電磁探査方法、及びコンピュータに地下の比抵抗分布を逆解析させるためのプログラムに関する。   The present invention is an electromagnetic exploration apparatus that performs underground exploration using electromagnetic induction action and estimates the resistivity distribution in the subsurface with high accuracy from the measured value of the secondary magnetic field. The present invention relates to an electromagnetic exploration apparatus that can easily process an offset error or the like remaining when the influence of the above is removed by an arithmetic processing, an electromagnetic exploration method thereof, and a program for causing a computer to reverse-analyze a resistivity distribution in the underground.

従来、地中探査法にはＥＭ法（Electromagnetic Method）やＭＴ法（Magneto telluric Method）などが知られている。ＥＭ法とは、地盤に対向させた送信側のループコイルに交番電流を流して１次磁場を発生させ、これに伴って地中に発生する渦電流によって形成される２次磁場を受信側で観測し、これによって地盤の比抵抗等を測定する地中探査方法である。   Conventionally, EM method (Electromagnetic Method), MT method (Magneto telluric Method), etc. are known as underground exploration methods. In the EM method, a primary magnetic field is generated by passing an alternating current through a loop coil on the transmitting side opposed to the ground, and a secondary magnetic field formed by an eddy current generated in the ground along with this is generated on the receiving side. This is an underground exploration method that observes and measures the resistivity of the ground.

これに対し、ＭＴ法は、地中で起こる電磁誘導現象により変動する電場と磁場を地面に接触させた電極とアンテナで観測して地盤の比抵抗等を測定する地中探査方法である。いずれも、電磁誘導を利用した地中探査法であるが、ＥＭ法は地面に電極を打ち込んだりしない。なお、ＭＴ法と同様に、電極を打ち込んで比抵抗分布を推定するものに電気探査法がある。従って、測定が容易になことから、ＥＭ法は地中の比抵抗の分布を推定する場合に多用されている。   On the other hand, the MT method is an underground exploration method in which an electric field and a magnetic field that change due to an electromagnetic induction phenomenon that occurs in the ground are observed with an electrode and an antenna that are in contact with the ground, and a specific resistance of the ground is measured. Both are underground exploration methods using electromagnetic induction, but the EM method does not drive electrodes into the ground. Similar to the MT method, there is an electrical exploration method that estimates the specific resistance distribution by implanting electrodes. Therefore, since the measurement is easy, the EM method is frequently used in estimating the resistivity distribution in the ground.

このようにＥＭ法によれば、人間がループコイル持って移動すると低コストで手軽に空中で地中探査が行える。地形の影響をあまり受けず、比抵抗分布の平面的な広がりと深度方向の変化を容易に把握できるために、３次元な探査が可能な優れた方法である。   As described above, according to the EM method, when a person moves with a loop coil, the underground exploration can be easily performed at low cost. It is an excellent method that enables three-dimensional exploration because it is less affected by topography and can easily grasp the planar spread of the resistivity distribution and changes in the depth direction.

しかし、人間によって手軽に地中探査が行えると言うメリットがある反面、広範囲の地中探査を行うのにはあまり馴染まない。このため、ヘリコプターでループコイルを曳航する多周波数型の空中電磁法（helicopterboren electromagnetic method）が提案されている。これは空中でループコイルに交流電流を流し、交流磁場が地中を通過する際に生ずる電磁誘導現象を利用して地下の比抵抗分布を求めるものである。   However, it has the merit of being able to perform underground exploration easily by humans, but it is not so familiar to a wide range of underground exploration. For this reason, a multi-frequency helicopterboren electromagnetic method in which a loop coil is towed by a helicopter has been proposed. In this method, an AC current is passed through a loop coil in the air, and an underground resistivity distribution is obtained by using an electromagnetic induction phenomenon that occurs when an AC magnetic field passes through the ground.

但し、この空中電磁法によるデータ処理と解析は、多数の各種測定値のデータベースの作成、測定データと位置データとの統合、測定ＥＭ成分（各周波数における同相成分Ｉ、離相成分Ｑ）のデータの相互のレベルを調整するレベリング、各測定値の確定、比抵抗計算、最後に解析の順に行われる。この中で、レベリングは比抵抗計算解析の中で最も困難で時間の要する煩わしいものである。   However, the data processing and analysis by this airborne electromagnetic method is the creation of a database of a large number of various measurement values, the integration of measurement data and position data, and the data of measurement EM components (in-phase component I and phase-phase component Q at each frequency) Leveling to adjust the mutual level of each, determination of each measured value, calculation of specific resistance, and finally analysis. Of these, leveling is the most difficult and time-consuming annoyance in specific resistance calculation analysis.

すなわち、比抵抗を計算するには２次磁場の正しい同相成分Ｉ、及び離相成分Ｑが必要であるが、従来からこのデータの０レベルを調整するための決定的な方法はない。その理由を説明すると、ＥＭ法においては、１次磁場（ＨＰ）に対する２次磁場（ＨＳ）の割合ＨＳ／ＨＰをＩ、Ｑに分離してｐｐｍ単位で測定している。このため、図２に示すようにＨＰの大きさを既知として、受信側でＨＰをキャンセル（相殺）してＨＳのみを測定し、間接的にＨＳ／ＨＰを求める方法をとっている。 That is, to calculate the specific resistance, the correct in-phase component I and the phase-separated component Q of the secondary magnetic field are required, but there is no conventional method for adjusting the zero level of this data. The reason will be explained. In the EM method, the ratio H S / H P of the secondary magnetic field (H S ) to the primary magnetic field (H P ) is separated into I and Q and measured in ppm. Therefore, as a known size of the H P as shown in FIG. 2, only the H S is measured by canceling (offsetting) the H P on the receiving side, indirectly taking method of obtaining the H S / H P ing.

図２を参照して説明すると（詳細は後述する）、送信コイルの近くに小さなバッキングコイル（受信コイルと逆巻きに直列に接続）を設けて１次磁場の影響を相殺し、２次磁場を増幅して同相成分と離相成分とに分けて、１次磁場に対する同相成分比Ｉ（ｐｐｍ）と離相成分比Ｑ（ｐｐｍ）とを測定している。   Referring to FIG. 2 (details will be described later), a small backing coil (connected in series with the receiving coil in reverse winding) is provided near the transmission coil to cancel the influence of the primary magnetic field and amplify the secondary magnetic field. Thus, the in-phase component ratio I (ppm) and the phase-separated component ratio Q (ppm) with respect to the primary magnetic field are measured separately for the in-phase component and the phase-separated component.

従って、ＨＳ／ＨＰの値を直接測定しているわけではないので、残留ＨＰによるオフセット誤差等のΔＨＰがどうしても残り問題となる。そこで受信側の１次磁場ＨＰをバッキングコイルで相殺した後の電位を見掛け上の０レベル（相対０電位）としている。図３においてはΔＨＰ＝（ＨＰ−Ｈ’’ Ｐ）が相当する。ここで−Ｈ’’は相殺のための磁場である。 Thus, since H S / H value does not have direct measure of P, [Delta] H P offset error due residual H P is inevitably remaining problems. Therefore the primary magnetic field H P on the receiving side is set to 0 level of the apparent potential after offset by bucking coil (relative zero potential). ΔH P = (H P -H ' ' P) corresponds in FIG. Here, −H ″ is a magnetic field for cancellation.

このオフセット誤差等は工場出荷時に初期設定されているが、例えば温度や地形など、場所が変われば多くの環境要因が影響し、一定値にはならない。現場（温度、地表からの距離などのパラメータ）で補正される必要がある。送信コイル、バッキングコイル、受信コイルの関係位置は決まっているため、地表面からの２次磁場の影響がなくなる高い高度、通常例えば１０ｍ以上の樹木などにループコイルを設置して補正するのが最良の方法とされている。ただし、近くにこうした樹木等が存在するときのみ可能な方法である。しかし、この方法でも完全な誤差は残る。要するに、結果として、現場で補正可能な誤差と、避けることのできない誤差があり、ＥＭ方法の問題となっている。   This offset error and the like are initially set at the time of shipment from the factory. However, if the location changes, for example, temperature or terrain, many environmental factors influence and do not become a constant value. It needs to be corrected at the site (parameters such as temperature and distance from the ground). Since the relative positions of the transmitting coil, backing coil, and receiving coil are fixed, it is best to correct by installing a loop coil at a high altitude where the influence of the secondary magnetic field from the ground surface is eliminated, for example, a tree of 10 m or more. It is said that. However, this is possible only when there are such trees nearby. However, complete error still remains with this method. In short, as a result, there are errors that can be corrected in the field and errors that cannot be avoided, which is a problem of the EM method.

こうした問題に対処するため、次の空中電磁法のレベリングにおけるドリフト補正方法が提案された（特許文献１参照）。特許部文献１のドリフト補正方法は、測定飛行前に通常のキャリブレーション（オフセット誤差やその他の誤差）を行い、高高度で０レベルの設定を行ってから、調査対象地域等の平坦地を選んで垂直多点測定によるドリフト補正のためのデータを取得する。   In order to cope with such a problem, a drift correction method in leveling of the following airborne electromagnetic method has been proposed (see Patent Document 1). The drift correction method described in Patent Document 1 performs normal calibration (offset error and other errors) before measurement flight, sets a zero level at a high altitude, and then selects a flat area such as a survey area. To acquire data for drift correction by vertical multipoint measurement.

次に通常の測定飛行を行って調査終了後に着陸する直前に、垂直多点測定を行った同一箇所で、同一内容の垂直多点測定を行い、データ処理時に通常のレベリング手法を用いてそれぞれ０レベルを設定し、実測値の大きさを求め、測定飛行前後の垂直多点測定値それぞれについて、インバージョン（逆解析）によりキャリブレーション時の利得及び位相誤差によるドリフトを求め、ドリフト補正を施すことにより正確な応答値を得る方法である。ドリフトには測定システムの誤差や残留磁場の影響、ノイズ部分がある。   Next, just before the normal measurement flight is performed and immediately after landing, the vertical multipoint measurement of the same content is performed at the same location where the vertical multipoint measurement was performed, and the normal leveling technique is used during data processing. Set the level, determine the magnitude of the measured value, and determine the drift due to gain and phase error during calibration for each vertical multipoint measured value before and after the measurement flight by inversion (inverse analysis), and apply drift correction This is a method for obtaining a more accurate response value. Drift includes measurement system errors, residual magnetic field effects, and noise.

インバージョンは、垂直多点測定を行った地点の地下が水平多層構造からなると仮定し、各周波数毎のドリフトの数と水平多層構造パラメータの数の総計を未知数とし、垂直多点測定によるデータ数が前記未知数の総数を上回るようにして、ドリフトを含む全未知数を最小２乗法で求めている。   Inversion assumes that the basement where the vertical multipoint measurement was performed consists of a horizontal multi-layer structure, the number of drifts for each frequency and the total number of horizontal multi-layer structure parameters are unknowns, and the number of data from the vertical multipoint measurement Is greater than the total number of unknowns, and all unknowns including drift are obtained by the least square method.

特開２００３−４３１５７号公報JP 2003-43157 A

さて、以上説明した特許部文献１のドリフト補正方法は、ヘリコプターによる対地高度２０ｍ〜１５０ｍの連続的測定で、データ数が未知数の総数を上回ったとき全未知数を最小二乗法で解く多周波数型の空中電磁法（ＨＥＭ）の補正方法であり、未知数を線形の最適化問題として解いている。具体的には多数の未知変量に初期値を与え、演算を繰り返し、最小解を求めている。   The drift correction method described in Patent Document 1 described above is a multi-frequency type that solves all unknowns by the least squares method when the number of data exceeds the total number of unknowns by continuous measurement at a ground altitude of 20 m to 150 m by a helicopter. This is a correction method for the airborne electromagnetic method (HEM), which solves unknowns as linear optimization problems. Specifically, initial values are given to many unknown variables, and the calculation is repeated to find the minimum solution.

しかし、対地高度誤差を除いたドリフトだけですらα、β、γ、δなど４個の未知数を有し、情報不足であるため、ヘリコプターによる対地高度２０ｍ〜１５０ｍの連続的測定を行い、データ数が未知数の総数を上回ったとき全未知数を最小二乗法で解くため、演算量が膨大で、高能力の計算機と、またコストが度外視されてもよいとき、のような探査方法である。なお、補正時に高度が上がると応答値は３乗に逆比例して悪化し、データ量が増加したからと言って、データの誤差は相対的に大きくなる。   However, even the drift excluding ground altitude error has 4 unknowns such as α, β, γ, and δ, and there is not enough information. Therefore, helicopter continuously measures ground altitude from 20m to 150m, and the number of data When the number of unknowns exceeds the total number of unknowns, the unknown method is solved by the least square method, so that the amount of computation is enormous, a high-performance computer, and the cost may be overlooked. When the altitude increases during correction, the response value deteriorates in inverse proportion to the third power, and the data error increases relatively just because the amount of data increases.

これに対し、人間がループコイルを移動させるスモールループコイル式の電磁探査方法においては、簡易に地中探査が可能になる。もし、このスモールループコイル式の電磁探査方法でオフセット誤差等が問題なく処理され、分析結果が高精度であれば、今後新たな電磁探査方法の途が開ける。   On the other hand, in the small loop coil type electromagnetic exploration method in which a human moves the loop coil, the underground exploration can be easily performed. If this small loop coil type electromagnetic exploration method can handle offset errors and the like without any problems and the analysis result is highly accurate, a new electromagnetic exploration method can be opened in the future.

そこで本発明は、スモールループコイルで地下を電磁探査するとき、２次磁場に基づいて地下の比抵抗分布を高精度に推定でき、１次磁場の影響を除くとき残留するオフセット誤差等を演算処理によって容易に処理できる電磁探査装置、また、２次磁場に基づいて地下の比抵抗分布を高精度に推定でき、１次磁場の影響を除くとき残留するオフセット誤差等を演算処理によって容易に処理できる電磁探査方法、及び、比抵抗分布を高精度に推定でき、オフセット量の処理を容易に実行できるプログラムを提供することを目的とする。   Therefore, the present invention can estimate the resistivity distribution of the underground with high accuracy based on the secondary magnetic field when performing electromagnetic exploration of the underground with a small loop coil, and calculate the offset error remaining when the influence of the primary magnetic field is removed. Electromagnetic exploration device that can be easily processed by the above, and the resistivity distribution in the basement can be estimated with high accuracy based on the secondary magnetic field, and the offset error remaining when the influence of the primary magnetic field is removed can be easily processed by arithmetic processing It is an object of the present invention to provide an electromagnetic exploration method and a program capable of estimating a resistivity distribution with high accuracy and easily executing an offset amount process.

本発明は、上記課題を解決するために、１次磁場を形成するための送信コイルが設けられた磁場発生部と、１次磁場により地中に形成される２次磁場の磁場強度を検出する受信コイルが設けられた磁場検出部と、受信コイルが検出する磁場強度から１次磁場の寄与分をキャンセルするためのバッキングコイルと、を備え、地下の比抵抗分布モデルを仮定してこれを基に磁場強度を計算し、この計算された磁場強度と受信コイルによって実測した磁場強度とを比較し、この２つの磁場強度の差が所定量内に収斂するまで比抵抗分布モデルの更新と計算とを続けて地下の比抵抗分布を推定する電磁探査装置であって、更新された比抵抗分布モデルに基づいて初期値付近で線形化された磁場強度を計算し、この計算された磁場強度に対して寄与分を補正するためのオフセット量を関係付け、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算し、この差に対して更新された比抵抗分布モデルの磁場強度とオフセット量との差が所定量内に収まるまで計算とモデル更新を行う逆解析手段を備え、予めキャリブレーションを行わずに比抵抗分布を逆解析することを主要な特徴とする。   In order to solve the above problems, the present invention detects a magnetic field intensity of a secondary magnetic field formed in the ground by a primary magnetic field and a magnetic field generator provided with a transmission coil for forming a primary magnetic field. A magnetic field detector provided with a receiving coil, and a backing coil for canceling the contribution of the primary magnetic field from the magnetic field intensity detected by the receiving coil. The magnetic field strength is calculated, the calculated magnetic field strength is compared with the magnetic field strength actually measured by the receiving coil, and the specific resistance distribution model is updated and calculated until the difference between the two magnetic field strengths converges within a predetermined amount. This is an electromagnetic exploration device that estimates the underground resistivity distribution, calculates the linearized magnetic field strength around the initial value based on the updated resistivity distribution model, and To contribute The offset amount for correction is related, the difference between the measured magnetic field strength and the magnetic field strength of the specific resistance distribution model before update is calculated, and the magnetic field strength and offset amount of the specific resistance distribution model updated for this difference are calculated. The main feature is that a reverse analysis means for performing calculation and model update until the difference between the two values falls within a predetermined amount is included, and the specific resistance distribution is reversely analyzed without performing calibration in advance.

また同様に、本発明は、１次磁場を形成して、該１次磁場の寄与分をキャンセルしながら地中に形成される２次磁場の磁場強度を実測すると共に、地下の比抵抗分布モデルを仮定し、これに基づいて磁場強度を計算し、この計算した磁場強度と実測した磁場強度とを比較し、この２つの磁場強度の差が所定量以下に収斂するまで比抵抗分布モデルの更新と計算とを続けて地下の比抵抗分布を推測する電磁探査方法であって、更新された比抵抗分布モデルに基づいて初期値付近で線形化された磁場強度を計算し、この計算された磁場強度に対して１次磁場の影響を補正するためのオフセット量を関係付け、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算し、この差に対して更新された磁場強度とオフセット量との差が所定量内に収斂するまで比抵抗分布モデルの更新と計算とをおこない、予めキャリブレーションを行わずに比抵抗分布を逆解析することを主要な特徴とする。   Similarly, the present invention forms a primary magnetic field, measures the magnetic field strength of the secondary magnetic field formed in the ground while canceling the contribution of the primary magnetic field, and uses a specific resistance distribution model in the underground. Based on this, the magnetic field strength is calculated, the calculated magnetic field strength is compared with the actually measured magnetic field strength, and the specific resistance distribution model is updated until the difference between the two magnetic field strengths converges to a predetermined amount or less. Is an electromagnetic exploration method that estimates the resistivity distribution in the subsurface by calculating the magnetic field strength linearized near the initial value based on the updated resistivity distribution model. The offset amount for correcting the influence of the primary magnetic field is related to the intensity, and the difference between the actually measured magnetic field intensity and the magnetic field intensity of the specific resistance distribution model before the update is calculated, and the difference is updated. The difference between magnetic field strength and offset amount is Until convergence to the amount subjected to the calculation and update of the resistivity distribution model, and main feature to inverse analysis resistivity distribution without advance calibration.

さらに、本発明のプログラムは、コンピュータに、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算させる第１手順と、更新された比抵抗分布モデルのラアプラシアンを計算し１次磁場の影響を補正するためのオフセット量を関係付ける第２手順と、更新された比抵抗分布モデルの磁場強度に対してヤコビアンを計算し、オフセット量の影響度を調整係数で調整しながら関係付けを行う行列を取得する第３手順と、行列をＱＲ分解して比抵抗分布の変化分とオフセット量、係数を得る第４手順と、比抵抗分布の変化分とオフセット量、係数がそれぞれ所定量内に収斂するまで比抵抗分布モデルを更新し、計算を繰り返す第５手順と、を実行させることを主要な特徴とする。   Further, the program of the present invention calculates a difference between the actually measured magnetic field strength and the magnetic field strength of the specific resistance distribution model before update, and calculates the updated Laplacian of the specific resistance distribution model. The second procedure to relate the offset amount to correct the influence of the secondary magnetic field, and calculate the Jacobian for the magnetic field strength of the updated specific resistance distribution model, and adjust the influence of the offset amount by adjusting the adjustment factor. A third procedure for obtaining a matrix for performing the attachment, a fourth procedure for obtaining a change in the resistivity distribution, an offset amount, and a coefficient by performing QR decomposition on the matrix, and a change in the resistivity distribution, the offset amount, and the coefficient for each. The main feature is to execute a fifth procedure in which the specific resistance distribution model is updated until convergence within the fixed amount and the calculation is repeated.

本発明の電磁探査装置によれば、スモールループコイルで地下を電磁探査するとき、２次磁場に基づいて地下の比抵抗分布を高精度に推定でき、１次磁場の影響を除くとき残留するオフセット誤差等を演算処理によって容易に処理できる。   According to the electromagnetic exploration apparatus of the present invention, when performing electromagnetic exploration in the underground with a small loop coil, the resistivity distribution in the underground can be accurately estimated based on the secondary magnetic field, and the residual offset when removing the influence of the primary magnetic field Errors and the like can be easily processed by arithmetic processing.

また、本発明の電磁探査方法によれば、スモールループコイルで地下を電磁探査するとき、２次磁場に基づいて地下の比抵抗分布を高精度に推定でき、１次磁場の影響を除くとき残留するオフセット誤差等を演算処理によって容易に処理できる。   In addition, according to the electromagnetic exploration method of the present invention, when performing electromagnetic exploration in the subsurface with a small loop coil, it is possible to accurately estimate the specific resistance distribution in the subsurface based on the secondary magnetic field, and to remove residual effects when removing the influence of the primary magnetic field. The offset error or the like can be easily processed by arithmetic processing.

さらに、本発明のプログラムによれば、地下の比抵抗分布を高精度に推定でき、オフセット量の処理を容易に実行できる。   Furthermore, according to the program of the present invention, the underground resistivity distribution can be estimated with high accuracy, and the offset amount can be easily processed.

本発明の第１の形態は、１次磁場を形成するための送信コイルが設けられた磁場発生部と、１次磁場により地中に形成される２次磁場の磁場強度を検出する受信コイルが設けられた磁場検出部と、受信コイルが検出する磁場強度から１次磁場の寄与分をキャンセルするためのバッキングコイルと、を備え、地下の比抵抗分布モデルを仮定してこれを基に磁場強度を計算し、この計算された磁場強度と受信コイルによって実測した磁場強度とを比較し、この２つの磁場強度の差が所定量内に収斂するまで比抵抗分布モデルの更新と計算とを続けて地下の比抵抗分布を推定する電磁探査装置であって、更新された比抵抗分布モデルに基づいて初期値付近で線形化された磁場強度を計算し、この計算された磁場強度に対して寄与分を補正するためのオフセット量を関係付け、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算し、この差に対して更新された比抵抗分布モデルの磁場強度とオフセット量との差が所定量内に収まるまで比抵抗分布モデルの更新と計算とを行う逆解析手段を備え、予めキャリブレーションを行わずに比抵抗分布を逆解析することを特徴とする電磁探査装置である。この構成によって、スモールループコイルで地下を電磁探査するとき、２次磁場に基づいて地下の比抵抗分布を高精度に推定でき、１次磁場の影響を除くとき残留するオフセット誤差等を演算処理によって容易に処理できる。   According to a first aspect of the present invention, there is provided a magnetic field generator provided with a transmission coil for forming a primary magnetic field, and a reception coil for detecting the magnetic field strength of a secondary magnetic field formed in the ground by the primary magnetic field. A magnetic field detecting unit provided and a backing coil for canceling the contribution of the primary magnetic field from the magnetic field intensity detected by the receiving coil; The calculated magnetic field strength is compared with the magnetic field strength actually measured by the receiving coil, and the specific resistance distribution model is continuously updated and calculated until the difference between the two magnetic field strengths converges within a predetermined amount. An electromagnetic exploration device that estimates the resistivity distribution in the subsurface, calculates the linear magnetic field strength near the initial value based on the updated resistivity distribution model, and contributes to the calculated magnetic field strength. For correcting Calculate the difference between the measured magnetic field strength and the magnetic field strength of the resistivity distribution model before the update, and calculate the difference between the magnetic field strength of the updated resistivity distribution model and the offset amount. An electromagnetic exploration apparatus comprising reverse analysis means for updating and calculating a specific resistance distribution model until it falls within a predetermined amount, and performing reverse analysis of the specific resistance distribution without performing calibration in advance. With this configuration, when electromagnetic exploration is performed in the underground with a small loop coil, the resistivity distribution in the underground can be estimated with high accuracy based on the secondary magnetic field. Easy to handle.

本発明の第２の形態は、第１の形態に従属する形態であって、受信コイルの高度を変えて二位置以上で磁場強度を検出したとき、逆解析手段が、この検出した二位置以上の磁場強度を磁場強度として統合すると共に、該磁場強度に対して独立したオフセット量として関係付けることを特徴とする電磁探査装置である。この構成によって、オフセット誤差の調整や測定高さを気にすることなく、二位置以上の磁場強度の情報を統合できる。   The second form of the present invention is a form subordinate to the first form. When the magnetic field strength is detected at two or more positions by changing the altitude of the receiving coil, the inverse analysis means detects the two or more positions detected. The electromagnetic exploration apparatus is characterized by integrating the magnetic field strengths of the magnetic field strengths as magnetic field strengths and relating the magnetic field strengths as independent offset amounts. With this configuration, information on magnetic field strengths at two or more positions can be integrated without worrying about offset error adjustment and measurement height.

本発明の第３の形態は、１次磁場を形成して、該１次磁場の寄与分をキャンセルしながら地中に形成される２次磁場の磁場強度を実測すると共に、地下の比抵抗分布モデルを仮定し、これに基づいて磁場強度を計算し、この計算した磁場強度と実測した磁場強度とを比較し、この２つの磁場強度の差が所定量以下に収斂するまで比抵抗分布モデルの更新と計算とを続けて地下の比抵抗分布を推測する電磁探査方法であって、更新された比抵抗分布モデルに基づいて初期値付近で線形化された磁場強度を計算し、この計算された磁場強度に対して１次磁場の影響を補正するためのオフセット量を関係付け、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算し、この差に対して更新された磁場強度とオフセット量との差が所定量内に収斂するまで比抵抗分布モデルの更新と計算とを行い、予めキャリブレーションを行わずに比抵抗分布を逆解析することを特徴とする電磁探査方法である。この構成によって、スモールループコイルで地下を電磁探査するとき、２次磁場に基づいて地下の比抵抗分布を高精度に推定でき、１次磁場の影響を除くとき残留するオフセット誤差等を演算処理によって容易に処理できる。   The third embodiment of the present invention forms a primary magnetic field, measures the magnetic field strength of the secondary magnetic field formed in the ground while canceling the contribution of the primary magnetic field, and distributes the resistivity of the underground. Assuming a model, the magnetic field strength is calculated based on this, the calculated magnetic field strength is compared with the actually measured magnetic field strength, and the resistivity distribution model is compared until the difference between the two magnetic field strengths converges to a predetermined amount or less. An electromagnetic exploration method that estimates the resistivity distribution in the subsurface by continuing to update and calculate, and calculates the linear magnetic field strength near the initial value based on the updated resistivity distribution model. The offset amount for correcting the influence of the primary magnetic field is related to the magnetic field strength, the difference between the actually measured magnetic field strength and the magnetic field strength of the specific resistance distribution model before update is calculated, and the difference is updated. The difference between the magnetic field strength and the offset amount Until convergence to the amount subjected to the calculation and update of the resistivity distribution model, an electromagnetic survey method, characterized by inverse analysis of the resistivity distribution without advance calibration. With this configuration, when electromagnetic exploration is performed in the underground with a small loop coil, the resistivity distribution in the underground can be estimated with high accuracy based on the secondary magnetic field. Easy to handle.

本発明の第４の形態は、第３の形態に従属する形態であって、高度を変えて２位置以上で磁場強度を検出し、この２位置以上の磁場強度を独立した対等な磁場強度として統合すると共に、該磁場強度に対して独立したオフセット量を関係付けることを特徴とする電磁探査方法である。この構成によって、オフセット誤差の調整や測定高さを気にすることなく、二位置以上の磁場強度の情報を統合できる。   The fourth mode of the present invention is a mode subordinate to the third mode, detects the magnetic field strength at two or more positions at different altitudes, and sets the magnetic field strengths at two or more positions as independent and equal magnetic field strengths. It is an electromagnetic exploration method characterized by integrating and relating an independent offset amount to the magnetic field strength. With this configuration, information on magnetic field strengths at two or more positions can be integrated without worrying about offset error adjustment and measurement height.

本発明の第５の形態は、コンピュータに、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算させる第１手順と、更新された比抵抗分布のラアプラシアンを計算し１次磁場の影響を補正するためのオフセット量を関係付ける第２手順と、更新された比抵抗分布モデルの磁場強度に対してヤコビアンを計算し、オフセット量の影響度を調整係数で調整して上記差との関係付けを行う行列を取得する第３手順と、行列をＱＲ分解して比抵抗分布の変化分とオフセット量を得る第４手順と、比抵抗分布の変化分とオフセット量がそれぞれ所定量内に収斂するまで比抵抗分布モデルを更新し、計算を繰り返す第５手順と、を実行させるためのプログラムである。この構成によって、地下の比抵抗分布を高精度に推定でき、オフセット量の処理を容易に実行できる。この第４手順において、比抵抗分布の変化分とオフセット量を得るだけでなく、調整係数の値も取得し、また、第５手順で比抵抗分布の変化分とオフセット量を得るだけでなく、調整係数の値が所定量内に収斂するようにするのも好適である。   In the fifth embodiment of the present invention, a first procedure for causing a computer to calculate the difference between the actually measured magnetic field strength and the magnetic field strength of the specific resistance distribution model before the update, and the Laaplacian of the updated specific resistance distribution are calculated. The second procedure relating the offset amount for correcting the influence of the secondary magnetic field, the Jacobian is calculated with respect to the magnetic field intensity of the updated specific resistance distribution model, and the degree of influence of the offset amount is adjusted by the adjustment coefficient. A third procedure for obtaining a matrix for associating with a difference, a fourth procedure for obtaining a change in the specific resistance distribution and an offset amount by QR decomposition of the matrix, and a change in the specific resistance distribution and the offset amount, respectively. This is a program for executing the fifth procedure in which the specific resistance distribution model is updated until convergence within the fixed amount and the calculation is repeated. With this configuration, the underground resistivity distribution can be estimated with high accuracy, and the offset amount can be easily processed. In the fourth procedure, not only the change in the specific resistance distribution and the offset amount are obtained, but also the value of the adjustment coefficient is obtained. In the fifth procedure, the change in the specific resistance distribution and the offset amount are obtained, It is also preferable that the value of the adjustment coefficient is converged within a predetermined amount.

本発明の第６の形態は、第５の形態に従属する形態であって、第１手順が、高度を変えて２位置以上で磁場強度を検出し、この２位置以上の磁場強度を独立した対等な磁場強度として統合した実測の磁場強度とし、第２手順が、更新された比抵抗分布モデルの磁場強度に対して１次磁場のほかに独立したオフセット量を関係付けることを特徴とするプログラムである。この構成によって、オフセット誤差の調整や測定高さを気にすることなく、二位置以上の磁場強度の情報を統合できる。   The sixth form of the present invention is a form subordinate to the fifth form, wherein the first procedure detects the magnetic field strength at two or more positions at different altitudes, and the magnetic field strengths at the two or more positions are independent. Measured magnetic field strength integrated as equal magnetic field strength, and the second procedure relates an independent offset amount in addition to the primary magnetic field to the magnetic field strength of the updated resistivity distribution model. It is. With this configuration, information on magnetic field strengths at two or more positions can be integrated without worrying about offset error adjustment and measurement height.

（実施の形態１）
以下、本発明の実施の形態１における電磁探査装置、電磁探査方法及びプログラムについて説明をする。図１は本発明の実施の形態１における電磁探査装置のブロック構造図、図２は測定の原理の説明図、図３は１次磁場と２次磁場、及びキャンセルのための磁場とオフセット量との関係を示す説明図である。 (Embodiment 1)
Hereinafter, the electromagnetic exploration apparatus, the electromagnetic exploration method, and the program according to Embodiment 1 of the present invention will be described. 1 is a block diagram of the electromagnetic exploration apparatus according to Embodiment 1 of the present invention, FIG. 2 is an explanatory diagram of the principle of measurement, FIG. 3 is a primary magnetic field and a secondary magnetic field, and a magnetic field and offset amount for cancellation. It is explanatory drawing which shows these relationships.

図１において、１は実施の形態１における電磁探査装置の１次磁場を発生するための磁場発生部であり、２は所定周波数の電流を流すスモールループの送信コイルである。本発明の実施の形態１では、１ｋＨｚ〜１０ｋＨｚ程度から選択された周波数の交番電流（交互に極性が変わる所定の電流であればよい）で１次磁場を形成し、この１次磁場が形成する渦電流により２次磁場を生成している。   In FIG. 1, reference numeral 1 denotes a magnetic field generator for generating a primary magnetic field of the electromagnetic exploration apparatus according to the first embodiment, and reference numeral 2 denotes a small-loop transmission coil for passing a current of a predetermined frequency. In the first embodiment of the present invention, a primary magnetic field is formed by an alternating current having a frequency selected from about 1 kHz to 10 kHz (which may be a predetermined current whose polarity changes alternately), and this primary magnetic field is formed. A secondary magnetic field is generated by the eddy current.

次に、図１に示す３は、この電磁探査装置によって生成された磁場を検出するための磁場検出部であり、４は磁場強度を測定するためのスモールループの受信コイルである。そして、５は受信コイルと巻回方向は逆に巻かれているが、受信コイルと直列に接続されたバッキングコイル、６は制御部、７は得られた情報を分析する分析装置である。   Next, 3 shown in FIG. 1 is a magnetic field detector for detecting the magnetic field generated by this electromagnetic exploration apparatus, and 4 is a small loop receiving coil for measuring the magnetic field strength. Reference numeral 5 is a receiving coil and a winding coil wound in the opposite direction, but is a backing coil connected in series with the receiving coil, 6 is a control unit, and 7 is an analyzer for analyzing the obtained information.

そして、図２は送信コイル２、受信コイル４、バッキングコイル５と１次磁場ＨＰ（その磁場強度をＨＰとする）、２次磁場Ｈｓ（その磁場強度をＨｓとする）の関係を示している。送信コイル２に磁界発生部１から交番電流、例えば複素数表現でｉ＝ｉ０ｅｊωｔが流されると、１次磁場強度ＨＰ＝ＨＰ０ｅｊωｔが発生する。このように磁束が変化することで、これを打ち消すように渦電流ｉｗが発生する。さらにこの渦電流Ｉｗが２次磁場Ｈｓ＝Ｈｓ０ｅｊωｔを発生する。しかし、受信コイル４には、上述した１次磁場とこの２次磁場が加わったＨＰ＋Ｈｓ＝ＨＰ０ｅｊωｔ＋Ｈｓ０ｅｊωｔの磁束が測定される。１次磁場ＨＰに対する２次磁場Ｈｓのオーダはｐｐｍオーダである。 Then, Figure 2 is transmitting coil 2, the receiving coil 4, a primary magnetic field H P bucking coils 5 (the magnetic field strength and H P), the secondary magnetic field H s (the magnetic field strength and H s) relations Is shown. When an alternating current, for example, i = i 0 e jωt is flowed from the magnetic field generator 1 to the transmission coil 2, the primary magnetic field strength H P = H P0 e jωt is generated. As the magnetic flux changes in this way, an eddy current iw is generated so as to cancel it. Furthermore the eddy current I w to generate secondary magnetic field H s = H s0 e jωt. However, the receiving coil 4 measures the above-described primary magnetic field and the magnetic flux of H P + H s = H P0 e jωt + H s0 e jωt to which the secondary magnetic field is added. Order of the secondary magnetic field H s to the primary magnetic field H P is the order of ppm.

そこで、受信コイル４と直列に接続されたバッキングコイル５を利用して、受信コイル４で受信する磁束から１次磁場ＨＰの影響をキャンセル（相殺）する。すなわち、電磁誘導でＨＰ ’＝ＨＰ０ ’ｅｊωｔ≒ＨＰにより、相殺のための電流を発生させ、受信コイル４で（−ＨＰ ’’）＝（−ＨＰ０ ’’ｅｊωｔ）≒（−ＨＰ）の相殺磁界を生成している。これにより、受信コイル４では（ＨＰ＋ＨＳ−ＨＰ０ ’’）＝（ＨＰ０ｅｊωｔ＋Ｈｓ０ｅｊωｔ−ＨＰ０ ’’ｅｊωｔ）の磁場となり、誤差（オフセット誤差）をΔＨＰ＝（ＨＰ−Ｈ’’ Ｐ）とすると、（Ｈｓ＋ΔＨＰ）＝（Ｈｓ０ｅｊωｔ＋ΔＨＰ）となり、キャリブレーションによってΔＨＰ≒０にすることが可能であるなら、受信コイルでＨｓ＝Ｈｓ０ｅｊωｔを検出できることが可能になる。 Therefore, by utilizing the backing coil 5 connected to the receiving coil 4 in series, canceling (offsetting) the influence of the primary magnetic field H P from the receiving magnetic flux in the receiving coil 4. That is, the H P '= H P0' e jωt ≒ H P by electromagnetic induction, current is generated for canceling, at the receiving coil 4 (-H P '') = (- H P0 '' e jωt) ≒ A canceling magnetic field of (−H P ) is generated. Thus, the receiving coil 4 (H P + H S -H P0 '') = (H P0 e jωt + H s0 e jωt -H P0 '' e jωt) becomes magnetic field, [Delta] H error (offset error) P = ( If H P -H '' P) to, (H s + ΔH P) = (H s0 e jωt + ΔH P) becomes, if the calibration can be a [Delta] H P ≒ 0, the receiving coil H s = It becomes possible to detect H s0 e jωt .

以上の構成を基にして、以下、実施の形態１における電磁探査装置、電磁探査方法がどのようにして比抵抗分布を求めるのか、について以下簡単に説明する。地盤中に電気伝導率σ（Ｓ／ｍ）の物質（ここでσ＝１／ρ（Ωｍ）、ρは比抵抗）が存在するとし、空気と地盤という２つの媒体が地表を境に接しており、空気中で地盤に向けて電磁波を送信するため、境界条件を満たしつつ、マクスウェルの方程式を解くことにより、地盤からの応答（磁場強度）の応答値（理論値）を計算できる。   Based on the above configuration, how the specific resistance distribution is obtained by the electromagnetic exploration apparatus and the electromagnetic exploration method in the first embodiment will be briefly described below. It is assumed that there is a substance with electrical conductivity σ (S / m) in the ground (where σ = 1 / ρ (Ωm), ρ is specific resistance), and two media, air and ground, touch the ground surface. Since electromagnetic waves are transmitted toward the ground in the air, the response value (theoretical value) of the response from the ground (magnetic field strength) can be calculated by solving Maxwell's equations while satisfying the boundary conditions.

しかし、この方程式は数値計算により差分や有限要素法を用いて解くしかない。そこで、地下の比抵抗分布（地下モデル）を仮定し（フォワードモデリング）、電流ｉを送信コイル４に流して１次磁界ＨＰを形成し、この１次磁場ＨＰに対する地下モデルでの渦電流ｉｗの発生、さらにはこれに由来して２次的に派生する２次磁場Ｈｓが計算できる。これに対して、この２次磁界のＨｓの実測値が得られているので、この実測値と応答値（理論値）との差がなくなるように比抵抗分布モデルを修正し、これを収斂させれば地中の比抵抗分布の可能性が大である。言い換えれば地下モデルを仮定して逆解析することが実施の形態１における電磁探査方法と言うことになる。 However, this equation can only be solved numerically using a difference or a finite element method. Therefore, assuming the resistivity distribution in the subsurface (the subsurface model) (forward modeling), by applying a current i to the transmitter coil 4 to form a primary magnetic field H P, eddy currents in the subsurface model for the primary field H P The generation of i w and the secondary magnetic field H s derived secondarily from this can be calculated. In contrast, since the measured value of the secondary magnetic field H s is obtained by modifying the resistivity distribution model such that the difference between the measured value and the response value (theoretical value) is eliminated, converging them If this is done, the possibility of a specific resistance distribution in the ground is great. In other words, reverse analysis assuming an underground model is the electromagnetic exploration method in the first embodiment.

さて、２次磁界ＨＳを測定するとき、１次磁場ＨＰの影響が十分キャンセルできているか、またその他の誤差はどれほどかが問題になる。すなわち、２次磁場ＨＳの上記誤差ΔＨＰが問題となる。バッキングコイル５を利用して１次磁場ＨＰの影響はほぼ解消できるが、これは完全でなく、誤差が残る。システム誤差等のようにキャリブレーションで解決できる誤差もあるが、現地環境の影響（温度、地磁気、その他の自然環境など）による誤差等を完全に取り除くことはできない。 Well, when measuring the secondary magnetic field H S, or the influence of the primary magnetic field H P is sufficiently canceled, or other error is how much is a problem. That is, the error [Delta] H P of the secondary field H S becomes a problem. Effect of the primary magnetic field H P by using the backing coil 5 can be almost eliminated, but this is not perfect, the error remains. Although there are errors that can be solved by calibration, such as system errors, errors due to the influence of the local environment (temperature, geomagnetism, other natural environments, etc.) cannot be completely removed.

そこで、本発明においては、こうした誤差を分析的に追求するのではなく、このような誤差をすべて含めて、地下モデルの比抵抗分布のデータと同様のデータと位置付け、地下モデルの要素として処理を行い、すべてに矛盾がないように逆解析するものである。   Therefore, in the present invention, rather than pursuing such errors analytically, all such errors are included as data similar to the data of the resistivity distribution of the underground model, and are processed as elements of the underground model. And reverse analysis so that everything is consistent.

以下この説明を行う。まず、マクスウェルの方程式を解くことに関して、であるが、地盤中での磁場と比抵抗が関係していることを具体的に示すと、均質な大地（半無限媒質）で周波数ｆが低いと仮定したとき、磁場強度Ｈｓ、ＨＰ、比抵抗ρ（Ωｍ）との間に次の（数１）の関係がある。ここでμ０は真空の透磁率（４π×１０−７Ｈ／ｍ）であり、ｓは送信コイル２と受信コイル４のコイル間隔（ｍ）である。 This will be described below. First, regarding solving Maxwell's equations, it is assumed that the magnetic field in the ground and the specific resistance are related. Specifically, the frequency f is assumed to be low on a homogeneous ground (semi-infinite medium). when, a relationship of the following equation (1) between the magnetic field strength H s, H P, the specific resistance [rho ([Omega] m). Here, μ 0 is the vacuum permeability (4π × 10 −7 H / m), and s is the coil interval (m) between the transmission coil 2 and the reception coil 4.

Figure 2009074953
この（数１）が示唆するように、それぞれが所定の比抵抗を有する複数のブロックから構成される地下モデルを仮定し、これに初期値を与え、周波数ｆ、磁場強度ＨＰを基に地表での２次磁場Ｈｓの理論値を計算すれば、実際に２次磁場Ｈｓを測定することで、その差が判明し、この差がなくなるように地下モデルの修正を行い、これを繰り返せば目的とする比抵抗分布を逆解析することができる。
Figure 2009074953
 As the (number 1) suggests, each assuming a subsurface model composed of a plurality of blocks having a predetermined specific resistance, this gives an initial value, the surface frequency f, and the magnetic field strength H P based on If the theoretical value of the secondary magnetic field H s is calculated, the difference is found by actually measuring the secondary magnetic field H s , and the underground model is corrected to eliminate this difference, and this can be repeated. For example, the target resistivity distribution can be inversely analyzed.

さて、再び図１に戻って、実施の形態１における電磁探査装置の構成について説明を続ける。６は電磁探査装置の制御部である。制御部６は送信コイル２に供給する電流ｉ＝ｉ０ｅｊωｔを制御し、受信コイル４で受信した磁場情報（ＨＳ＋ΔＨＰ）≒Ｈｓから２次磁場Ｈｓの同相成分Ｉ（実数部）及び離相成分Ｑ（虚数部）の測定値を求めることができる。周波数を様々変更して測定することもできる。 Now, returning to FIG. 1 again, the description of the configuration of the electromagnetic exploration apparatus in the first embodiment will be continued. Reference numeral 6 denotes a control unit of the electromagnetic exploration apparatus. The control unit 6 controls the current i = i 0 e jωt supplied to the transmitter coil 2, the magnetic field information received by the receiving coil 4 (H S + ΔH P) phase component I (real number ≒ H s from the secondary magnetic field H s Part) and the measured value of the phase separation component Q (imaginary part). It is also possible to measure by changing the frequency.

なお、地盤の比抵抗ρは（数２）によって演算する。（数１）を変形したものである。   The specific resistance ρ of the ground is calculated by (Equation 2). (Equation 1) is modified.

Figure 2009074953
１次磁場ＨＰと２次磁場Ｈｓとの関係、ΔＨＰ＝（ＨＰ−Ｈ’’ Ｐ）の関係を示したのが図３である。合成磁場Ｈは１次磁場ＨＰと交角θであり、１次磁場ＨＰと２次磁場Ｈｓの位相差（π／２＋φ）のφは（数３）となる。これからも分かるように−ΔＨＰが地下モデルの比抵抗分布の正確さに大きく影響することが分かる。
Figure 2009074953
 Relationship between the primary magnetic field H P and the secondary magnetic field H s, the showed [Delta] H P = relation (H P -H '' P) diagrams 3. Synthetic magnetic field H is primary magnetic field H P and the intersection angle theta, the phi of the phase difference of the primary magnetic field H P and the secondary magnetic field H s (π / 2 + φ ) becomes equation (3). It can be seen that - [Delta] H P as well understood greatly affects the accuracy of the resistivity distribution in the subsurface model from now.

Figure 2009074953
さて、実施の形態１の制御部６は、１次磁界ＨＰを形成するために送信コイル２の電流Ｉを制御し、磁場検出部３で検出されたＨＳの同相成分Ｉ及び離相成分Ｑを取り出し、処理結果を分析装置７に渡す。
Figure 2009074953
 Now, the control unit 6 in the first embodiment, the primary magnetic field H P controls the current I of the transmission coil 2 to form the in-phase component I and Hanaresho component of the detected H S by the magnetic field detecting portion 3 Q is taken out and the processing result is passed to the analyzer 7.

この分析装置７は、実施の形態１の場合はパーソナルコンピュータであって、ＣＰＵ（中央処理演算装置）７ａと記憶装置７ｂを備えている。記憶装置７ｂには、ＲＯＭ（Read only Memory）と一時記憶のためのＲＡＭ（Random
access Memory）、さらに実施の形態１のプログラムを格納するための不揮発性メモリが設けられている。ＣＰＵ７ａはＲＯＭや不揮発性メモリに格納された各機能を実行するプログラムを読み出して、それぞれの機能を実行する機能実現手段として機能する。 The analysis device 7 is a personal computer in the case of the first embodiment, and includes a CPU (Central Processing Unit) 7a and a storage device 7b. The storage device 7b includes a ROM (Read Only Memory) and a temporary storage RAM (Random
access Memory) and a non-volatile memory for storing the program of the first embodiment. The CPU 7a functions as a function realizing unit that reads out a program for executing each function stored in the ROM or the nonvolatile memory and executes each function.

従って、実施の形態１の分析装置７のＣＰＵ７ａには、後で詳述する手順で磁場の計算を行うと共に、所定の比抵抗分布を有する地下モデルを逐次更新しながら目的の比抵抗分布を有する地下モデルにまで到達させるプログラムがデータと共に読み込まれ、機能実現手段（本発明の逆解析手段）として地盤を逆解析する機能を実行する。なお、このプログラムを外付けの記憶媒体に格納しておくのもよい。   Therefore, the CPU 7a of the analyzer 7 according to the first embodiment calculates the magnetic field according to the procedure described in detail later, and has the target specific resistance distribution while sequentially updating the underground model having a predetermined specific resistance distribution. A program for reaching the underground model is read together with the data, and a function of performing reverse analysis of the ground is executed as function realization means (inverse analysis means of the present invention). This program may be stored in an external storage medium.

以下、実施の形態１の電磁探査装置、電磁探査方法で行われる処理の詳細について説明する。地下モデルは地盤を複数のブロックで分割して構成する。各ブロックの比抵抗ρの組をベクトル

Figure 2009074953
（外字１、以下ｍ）とし、電磁探査データ（実測値）の組をベクトル
Figure 2009074953
（外字２、以下ｄ）と表す。地下モデルはマクスウェルの方程式を差分または有限要素法で解くものとする。 Hereinafter, details of processing performed by the electromagnetic exploration apparatus and the electromagnetic exploration method of the first embodiment will be described. The underground model is constructed by dividing the ground into multiple blocks. Vector of specific resistance ρ of each block
Figure 2009074953
(External character 1, m below), vector set of electromagnetic exploration data (actual measurement)
Figure 2009074953
(External character 2, hereinafter d). The underground model is assumed to solve Maxwell's equations by the difference or finite element method.

さらに、各ブロックにおける比抵抗ρの組ｍを入力すると、地下モデルに対応した電磁探査における応答値（各ブロックが形成する２次磁場の総和としてのモデル計算値）を出力する関数を

Figure 2009074953
（外字３、以下ｆ（ｍ））とする。 Furthermore, when a set m of specific resistances ρ in each block is input, a function that outputs a response value (model calculation value as a sum of secondary magnetic fields formed by each block) in the electromagnetic survey corresponding to the underground model is output.
Figure 2009074953
(External character 3, hereinafter referred to as f (m)).

すなわち、ブロック単位でそれぞれの比抵抗ρをもつ地下モデルに対して、地表において、この比抵抗分布のｍに対応した２次磁場（モデル計算値）を生成する関数である。電磁探査データは、地表上の二位置の高さあるいは三位置以上の高さで実測した電磁探査データｄを統合して構成される。このとき、電磁探査データとの差を示すオフセット量（システムのオフセット誤差、その他の誤差）をベクトル

Figure 2009074953
（外字４、以下ｓ）で表されるとすると、（数４）の関係になる。 That is, it is a function that generates a secondary magnetic field (model calculation value) corresponding to m of this specific resistance distribution on the ground surface for an underground model having a specific resistance ρ in block units. The electromagnetic exploration data is configured by integrating electromagnetic exploration data d measured at two positions on the ground surface or at three or more positions. At this time, the offset amount (system offset error and other errors) indicating the difference from the electromagnetic survey data is a vector.
Figure 2009074953
If expressed by (external character 4, hereinafter s), the relationship of (Expression 4) is obtained.

Figure 2009074953
ここで、
Figure 2009074953
（外字５、以下Ｇ）はオフセット量ｓを探査データｄの各要素に関係付けるマトリックスであり、各列の適当な位置だけが１であり、他の要素はすべて０の行列である。ｓは比抵抗ρの組ｍと同様に求めるべき未知数のベクトルである。
Figure 2009074953
 here,
Figure 2009074953
(External character 5, G hereinafter) is a matrix that relates the offset amount s to each element of the exploration data d. Only the appropriate position of each column is 1, and the other elements are all 0 matrices. s is a vector of unknowns to be obtained in the same manner as the specific resistance ρ set m.

さて、（数４）を直接解くことはできないので、最小二乗法でこれを解くことになる。すなわち、本発明の実施の形態１における電磁探査方法は、地下の比抵抗分布のモデルを（数５）に示す目的関数φを最小化する比抵抗ρの組ｍとｓを決定する問題に帰着する。ここで

Figure 2009074953
（外字６、以下ノルム）はベクトルのノルム（要素の二乗和）であり、
Figure 2009074953
（外字７、以下Ｃ）はラプラス（二次微分）線形操作を表している。 Now, since (Formula 4) cannot be solved directly, it is solved by the least square method. That is, the electromagnetic exploration method according to Embodiment 1 of the present invention results in a problem of determining a set m and s of resistivity ρ that minimizes the objective function φ shown in (Equation 5) as a model of underground resistivity distribution. To do. here
Figure 2009074953
(External character 6, "norm") is the vector norm (element sum of squares).
Figure 2009074953
(External character 7, hereinafter C) represents a Laplace (secondary differential) linear operation.

Figure 2009074953
（数５）の第１項は探査データとモデル計算値及び誤差との差の二乗和を表し、第２項は比抵抗分布の粗さを表す。このλはラグランジェの未定係数（本発明の調整係数）であって、本来比抵抗分布の粗さは最小の０でなければならないという条件付きにしたものである。この第２項を加えたことによって第１項の残差と第２項のバランスが調整され、探査データの地下モデルへの当てはまりが最小化されるだけでなく、オフセット量が明らかになり、比抵抗分布が滑らかに変化する地下モデルを求めることができる。ただ、λについても最小値（データ残差）を与えるλを求めるように同時計算するのがよいが、計算時間がかかる上に、経験上λを固定した場合と大差ないので、複数の、例えば３値の中で最小値を与えるλを選択する方法を選んだり、経験上良好な結果を与える所定値λ０に固定した値を使用したりするのでもよい。
Figure 2009074953
 The first term of (Expression 5) represents the sum of squares of the difference between the search data, the model calculation value, and the error, and the second term represents the roughness of the specific resistance distribution. This λ is a Lagrange's undetermined coefficient (adjustment coefficient of the present invention), and the condition is that the roughness of the resistivity distribution should be the minimum of 0. The addition of this second term adjusts the balance between the first term residual and the second term, not only minimizing the fit of the exploration data to the underground model, but also reveals the amount of offset. An underground model in which the resistance distribution changes smoothly can be obtained. However, for λ, it is better to calculate simultaneously so as to obtain λ that gives the minimum value (data residual). However, it takes a long time to calculate and empirically does not differ greatly from the case where λ is fixed. A method of selecting λ giving the minimum value among the three values may be selected, or a value fixed to the predetermined value λ 0 giving a good result from experience may be used.

なお、実施の形態１における電磁探査装置、電磁探査方法で実測した電磁探査データは、地表で測定した１回目の電磁探査データと、地表面から１ｍ〜２ｍの高さで測定した２回目の電磁探査データとを統合したデータである。上述したように、更に３回以上の探査データまで統合した電磁探査データであってもよい。オフセット量ｓは１回目，２回目・・の電磁探査データ間で独立した値である。   The electromagnetic exploration data measured by the electromagnetic exploration apparatus and the electromagnetic exploration method in the first embodiment includes the first electromagnetic exploration data measured on the ground surface and the second electromagnetic exploration measured at a height of 1 m to 2 m from the ground surface. This data is integrated with exploration data. As described above, the electromagnetic exploration data may be integrated up to three or more exploration data. The offset amount s is an independent value between the first, second,... Electromagnetic survey data.

さて、ｆ（ｍ）はｍに関して非線形であるため、初期値

Figure 2009074953
（外字８、以下ｍｋ−１）を与えて、初期値周りでｆ（ｍ）のテイラー展開を行って線形化する。すると、（数５）は、初期値ｍｋ−１からの変化分
Figure 2009074953
（外字９、以下Δｍｋ）、すなわち、（数６）を最小にするΔｍｋとオフセット量ｓを求めることに帰着する。オフセット量ｓはランダム誤差を除いた誤差を吸収する。 Now, since f (m) is non-linear with respect to m, the initial value
Figure 2009074953
(External character 8, hereinafter, m k-1 ) is given, and linear expansion is performed by performing Taylor expansion of f (m) around the initial value. Then, (Formula 5) is the change from the initial value m k−1.
Figure 2009074953
(External character 9, hereinafter Δm k ), that is, Δm k and the offset amount s that minimize (Equation 6) result. The offset amount s absorbs errors excluding random errors.

Figure 2009074953
ここで、
Figure 2009074953
（外字１０、以下Ｊ）はヤコビアン（微係数行列）である。ここで、
Figure 2009074953
（外字１１、以下Δｄ）は（数７）の関係を有する。
Figure 2009074953
 here,
Figure 2009074953
(External character 10, hereinafter J) is a Jacobian (derivative coefficient matrix). here,
Figure 2009074953
(External character 11, hereinafter Δd) has the relationship of (Equation 7).

Figure 2009074953
以上を言い換えると、（数６）を最小化することは次の観測方程式（数８）の最小二乗解を求めることと等価である。
Figure 2009074953
 In other words, minimizing (Equation 6) is equivalent to finding the least squares solution of the following observation equation (Equation 8).

Figure 2009074953
（数８）を簡潔な形に形式的に書き換えると（数９）となる。ｎ×ｍ行列
Figure 2009074953
（外字１２、以下Ａ）は修正グラム・シュミット法やハウスホルダー法により（数１０）のように直交分解、ここではＱＲ分解が行える。
Figure 2009074953
 When (Formula 8) is formally rewritten into a simple form, (Formula 9) is obtained. n × m matrix
Figure 2009074953
(External character 12, hereinafter A) can be subjected to orthogonal decomposition, (QR decomposition) as shown in (Equation 10) by the modified Gram-Schmidt method or the Householder method.

Figure 2009074953
Figure 2009074953

Figure 2009074953
ここで、
Figure 2009074953
（外字１３、以下Ｑ）は列ベクトルが正規直交するｎ×ｍ行列（すなわち、ＱＴＱ＝Ｉ、ここでＱＴはＱの転置行列）であり、
Figure 2009074953
（外字１４、以下Ｒ）は列ベクトルが正規直交するｍ×ｍ行列の右上三角行列である。言い換えれば、ＱＲ分解できると言うことは、このようなＱとＲが存在することを意味する。このときの最小二乗解は（数１１）となる。
Figure 2009074953
 here,
Figure 2009074953
(External character 13, Q hereinafter) is an n × m matrix (that is, Q T Q = I, where Q T is a transposed matrix of Q) in which column vectors are orthonormal.
Figure 2009074953
(External character 14, hereinafter R) is an upper right triangular matrix of an m × m matrix in which column vectors are orthonormal. In other words, being able to perform QR decomposition means that such Q and R exist. The least squares solution at this time is (Equation 11).

Figure 2009074953
この（数１１）は後退代入していくだけで解くことができる。これによって、初期値ｍｋ−１からの変化分Δｍｋが求められ、（数１２）によって地下モデルを逐次修正して、地下モデルの更新を行いながら、ｍとオフセット量ｓが所定の値の範囲内にそれぞれ収斂するようにする。これにより変化分Δｍｋが０に近づく。あるいは所定回数修正を繰り返してもよい。このような処理によって、比抵抗ρの組ｍから構成された目的とする地下モデルと、オフセット量ｓが求まる。
Figure 2009074953
 This (Equation 11) can be solved simply by performing backward substitution. As a result, a change Δm k from the initial value m k−1 is obtained, and while the underground model is sequentially corrected by (Equation 12) and the underground model is updated, m and the offset amount s have predetermined values. Try to converge within the range. As a result, the change Δm k approaches zero. Alternatively, the correction may be repeated a predetermined number of times. By such processing, the target underground model configured from the set m of the specific resistance ρ and the offset amount s are obtained.

Figure 2009074953
このように実施の形態１の電磁探査装置、電磁探査方法によれば、従来のように高高度でのレベリングを行ってオフセット誤差（０レベルの設定）を調整することなく、１次磁場の影響として残留する誤差や測定位置、環境に由来するオフセット量を一括して処理でき、良好な比抵抗分布をもつ地下モデルを得ることができる。比抵抗分布と共にオフセット量を計算するので、高い場所でのレベリング作業が不要になり、測定段階でオフセット誤差を考慮する必要がなくなる。
Figure 2009074953
 As described above, according to the electromagnetic exploration apparatus and the electromagnetic exploration method of the first embodiment, the influence of the primary magnetic field is performed without adjusting the offset error (setting of 0 level) by performing leveling at a high altitude as in the past. As a result, residual errors, measurement positions, and offset amounts derived from the environment can be collectively processed, and an underground model having a good specific resistance distribution can be obtained. Since the offset amount is calculated together with the specific resistance distribution, leveling work at a high place becomes unnecessary, and it is not necessary to consider the offset error at the measurement stage.

次に、図４に基づいて実施の形態１のプログラムの手順について説明する。図４は本発明の実施の形態１におけるプログラムのフローチャートである。まず、実測の探査データｄとモデル計算値を出力するｆ（ｍ）を読み出す（ｓｔｅｐ１）。次いで、比抵抗の組ｍｋの初期値ｍ０とラグランジェ係数λの初期値λ０（固定したλの場合は固定値）を設定する（ｓｔｅｐ２）。 Next, the procedure of the program according to the first embodiment will be described with reference to FIG. FIG. 4 is a flowchart of the program in the first embodiment of the present invention. First, the actual search data d and f (m) for outputting the model calculation value are read (step 1). Then, (in the case of fixed lambda fixed value) initial value m 0 and the initial value of the Lagrange coefficient lambda lambda 0 of the set m k of resistivity set the (step2).

続いて、ｍｋ−１＝ｍ０として、Δｄ＝ｄ−ｆ（ｍｋ−１）を計算し（ｓｔｅｐ３）、比抵抗分布のラプラシアンＣｍｋ−１を計算し、これを基に−λＣｍｋ−１を計算する（ｓｔｅｐ４）。さらに、ｆ（ｍｋ）のヤコビアンＪを計算してｎ×ｍ行列Ａを計算する（ｓｔｅｐ５）。 Subsequently, assuming that m k−1 = m 0 , Δd = df (m k−1 ) is calculated (step 3), and the Laplacian Cm k−1 of the specific resistance distribution is calculated. Based on this, −λCm k -1 is calculated (step 4). Further, the Jacobian J of f (m k ) is calculated to calculate the n × m matrix A (step 5).

次に、得られた行列ＡをＱＲ分解して（ｓｔｅｐ６）、Δｍｋ，ｓｋ，λｋ（固定したλの場合は除く）を求める（ｓｔｅｐ７）。最小二乗解を与えるΔｍｋ，ｓｋ，λｋ（固定したλの場合は除く）を用いて、Δｄ−ＪΔｍｋ−１−Ｇｓのノルムが所定量εより小さくなって収斂したか否かを判定する（ｓｔｅｐ８）。 Next, the obtained matrix A is subjected to QR decomposition (step 6) to obtain Δm k , s k , λ k (except in the case of fixed λ) (step 7). Whether or not the norm of Δd−JΔm k−1 −Gs is smaller than a predetermined amount ε is converged by using Δm k , s k , λ k (except in the case of fixed λ) that gives the least square solution. Determination is made (step 8).

ｓｔｅｐ８において収斂していない場合は、ｍｋ−１＋Δｍｋを計算して（ｓｔｅｐ９）、ｓｔｅｐ３のｍｋ−１に代えてｍｋを代入する（ｓｔｅｐ１０）。ｓｔｅｐ８において、Δｄ−ＪΔｍｋ−１−Ｇｓのノルムが所定量εより小さくなって収斂した場合、計算を終了する。 If not converged at step 8, m k-1 + Δm k is calculated (step 9), and m k is substituted for m k-1 at step 3 (step 10). In step 8, when the norm of Δd−JΔm k−1 −Gs is smaller than the predetermined amount ε and converges, the calculation ends.

このように実施の形態１の電磁探査方法を実行するプログラムによれば、高高度でのレベリングを行ってオフセット誤差（０レベルの設定）を調整することなく、１次磁場の影響として残留する誤差や測定位置、環境に由来するオフセット量を容易且つ高精度に処理でき、良好な比抵抗分布をもつ地下モデルを得ることができる。パーソナルコンピュータ等のコンピュータの記憶装置に実施の形態１のプログラムを格納しておき、上述した手順で、比抵抗分布と共にオフセット量を計算すすればよい。従って、高い場所でのレベリング作業が不要になり、予め（測定段階で）オフセット誤差を補正する必要がなくなる。   As described above, according to the program for executing the electromagnetic exploration method of the first embodiment, the error remaining as the influence of the primary magnetic field without adjusting the offset error (setting of 0 level) by performing leveling at a high altitude. In addition, the offset amount derived from the measurement position and environment can be processed easily and with high accuracy, and an underground model having a good specific resistance distribution can be obtained. The program of the first embodiment may be stored in a storage device of a computer such as a personal computer, and the offset amount may be calculated together with the specific resistance distribution by the procedure described above. Accordingly, leveling work at a high place becomes unnecessary, and it is not necessary to correct the offset error in advance (at the measurement stage).

（実施例１）
本発明の実施例の作用効果をみるために、図５のような２次元の地下モデルで計算によるモデル実験を行った。図５は本発明の実施例１におけるモデル実験の構造の説明図、図６（ａ）は比較例としてのモデル実験のオフセット誤差がない場合の説明図、図６（ｂ）は比較例としてのモデル実験のオフセット誤差がある場合の説明図、７（ａ）は本発明の実施例１におけるモデル実験の初期値１００Ωｍの場合の説明図、図７（ｂ）は本発明の実施例１におけるモデル実験の初期値１０Ωｍの場合の説明図である。 Example 1
In order to see the effect of the Example of this invention, the model experiment by calculation was performed by the two-dimensional underground model like FIG. FIG. 5 is an explanatory diagram of the structure of the model experiment in Example 1 of the present invention, FIG. 6A is an explanatory diagram when there is no offset error of the model experiment as a comparative example, and FIG. 6B is an example of the comparative example. FIG. 7A is an explanatory diagram when there is an offset error in the model experiment, 7A is an explanatory diagram when the initial value of the model experiment in the first embodiment of the present invention is 100 Ωm, and FIG. 7B is a model in the first embodiment of the present invention. It is explanatory drawing in the case of the initial value of experiment 10ohmm.

図５に示すように、地下モデルには比抵抗ρが２Ωｍのブロックで形成された階段状になった山の部分が３つある。深さ４ｍから２ｍまで膨出し、これが再び６ｍの深さにまで凹み、再度深さ２ｍにまで膨出し、これをもう一度繰り返した連山状の分布である。地表側はこれを裏返した形状で比抵抗ρが２０Ωｍとした。   As shown in FIG. 5, the underground model has three stepped mountain portions formed by blocks having a specific resistance ρ of 2 Ωm. This bulges from a depth of 4 m to 2 m, which again dents to a depth of 6 m, bulges to a depth of 2 m again, and repeats this once again. The surface side was turned upside down and the specific resistance ρ was 20 Ωm.

図６（ａ）はシステム上のオフセット誤差がない（補正済み）とした場合の理想的な電磁探査装置、電磁探査方法による解析結果である。等高線は比抵抗ρが一定値を示す。比較的正しく比抵抗ρが２Ωｍの山を検出している。しかし、２つの山（膨出部分）しか検出できていない。そして、図６（ｂ）はオフセット誤差を残し、これを考慮していない従来の電磁探査装置による解析結果である。実験モデルとはまったく別の地下モデルになっている。逆に言えば従来の電磁探査装置でオフセット誤差等を補正しなければ、この程度の結果しか得られない、と言うことである。   FIG. 6A shows an analysis result by an ideal electromagnetic exploration apparatus and electromagnetic exploration method when there is no offset error on the system (corrected). Contour lines show a specific value of specific resistance ρ. The peak having a specific resistance ρ of 2 Ωm is detected relatively correctly. However, only two peaks (bulging portions) can be detected. FIG. 6B shows an analysis result obtained by a conventional electromagnetic exploration apparatus that does not consider an offset error. It is a completely different underground model from the experimental model. In other words, if the offset error or the like is not corrected by a conventional electromagnetic exploration device, only this result can be obtained.

これに対して、図７（ａ）（ｂ）は本発明のオフセット量を考慮して処理する場合の解析結果である。図７（ａ）の初期値は１００Ωｍである。この結果をみれば、比抵抗ρが２Ωｍの山が３つほぼ正確な位置で捉えられている。また、図７（ｂ）の初期値は１０Ωｍである。この結果も、図７（ａ）と同様に、比抵抗ρが２Ωｍの山が３つほぼ正確な位置で捉えられている。これらの解析結果によれば、本発明のオフセット量を考慮した処理が、オフセット誤差がない（補正済みの）場合よりも、はるかに正確に地盤構造を捉えていることが分かる。なお、データには標準偏差が１００ｐｐｍの正規分布誤差（ノイズ）を加えて計算を行った。   On the other hand, FIGS. 7A and 7B show analysis results when processing is performed in consideration of the offset amount of the present invention. The initial value in FIG. 7A is 100 Ωm. From this result, three peaks with a specific resistance ρ of 2 Ωm are captured at almost accurate positions. The initial value in FIG. 7B is 10 Ωm. Similarly to FIG. 7A, this result shows that three peaks having a specific resistance ρ of 2 Ωm are captured at almost accurate positions. According to these analysis results, it can be seen that the processing considering the offset amount of the present invention captures the ground structure much more accurately than when there is no offset error (corrected). The calculation was performed by adding a normal distribution error (noise) with a standard deviation of 100 ppm to the data.

本発明の電磁探査方法で、実際に現地に赴いて電磁探査を行った解析結果を示す。探査は韓国Ｙｏｅｎｋｗａｎｇで行われた。図８（ａ）は本発明の実施例１における現地での電磁探査を初期値１００Ωｍで計算した場合の解析結果の説明図である。これによればなだらかな地層が形成されているのが分かる。また、図８（ｂ）は本発明の実施例１における現地での電磁探査を初期値２０Ωｍで計算した場合の解析結果の説明図である。図８（ａ）とほとんど同様の解析結果を示している。   An analysis result obtained by actually visiting the site and conducting an electromagnetic survey by the electromagnetic survey method of the present invention is shown. Exploration was conducted in Yoengwang, Korea. FIG. 8A is an explanatory diagram of an analysis result when the electromagnetic survey in the field in Example 1 of the present invention is calculated with an initial value of 100 Ωm. According to this, it can be seen that a gentle formation is formed. FIG. 8B is an explanatory diagram of an analysis result when the electromagnetic survey in the field in Example 1 of the present invention is calculated with an initial value of 20 Ωm. An analysis result almost similar to that shown in FIG.

図９は比較例としての電気探査方法で本発明の実施例１の電磁探査と同時に行った解析結果の説明図である。電気探査法は浅い地盤で正確だと言われているが、本実験では、実施例１の電磁探査と同時に、この電気探査による解析を行った。その結果を示している。電気探査法によって解析された地盤は、本発明の電磁探査方法で解析した地盤に似ているが、実施例１と比べて地層の形態がそれほどよくない。   FIG. 9 is an explanatory view of an analysis result performed simultaneously with the electromagnetic exploration of Example 1 of the present invention by the electric exploration method as a comparative example. Although it is said that the electric exploration method is accurate on shallow ground, in this experiment, analysis by this electric exploration was performed simultaneously with the electromagnetic exploration of Example 1. The result is shown. The ground analyzed by the electric exploration method is similar to the ground analyzed by the electromagnetic exploration method of the present invention, but the formation of the formation is not so good as compared with the first embodiment.

図１０（ａ）はモデル実験で計算を繰り返した回数とデータ残差の関係を示した説明図である。データ残差とは実測値と計算値の差のことを意味する。すなわち、この１回の計算でそれぞれ比抵抗分布とオフセット量が同時に得られたことを意味している。横軸は反復回数であり、縦軸がデータ残差である。これによれば、ケース１は初期値を１００Ωｍにした場合、４回の反復計算で標準偏差誤差のほぼ１００ｐｐｍに収斂しており、ケース２は初期値を１０Ωｍにした場合は３回の計算だけで標準偏差誤差のほぼ１００ｐｐｍに収斂している。   FIG. 10A is an explanatory diagram showing the relationship between the number of times the calculation is repeated in the model experiment and the data residual. The data residual means the difference between the actually measured value and the calculated value. That is, it means that the specific resistance distribution and the offset amount are obtained at the same time by one calculation. The horizontal axis is the number of iterations, and the vertical axis is the data residual. According to this, Case 1 converges to approximately 100 ppm of standard deviation error by 4 iterations when the initial value is 100 Ωm, and Case 2 only 3 computations when the initial value is 10 Ωm. The standard deviation error converges to almost 100 ppm.

同様に、図１０（ｂ）は韓国Ｙｏｅｎｋｗａｎｇで測定したデータを使って繰り返して計算した回数とデータ残差の関係を示した説明図である。同じく、横軸は反復回数であり、縦軸がデータ残差である。ケース１は初期値を１００Ωｍとしたものであるが、４回ほどの繰り返し計算によってほぼ１００ｐｐｍに収斂している。また、初期値を１０Ωｍとした場合は２回の繰り返し計算によってほぼ１００ｐｐｍに収斂した。なお、この１００ｐｐｍは上記標準偏差誤差とは異なるが、この実験の場合一致した値に収斂した。   Similarly, FIG. 10B is an explanatory diagram showing the relationship between the number of times repeatedly calculated using the data measured in Korea Youngwang and the data residual. Similarly, the horizontal axis is the number of iterations and the vertical axis is the data residual. Case 1 has an initial value of 100 Ωm, but is converged to approximately 100 ppm by repeated calculation about four times. Further, when the initial value was 10 Ωm, it converged to about 100 ppm by two repeated calculations. This 100 ppm is different from the standard deviation error, but converged to a consistent value in this experiment.

さらに、本発明の電磁探査方法による実験結果と電気探査法による実験結果の比較を行ったものを図１１として示す。図１１は本発明の実施例１における電磁探査方法の実験結果と電気探査法による実験結果の比較を行った比較図である。横軸は本発明の電磁探査から求められた比抵抗であり、縦軸は電気探査から求められた比抵抗である。対数表示している。比較的良い相関をしている。   Further, FIG. 11 shows a comparison between the experimental results of the electromagnetic exploration method of the present invention and the experimental results of the electric exploration method. FIG. 11 is a comparison diagram comparing the experimental results of the electromagnetic exploration method and the experimental results of the electric exploration method in Example 1 of the present invention. The horizontal axis represents the specific resistance obtained from the electromagnetic exploration of the present invention, and the vertical axis represents the specific resistance obtained from the electric exploration. Logarithmic display. There is a relatively good correlation.

従って、本発明の電磁探査方法によって地中探査を行えば、１０ｍ以上の高度でレベリングを行ってオフセット誤差を補正することなく、たった２回〜４回の繰り返し計算により簡単にオフセット量を高精度に処理できる。このため短時間での地下探査、低コストの地下探査が可能となる。演算時間が少ない上に、きわめて良好な比抵抗分布を推定できる。比抵抗分布と共にオフセット量を計算するので、測定段階では（予め）オフセット誤差を考慮する必要がなくなる。   Therefore, if the underground exploration is performed by the electromagnetic exploration method of the present invention, the offset amount can be easily obtained with high accuracy by repeating the calculation twice to four times without leveling at an altitude of 10 m or more and correcting the offset error. Can be processed. Therefore, it is possible to perform underground exploration in a short time and low-cost underground exploration. The calculation time is short and a very good specific resistance distribution can be estimated. Since the offset amount is calculated together with the specific resistance distribution, it is not necessary to consider the offset error (in advance) at the measurement stage.

本発明は、電磁誘導作用を利用して地中探査を行う電磁探査装置、コンピュータに電磁探査の比抵抗分布を推定させるためのプログラムに適用できる。   INDUSTRIAL APPLICABILITY The present invention can be applied to an electromagnetic exploration apparatus that performs underground exploration using an electromagnetic induction effect and a program for causing a computer to estimate the resistivity distribution of electromagnetic exploration.

本発明の実施の形態１における電磁探査装置のブロック構造図Block structure diagram of electromagnetic survey device in Embodiment 1 of the present invention 測定の原理の説明図Illustration of the principle of measurement １次磁場と２次磁場、及びキャンセルのための磁場とオフセット量との関係を示す説明図Explanatory drawing which shows the relationship between a primary magnetic field and a secondary magnetic field, and the magnetic field for cancellation, and an offset amount 本発明の実施の形態１におけるプログラムのフローチャートFlowchart of the program in the first embodiment of the present invention 本発明の実施例１におけるモデル実験の構造の説明図Explanatory drawing of structure of model experiment in Example 1 of the present invention （ａ）比較例としてのモデル実験のオフセット誤差がない場合の説明図、（ｂ）比較例としてのモデル実験のオフセット誤差がある場合の説明図(A) An explanatory diagram when there is no offset error of a model experiment as a comparative example, (b) an explanatory diagram when there is an offset error of a model experiment as a comparative example （ａ）本発明の実施例１におけるモデル実験の初期値１００Ωｍの場合の説明図、（ｂ）本発明の実施例１におけるモデル実験の初期値１０Ωｍの場合の説明図(A) An explanatory diagram in the case of an initial value of 100 Ωm of the model experiment in Example 1 of the present invention, (b) an explanatory diagram in the case of an initial value of 10 Ωm of the model experiment in the Example 1 of the present invention. （ａ）本発明の実施例１における現地での電磁探査を初期値１００Ωｍで計算した場合の解析結果の説明図、（ｂ）本発明の実施例１における現地での電磁探査を初期値２０Ωｍで計算した場合の解析結果の説明図(A) Explanatory drawing of the analysis result at the time of calculating the local electromagnetic survey in Example 1 of the present invention with an initial value of 100 Ωm, (b) The electromagnetic survey in the field of Example 1 of the present invention with an initial value of 20 Ωm Explanatory diagram of analysis results when calculated 比較例としての電気探査方法で本発明の実施例１の電磁探査と同時に行った解析結果の説明図Explanatory drawing of the analysis result performed simultaneously with the electromagnetic exploration of Example 1 of this invention by the electric exploration method as a comparative example （ａ）モデル実験で計算を繰り返した回数とデータ残差の関係を示した説明図、（ｂ）韓国Ｙｏｅｎｋｗａｎｇで測定したデータを使って繰り返して計算した回数とデータ残差の関係を示した説明図(A) Explanatory diagram showing the relationship between the number of times the calculation was repeated in the model experiment and the data residual, (b) Description showing the relationship between the number of times the calculation was repeated using data measured in Korea Youngwang and the data residual Figure 本発明の実施例１における電磁探査方法の実験結果と電気探査法による実験結果の比較を行った比較図Comparison diagram comparing the experimental results of the electromagnetic exploration method and the electric exploration method in Example 1 of the present invention

符号の説明Explanation of symbols

１ 磁場発生部
２ 送信コイル
３ 磁場検出部
４ 受信コイル
５ バッキングコイル
６ 制御部
７ 分析装置
７ａ ＣＰＵ
７ｂ 記憶装置 DESCRIPTION OF SYMBOLS 1 Magnetic field generation part 2 Transmission coil 3 Magnetic field detection part 4 Reception coil 5 Backing coil 6 Control part 7 Analyzer 7a CPU
7b storage device

Claims (6)

１次磁場を形成するための送信コイルが設けられた磁場発生部と、前記１次磁場により地中に形成される２次磁場の磁場強度を検出する受信コイルが設けられた磁場検出部と、前記受信コイルが検出する磁場強度から前記１次磁場の寄与分をキャンセルするためのバッキングコイルと、を備え、
地下の比抵抗分布モデルを仮定してこれを基に磁場強度を計算し、この計算された磁場強度と前記受信コイルによって実測した磁場強度とを比較し、この２つの磁場強度の差が所定量内に収斂するまで比抵抗分布モデルの更新と計算とを続けて地下の比抵抗分布を推定する電磁探査装置であって、
更新された比抵抗分布モデルに基づいて初期値付近で線形化された磁場強度を計算し、この計算された磁場強度に対して前記寄与分を補正するためのオフセット量を関係付け、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算し、この差に対して前記更新された比抵抗分布モデルの磁場強度と前記オフセット量との差が所定量内に収まるまで比抵抗分布モデルの更新と計算とを行う逆解析手段を備え、予めキャリブレーションを行わずに比抵抗分布を逆解析することを特徴とする電磁探査装置。 A magnetic field generation unit provided with a transmission coil for forming a primary magnetic field, a magnetic field detection unit provided with a reception coil for detecting the magnetic field intensity of a secondary magnetic field formed in the ground by the primary magnetic field, A backing coil for canceling the contribution of the primary magnetic field from the magnetic field intensity detected by the receiving coil,
Assuming an underground resistivity distribution model, the magnetic field strength is calculated based on this model, the calculated magnetic field strength is compared with the magnetic field strength actually measured by the receiving coil, and the difference between the two magnetic field strengths is a predetermined amount. An electromagnetic exploration device that estimates the resistivity distribution in the subsurface by updating and calculating the resistivity distribution model until it converges within
Based on the updated resistivity distribution model, the magnetic field strength linearized near the initial value is calculated, the offset amount for correcting the contribution is related to the calculated magnetic field strength, and the measured magnetic field The difference between the strength and the magnetic field strength of the resistivity distribution model before update is calculated, and the difference is compared until the difference between the magnetic field strength of the updated resistivity distribution model and the offset amount falls within a predetermined amount. An electromagnetic exploration apparatus comprising reverse analysis means for updating and calculating a resistance distribution model, and performing reverse analysis of a specific resistance distribution without performing calibration in advance. 前記受信コイルの高度を変えて二位置以上で磁場強度を検出したとき、前記逆解析手段が、この検出した二位置以上の磁場強度を磁場強度として統合すると共に、該磁場強度に対して独立したオフセット量として関係付けることを特徴とする請求項１記載の電磁探査装置。   When the magnetic field strength is detected at two or more positions by changing the altitude of the receiving coil, the inverse analysis means integrates the detected magnetic field strengths at two or more positions as the magnetic field strength and is independent of the magnetic field strength. The electromagnetic exploration device according to claim 1, wherein the electromagnetic exploration device is related as an offset amount. １次磁場を形成して、該１次磁場の寄与分をキャンセルしながら地中に形成される２次磁場の磁場強度を実測すると共に、地下の比抵抗分布モデルを仮定し、これに基づいて磁場強度を計算し、この計算した磁場強度と実測した磁場強度とを比較し、この２つの磁場強度の差が所定量以下に収斂するまで前記比抵抗分布モデルの更新と計算とを続けて地下の比抵抗分布を推測する電磁探査方法であって、
更新された比抵抗分布モデルに基づいて初期値付近で線形化された磁場強度を計算し、この計算された磁場強度に対して前記１次磁場の影響を補正するためのオフセット量を関係付け、実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算し、この差に対して前記更新された磁場強度と前記オフセット量との差が所定量内に収斂するまで比抵抗分布モデルの更新と計算とを行い、予めキャリブレーションを行わずに比抵抗分布を逆解析することを特徴とする電磁探査方法。 The primary magnetic field is formed, the magnetic field strength of the secondary magnetic field formed in the ground is canceled while canceling the contribution of the primary magnetic field, and an underground specific resistance distribution model is assumed. The magnetic field strength is calculated, the calculated magnetic field strength is compared with the actually measured magnetic field strength, and the resistivity distribution model is continuously updated and calculated until the difference between the two magnetic field strengths converges to a predetermined amount or less. An electromagnetic exploration method for estimating the specific resistance distribution of
Based on the updated resistivity distribution model, the linearized magnetic field strength is calculated near the initial value, and the offset amount for correcting the influence of the primary magnetic field is related to the calculated magnetic field strength, The difference between the actually measured magnetic field strength and the magnetic field strength of the specific resistance distribution model before update is calculated, and until the difference between the updated magnetic field strength and the offset amount converges within a predetermined amount, the specific resistance is calculated. An electromagnetic exploration method characterized in that a distribution model is updated and calculated, and a specific resistance distribution is inversely analyzed without performing calibration in advance. 高度を変えて２位置以上で磁場強度を検出し、この２位置以上の磁場強度を独立した対等な磁場強度として統合すると共に、該磁場強度に対して独立したオフセット量を関係付けることを特徴とする請求項３の電磁探査方法。   The magnetic field strength is detected at two or more positions at different altitudes, and the magnetic field strengths at two or more positions are integrated as independent and equal magnetic field strengths, and an independent offset amount is related to the magnetic field strengths. The electromagnetic exploration method according to claim 3. コンピュータに、
実測した磁場強度と更新前の比抵抗分布モデルの磁場強度との差を計算させる第１手順と、
更新された比抵抗分布のラアプラシアンを計算し前記１次磁場の影響を補正するためのオフセット量を関係付ける第２手順と、
更新された比抵抗分布モデルの磁場強度に対してヤコビアンを計算し、前記オフセット量の影響度を調整係数で調整して前記差との関係付けを行う行列を取得する第３手順と、
前記行列をＱＲ分解して前記比抵抗分布の変化分と前記オフセット量を得る第４手順と、
前記比抵抗分布の変化分と前記オフセット量がそれぞれ所定量内に収斂するまで比抵抗分布モデルを更新し、計算を繰り返す第５手順と、
を実行させるためのプログラム。 On the computer,
A first procedure for calculating a difference between the actually measured magnetic field strength and the magnetic field strength of the specific resistance distribution model before update;
A second procedure for calculating a Laplacian of the updated specific resistance distribution and relating an offset amount for correcting the influence of the primary magnetic field;
A third step of calculating a Jacobian with respect to the magnetic field strength of the updated resistivity distribution model, obtaining a matrix for adjusting the influence of the offset amount by an adjustment coefficient, and associating with the difference;
A fourth procedure for QR-decomposing the matrix to obtain a change in the resistivity distribution and the offset amount;
A fifth procedure in which the resistivity distribution model is updated and the calculation is repeated until the change in the resistivity distribution and the offset amount converge within a predetermined amount;
A program for running 前記第１手順が、高度を変えて２位置以上で磁場強度を検出し、この２位置以上の磁場強度を独立した対等な磁場強度として統合した実測の磁場強度とし、
前記第２手順が、更新された比抵抗分布モデルの磁場強度に対して前記１次磁場のほかに独立したオフセット量を関係付けることを特徴とする請求項５のプログラム。 The first procedure detects the magnetic field strength at two or more positions at different altitudes, and the measured magnetic field strength is integrated as independent and equal magnetic field strengths at two or more positions.
6. The program according to claim 5, wherein the second procedure relates an independent offset amount in addition to the primary magnetic field to the magnetic field strength of the updated resistivity distribution model.
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JP2009128151A (en) * 2007-11-22 2009-06-11 Japan Atomic Energy Agency Method and apparatus for processing observation data in earth magnetism earth current method
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JPWO2015136931A1 (en) * 2014-03-12 2017-04-06 国立大学法人神戸大学 Conductivity distribution deriving method and conductivity distribution deriving apparatus
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JP2016133439A (en) * 2015-01-21 2016-07-25 株式会社奥村組 Subsoil resistivity distribution analyzing method by resistivity tomography
WO2022247992A1 (en) 2021-05-28 2022-12-01 DR. FISCHER, Andreas Detection of objects with a magnetic or electromagnetic signature in a measurement field
CN114383631A (en) * 2021-12-10 2022-04-22 中国兵器工业集团第二一四研究所苏州研发中心 Real-time calibration method based on least square, Taylor expansion and comprehensive residual combination
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